msc2010_flat.json

[{
	"code": "00-XX",
	"title": " General",
	"parentcode": null,
	"level": 1
}, {
	"code": "00-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "00-XX",
	"level": 2
}, {
	"code": "00-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "00-XX",
	"level": 2
}, {
	"code": "00Axx",
	"title": " General and miscellaneous specific topics",
	"parentcode": "00-XX",
	"level": 2
}, {
	"code": "00A05",
	"title": " General mathematics",
	"parentcode": "00Axx",
	"level": 3
}, {
	"code": "00A06",
	"title": " Mathematics for nonmathematicians (engineering, social sciences, etc.)",
	"parentcode": "00Axx",
	"level": 3
}, {
	"code": "00A07",
	"title": " Problem books",
	"parentcode": "00Axx",
	"level": 3
}, {
	"code": "00A08",
	"title": " Recreational mathematics [See also 97A20]",
	"parentcode": "00Axx",
	"level": 3
}, {
	"code": "00A09",
	"title": " Popularization of mathematics",
	"parentcode": "00Axx",
	"level": 3
}, {
	"code": "00A15",
	"title": " Bibliographies",
	"parentcode": "00Axx",
	"level": 3
}, {
	"code": "00A17",
	"title": " External book reviews",
	"parentcode": "00Axx",
	"level": 3
}, {
	"code": "00A20",
	"title": " Dictionaries and other general reference works",
	"parentcode": "00Axx",
	"level": 3
}, {
	"code": "00A22",
	"title": " Formularies",
	"parentcode": "00Axx",
	"level": 3
}, {
	"code": "00A30",
	"title": " Philosophy of mathematics [See also 03A05]",
	"parentcode": "00Axx",
	"level": 3
}, {
	"code": "00A35",
	"title": " Methodology of mathematics, didactics [See also 97Cxx, 97Dxx]",
	"parentcode": "00Axx",
	"level": 3
}, {
	"code": "00A65",
	"title": " Mathematics and music",
	"parentcode": "00Axx",
	"level": 3
}, {
	"code": "00A66",
	"title": " Mathematics and visual arts, visualization",
	"parentcode": "00Axx",
	"level": 3
}, {
	"code": "00A67",
	"title": " Mathematics and architecture",
	"parentcode": "00Axx",
	"level": 3
}, {
	"code": "00A69",
	"title": " General applied mathematics {For physics, see 00A79 and Sections 70 through 86}",
	"parentcode": "00Axx",
	"level": 3
}, {
	"code": "00A71",
	"title": " Theory of mathematical modeling",
	"parentcode": "00Axx",
	"level": 3
}, {
	"code": "00A72",
	"title": " General methods of simulation",
	"parentcode": "00Axx",
	"level": 3
}, {
	"code": "00A73",
	"title": " Dimensional analysis",
	"parentcode": "00Axx",
	"level": 3
}, {
	"code": "00A79",
	"title": " Physics (use more specific entries from Sections 70 through 86 when possible)",
	"parentcode": "00Axx",
	"level": 3
}, {
	"code": "00A99",
	"title": " Miscellaneous topics",
	"parentcode": "00Axx",
	"level": 3
}, {
	"code": "00Bxx",
	"title": " Conference proceedings and collections of papers",
	"parentcode": "00-XX",
	"level": 2
}, {
	"code": "00B05",
	"title": " Collections of abstracts of lectures",
	"parentcode": "00Bxx",
	"level": 3
}, {
	"code": "00B10",
	"title": " Collections of articles of general interest",
	"parentcode": "00Bxx",
	"level": 3
}, {
	"code": "00B15",
	"title": " Collections of articles of miscellaneous specific content",
	"parentcode": "00Bxx",
	"level": 3
}, {
	"code": "00B20",
	"title": " Proceedings of conferences of general interest",
	"parentcode": "00Bxx",
	"level": 3
}, {
	"code": "00B25",
	"title": " Proceedings of conferences of miscellaneous specific interest",
	"parentcode": "00Bxx",
	"level": 3
}, {
	"code": "00B30",
	"title": " Festschriften",
	"parentcode": "00Bxx",
	"level": 3
}, {
	"code": "00B50",
	"title": " Volumes of selected translations",
	"parentcode": "00Bxx",
	"level": 3
}, {
	"code": "00B55",
	"title": " Miscellaneous volumes of translations",
	"parentcode": "00Bxx",
	"level": 3
}, {
	"code": "00B60",
	"title": " Collections of reprinted articles [See also 01A75]",
	"parentcode": "00Bxx",
	"level": 3
}, {
	"code": "00B99",
	"title": " None of the above, but in this section",
	"parentcode": "00Bxx",
	"level": 3
}, {
	"code": "01-XX",
	"parentcode": null,
	"title": "History and biography [See also the classification number –03 in the other sections]",
	"level": 1
}, {
	"code": "01-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "01-XX",
	"level": 2
}, {
	"code": "01-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "01-XX",
	"level": 2
}, {
	"code": "01-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "01-XX",
	"level": 2
}, {
	"code": "01-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "01-XX",
	"level": 2
}, {
	"code": "01-08",
	"title": " Computational methods",
	"parentcode": "01-XX",
	"level": 2
}, {
	"code": "01Axx",
	"title": " History of mathematics and mathematicians",
	"parentcode": "01-XX",
	"level": 2
}, {
	"code": "01A05",
	"title": " General histories, source books",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A07",
	"title": " Ethnomathematics, general",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A10",
	"title": " Paleolithic, Neolithic",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A12",
	"title": " Indigenous cultures of the Americas",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A13",
	"title": " Other indigenous cultures (non-European)",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A15",
	"title": " Indigenous European cultures (pre-Greek, etc.)",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A16",
	"title": " Egyptian",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A17",
	"title": " Babylonian",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A20",
	"title": " Greek, Roman",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A25",
	"title": " China",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A27",
	"title": " Japan",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A29",
	"title": " Southeast Asia",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A30",
	"title": " Islam (Medieval)",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A32",
	"title": " India",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A35",
	"title": " Medieval",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A40",
	"title": " 15th and 16th centuries, Renaissance",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A45",
	"title": " 17th century",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A50",
	"title": " 18th century",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A55",
	"title": " 19th century",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A60",
	"title": " 20th century",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A61",
	"title": " Twenty-first century",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A65",
	"title": " Contemporary",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A67",
	"title": " Future prospectives",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A70",
	"title": " Biographies, obituaries, personalia, bibliographies",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A72",
	"title": " Schools of mathematics",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A73",
	"title": " Universities",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A74",
	"title": " Other institutions and academies",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A75",
	"title": " Collected or selected works; reprintings or translations of classics [See also 00B60]",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A80",
	"title": " Sociology (and profession) of mathematics",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A85",
	"title": " Historiography",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A90",
	"title": " Bibliographic studies",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "01A99",
	"title": " Miscellaneous topics",
	"parentcode": "01Axx",
	"level": 3
}, {
	"code": "03-XX",
	"parentcode": null,
	"title": "Mathematical logic and foundations",
	"level": 1
}, {
	"code": "03-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "03-XX",
	"level": 2
}, {
	"code": "03-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "03-XX",
	"level": 2
}, {
	"code": "03-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "03-XX",
	"level": 2
}, {
	"code": "03-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "03-XX",
	"level": 2
}, {
	"code": "03-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "03-XX",
	"level": 2
}, {
	"code": "03-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "03-XX",
	"level": 2
}, {
	"code": "03Axx",
	"title": " Philosophical aspects of logic and foundations",
	"parentcode": "03-XX",
	"level": 2
}, {
	"code": "03A05",
	"title": " Philosophical and critical {For philosophy of mathematics, see also 00A30}",
	"parentcode": "03Axx",
	"level": 3
}, {
	"code": "03A10",
	"title": " Logic in the philosophy of science",
	"parentcode": "03Axx",
	"level": 3
}, {
	"code": "03A99",
	"title": " None of the above, but in this section",
	"parentcode": "03Axx",
	"level": 3
}, {
	"code": "03Bxx",
	"title": " General logic",
	"parentcode": "03-XX",
	"level": 2
}, {
	"code": "03B05",
	"title": " Classical propositional logic",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B10",
	"title": " Classical first-order logic",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B15",
	"title": " Higher-order logic and type theory",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B20",
	"title": " Subsystems of classical logic (including intuitionistic logic)",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B22",
	"title": " Abstract deductive systems",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B25",
	"title": " Decidability of theories and sets of sentences [See also 11U05, 12L05, 20F10]",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B30",
	"title": " Foundations of classical theories (including reverse mathematics) [See also 03F35]",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B35",
	"title": " Mechanization of proofs and logical operations [See also 68T15]",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B40",
	"title": " Combinatory logic and lambda-calculus [See also 68N18]",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B42",
	"title": " Logics of knowledge and belief (including belief change)",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B44",
	"title": " Temporal logic",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B45",
	"title": " Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B47",
	"title": " Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52}",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B48",
	"title": " Probability and inductive logic [See also 60A05]",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B50",
	"title": " Many-valued logic",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B52",
	"title": " Fuzzy logic; logic of vagueness [See also 68T27, 68T37, 94D05]",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B53",
	"title": " Paraconsistent logics",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B55",
	"title": " Intermediate logics",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B60",
	"title": " Other nonclassical logic",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B62",
	"title": " Combined logics",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B65",
	"title": " Logic of natural languages [See also 68T50, 91F20]",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B70",
	"title": " Logic in computer science [See also 68-XX]",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B80",
	"title": " Other applications of logic",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03B99",
	"title": " None of the above, but in this section",
	"parentcode": "03Bxx",
	"level": 3
}, {
	"code": "03Cxx",
	"title": " Model theory",
	"parentcode": "03-XX",
	"level": 2
}, {
	"code": "03C05",
	"title": " Equational classes, universal algebra [See also 08Axx, 08Bxx, 18C05]",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C07",
	"title": " Basic properties of first-order languages and structures",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C10",
	"title": " Quantifier elimination, model completeness and related topics",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C13",
	"title": " Finite structures [See also 68Q15, 68Q19]",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C15",
	"title": " Denumerable structures",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C20",
	"title": " Ultraproducts and related constructions",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C25",
	"title": " Model-theoretic forcing",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C30",
	"title": " Other model constructions",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C35",
	"title": " Categoricity and completeness of theories",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C40",
	"title": " Interpolation, preservation, definability",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C45",
	"title": " Classification theory, stability and related concepts [See also 03C48]",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C48",
	"title": " Abstract elementary classes and related topics [See also 03C45]",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C50",
	"title": " Models with special properties (saturated, rigid, etc.)",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C52",
	"title": " Properties of classes of models",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C55",
	"title": " Set-theoretic model theory",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C57",
	"title": " Effective and recursion-theoretic model theory [See also 03D45]",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C60",
	"title": " Model-theoretic algebra [See also 08C10, 12Lxx, 13L05]",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C62",
	"title": " Models of arithmetic and set theory [See also 03Hxx]",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C64",
	"title": " Model theory of ordered structures; o-minimality",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C65",
	"title": " Models of other mathematical theories",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C68",
	"title": " Other classical first-order model theory",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C70",
	"title": " Logic on admissible sets",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C75",
	"title": " Other infinitary logic",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C80",
	"title": " Logic with extra quantifiers and operators [See also 03B42, 03B44, 03B45, 03B48]",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C85",
	"title": " Second- and higher-order model theory",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C90",
	"title": " Nonclassical models (Boolean-valued, sheaf, etc.)",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C95",
	"title": " Abstract model theory",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C98",
	"title": " Applications of model theory [See also 03C60]",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03C99",
	"title": " None of the above, but in this section",
	"parentcode": "03Cxx",
	"level": 3
}, {
	"code": "03Dxx",
	"title": " Computability and recursion theory",
	"parentcode": "03-XX",
	"level": 2
}, {
	"code": "03D03",
	"title": " Thue and Post systems, etc.",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03D05",
	"title": " Automata and formal grammars in connection with logical questions [See also 68Q45, 68Q70, 68R15]",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03D10",
	"title": " Turing machines and related notions [See also 68Q05]",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03D15",
	"title": " Complexity of computation (including implicit computational complexity) [See also 68Q15, 68Q17]",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03D20",
	"title": " Recursive functions and relations, subrecursive hierarchies",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03D25",
	"title": " Recursively (computably) enumerable sets and degrees",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03D28",
	"title": " Other Turing degree structures",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03D30",
	"title": " Other degrees and reducibilities",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03D32",
	"title": " Algorithmic randomness and dimension [See also 68Q30]",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03D35",
	"title": " Undecidability and degrees of sets of sentences",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03D40",
	"title": " Word problems, etc. [See also 06B25, 08A50, 20F10, 68R15]",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03D45",
	"title": " Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55]",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03D50",
	"title": " Recursive equivalence types of sets and structures, isols",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03D55",
	"title": " Hierarchies",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03D60",
	"title": " Computability and recursion theory on ordinals, admissible sets, etc.",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03D65",
	"title": " Higher-type and set recursion theory",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03D70",
	"title": " Inductive definability",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03D75",
	"title": " Abstract and axiomatic computability and recursion theory",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03D78",
	"title": " Computation over the reals {For constructive aspects, see 03F60}",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03D80",
	"title": " Applications of computability and recursion theory",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03D99",
	"title": " None of the above, but in this section",
	"parentcode": "03Dxx",
	"level": 3
}, {
	"code": "03Exx",
	"title": " Set theory",
	"parentcode": "03-XX",
	"level": 2
}, {
	"code": "03E02",
	"title": " Partition relations",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E04",
	"title": " Ordered sets and their cofinalities; pcf theory",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E05",
	"title": " Other combinatorial set theory",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E10",
	"title": " Ordinal and cardinal numbers",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E15",
	"title": " Descriptive set theory [See also 28A05, 54H05]",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E17",
	"title": " Cardinal characteristics of the continuum",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E20",
	"title": " Other classical set theory (including functions, relations, and set algebra)",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E25",
	"title": " Axiom of choice and related propositions",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E30",
	"title": " Axiomatics of classical set theory and its fragments",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E35",
	"title": " Consistency and independence results",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E40",
	"title": " Other aspects of forcing and Boolean-valued models",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E45",
	"title": " Inner models, including constructibility, ordinal definability, and core models",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E47",
	"title": " Other notions of set-theoretic definability",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E50",
	"title": " Continuum hypothesis and Martin's axiom [See also  03E57]",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E55",
	"title": " Large cardinals",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E57",
	"title": " Generic absoluteness and forcing axioms [See also  03E50]",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E60",
	"title": " Determinacy principles",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E65",
	"title": " Other hypotheses and axioms",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E70",
	"title": " Nonclassical and second-order set theories",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E72",
	"title": " Fuzzy set theory",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E75",
	"title": " Applications of set theory",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03E99",
	"title": " None of the above, but in this section",
	"parentcode": "03Exx",
	"level": 3
}, {
	"code": "03Fxx",
	"title": " Proof theory and constructive mathematics",
	"parentcode": "03-XX",
	"level": 2
}, {
	"code": "03F03",
	"title": " Proof theory, general",
	"parentcode": "03Fxx",
	"level": 3
}, {
	"code": "03F05",
	"title": " Cut-elimination and normal-form theorems",
	"parentcode": "03Fxx",
	"level": 3
}, {
	"code": "03F07",
	"title": " Structure of proofs",
	"parentcode": "03Fxx",
	"level": 3
}, {
	"code": "03F10",
	"title": " Functionals in proof theory",
	"parentcode": "03Fxx",
	"level": 3
}, {
	"code": "03F15",
	"title": " Recursive ordinals and ordinal notations",
	"parentcode": "03Fxx",
	"level": 3
}, {
	"code": "03F20",
	"title": " Complexity of proofs",
	"parentcode": "03Fxx",
	"level": 3
}, {
	"code": "03F25",
	"title": " Relative consistency and interpretations",
	"parentcode": "03Fxx",
	"level": 3
}, {
	"code": "03F30",
	"title": " First-order arithmetic and fragments",
	"parentcode": "03Fxx",
	"level": 3
}, {
	"code": "03F35",
	"title": " Second- and higher-order arithmetic and fragments [See also 03B30]",
	"parentcode": "03Fxx",
	"level": 3
}, {
	"code": "03F40",
	"title": " Gödel numberings and issues of incompleteness",
	"parentcode": "03Fxx",
	"level": 3
}, {
	"code": "03F45",
	"title": " Provability logics and related algebras (e.g., diagonalizable algebras) [See also 03B45, 03G25, 06E25]",
	"parentcode": "03Fxx",
	"level": 3
}, {
	"code": "03F50",
	"title": " Metamathematics of constructive systems",
	"parentcode": "03Fxx",
	"level": 3
}, {
	"code": "03F52",
	"title": " Linear logic and other substructural logics [See also 03B47]",
	"parentcode": "03Fxx",
	"level": 3
}, {
	"code": "03F55",
	"title": " Intuitionistic mathematics",
	"parentcode": "03Fxx",
	"level": 3
}, {
	"code": "03F60",
	"title": " Constructive and recursive analysis [See also 03B30, 03D45, 03D78, 26E40, 46S30, 47S30]",
	"parentcode": "03Fxx",
	"level": 3
}, {
	"code": "03F65",
	"title": " Other constructive mathematics [See also 03D45]",
	"parentcode": "03Fxx",
	"level": 3
}, {
	"code": "03F99",
	"title": " None of the above, but in this section",
	"parentcode": "03Fxx",
	"level": 3
}, {
	"code": "03Gxx",
	"title": " Algebraic logic",
	"parentcode": "03-XX",
	"level": 2
}, {
	"code": "03G05",
	"title": " Boolean algebras [See also 06Exx]",
	"parentcode": "03Gxx",
	"level": 3
}, {
	"code": "03G10",
	"title": " Lattices and related structures [See also 06Bxx]",
	"parentcode": "03Gxx",
	"level": 3
}, {
	"code": "03G12",
	"title": " Quantum logic [See also 06C15, 81P10]",
	"parentcode": "03Gxx",
	"level": 3
}, {
	"code": "03G15",
	"title": " Cylindric and polyadic algebras; relation algebras",
	"parentcode": "03Gxx",
	"level": 3
}, {
	"code": "03G20",
	"title": " Łukasiewicz and Post algebras [See also 06D25, 06D30]",
	"parentcode": "03Gxx",
	"level": 3
}, {
	"code": "03G25",
	"title": " Other algebras related to logic [See also 03F45, 06D20, 06E25, 06F35]",
	"parentcode": "03Gxx",
	"level": 3
}, {
	"code": "03G27",
	"title": " Abstract algebraic logic",
	"parentcode": "03Gxx",
	"level": 3
}, {
	"code": "03G30",
	"title": " Categorical logic, topoi [See also 18B25, 18C05, 18C10]",
	"parentcode": "03Gxx",
	"level": 3
}, {
	"code": "03G99",
	"title": " None of the above, but in this section",
	"parentcode": "03Gxx",
	"level": 3
}, {
	"code": "03Hxx",
	"title": " Nonstandard models [See also 03C62]",
	"parentcode": "03-XX",
	"level": 2
}, {
	"code": "03H05",
	"title": " Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05]",
	"parentcode": "03Hxx",
	"level": 3
}, {
	"code": "03H10",
	"title": " Other applications of nonstandard models (economics, physics, etc.)",
	"parentcode": "03Hxx",
	"level": 3
}, {
	"code": "03H15",
	"title": " Nonstandard models of arithmetic [See also 11U10, 12L15, 13L05]",
	"parentcode": "03Hxx",
	"level": 3
}, {
	"code": "03H99",
	"title": " None of the above, but in this section",
	"parentcode": "03Hxx",
	"level": 3
}, {
	"code": "05-XX",
	"title": " Combinatorics {For finite fields, see 11Txx}",
	"parentcode": null,
	"level": 1
}, {
	"code": "05-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "05-XX",
	"level": 2
}, {
	"code": "05-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "05-XX",
	"level": 2
}, {
	"code": "05-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "05-XX",
	"level": 2
}, {
	"code": "05-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "05-XX",
	"level": 2
}, {
	"code": "05-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "05-XX",
	"level": 2
}, {
	"code": "05-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "05-XX",
	"level": 2
}, {
	"code": "05Axx",
	"title": " Enumerative combinatorics {For enumeration in graph theory, see 05C30}",
	"parentcode": "05-XX",
	"level": 2
}, {
	"code": "05A05",
	"title": " Permutations, words, matrices",
	"parentcode": "05Axx",
	"level": 3
}, {
	"code": "05A10",
	"title": " Factorials, binomial coefficients, combinatorial functions [See also 11B65, 33Cxx]",
	"parentcode": "05Axx",
	"level": 3
}, {
	"code": "05A15",
	"title": " Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]",
	"parentcode": "05Axx",
	"level": 3
}, {
	"code": "05A16",
	"title": " Asymptotic enumeration",
	"parentcode": "05Axx",
	"level": 3
}, {
	"code": "05A17",
	"title": " Partitions of integers [See also 11P81, 11P82, 11P83]",
	"parentcode": "05Axx",
	"level": 3
}, {
	"code": "05A18",
	"title": " Partitions of sets",
	"parentcode": "05Axx",
	"level": 3
}, {
	"code": "05A19",
	"title": " Combinatorial identities, bijective combinatorics",
	"parentcode": "05Axx",
	"level": 3
}, {
	"code": "05A20",
	"title": " Combinatorial inequalities",
	"parentcode": "05Axx",
	"level": 3
}, {
	"code": "05A30",
	"title": " $q$-calculus and related topics [See also 33Dxx]",
	"parentcode": "05Axx",
	"level": 3
}, {
	"code": "05A40",
	"title": " Umbral calculus",
	"parentcode": "05Axx",
	"level": 3
}, {
	"code": "05A99",
	"title": " None of the above, but in this section",
	"parentcode": "05Axx",
	"level": 3
}, {
	"code": "05Bxx",
	"title": " Designs and configurations {For applications of design theory, see 94C30}",
	"parentcode": "05-XX",
	"level": 2
}, {
	"code": "05B05",
	"title": " Block designs [See also 51E05, 62K10]",
	"parentcode": "05Bxx",
	"level": 3
}, {
	"code": "05B07",
	"title": " Triple systems",
	"parentcode": "05Bxx",
	"level": 3
}, {
	"code": "05B10",
	"title": " Difference sets (number-theoretic, group-theoretic, etc.) [See also 11B13]",
	"parentcode": "05Bxx",
	"level": 3
}, {
	"code": "05B15",
	"title": " Orthogonal arrays, Latin squares, Room squares",
	"parentcode": "05Bxx",
	"level": 3
}, {
	"code": "05B20",
	"title": " Matrices (incidence, Hadamard, etc.)",
	"parentcode": "05Bxx",
	"level": 3
}, {
	"code": "05B25",
	"title": " Finite geometries [See also 51D20, 51Exx]",
	"parentcode": "05Bxx",
	"level": 3
}, {
	"code": "05B30",
	"title": " Other designs, configurations [See also 51E30]",
	"parentcode": "05Bxx",
	"level": 3
}, {
	"code": "05B35",
	"title": " Matroids, geometric lattices [See also 52B40, 90C27]",
	"parentcode": "05Bxx",
	"level": 3
}, {
	"code": "05B40",
	"title": " Packing and covering [See also 11H31, 52C15, 52C17]",
	"parentcode": "05Bxx",
	"level": 3
}, {
	"code": "05B45",
	"title": " Tessellation and tiling problems [See also 52C20, 52C22]",
	"parentcode": "05Bxx",
	"level": 3
}, {
	"code": "05B50",
	"title": " Polyominoes",
	"parentcode": "05Bxx",
	"level": 3
}, {
	"code": "05B99",
	"title": " None of the above, but in this section",
	"parentcode": "05Bxx",
	"level": 3
}, {
	"code": "05Cxx",
	"title": " Graph theory {For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15}",
	"parentcode": "05-XX",
	"level": 2
}, {
	"code": "05C05",
	"title": " Trees",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C07",
	"title": " Vertex degrees [See also 05E30]",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C10",
	"title": " Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C12",
	"title": " Distance in graphs",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C15",
	"title": " Coloring of graphs and hypergraphs",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C17",
	"title": " Perfect graphs",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C20",
	"title": " Directed graphs (digraphs), tournaments",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C21",
	"title": " Flows in graphs",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C22",
	"title": " Signed and weighted graphs",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C25",
	"title": " Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65]",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C30",
	"title": " Enumeration in graph theory",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C31",
	"title": " Graph polynomials",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C35",
	"title": " Extremal problems [See also 90C35]",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C38",
	"title": " Paths and cycles [See also 90B10]",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C40",
	"title": " Connectivity",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C42",
	"title": " Density (toughness, etc.)",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C45",
	"title": " Eulerian and Hamiltonian graphs",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C50",
	"title": " Graphs and linear algebra (matrices, eigenvalues, etc.)",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C51",
	"title": " Graph designs and isomomorphic decomposition  [See also 05B30]",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C55",
	"title": " Generalized Ramsey theory [See also 05D10]",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C57",
	"title": " Games on graphs [See also 91A43, 91A46]",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C60",
	"title": " Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C62",
	"title": " Graph representations (geometric and intersection representations, etc.) {For graph drawing, see also 68R10}",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C63",
	"title": " Infinite graphs",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C65",
	"title": " Hypergraphs",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C69",
	"title": " Dominating sets, independent sets, cliques",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C70",
	"title": " Factorization, matching, partitioning, covering and packing",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C72",
	"title": " Fractional graph theory, fuzzy graph theory",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C75",
	"title": " Structural characterization of families of graphs",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C76",
	"title": " Graph operations (line graphs, products, etc.)",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C78",
	"title": " Graph labelling (graceful graphs, bandwidth, etc.)",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C80",
	"title": " Random graphs [See also 60B20]",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C81",
	"title": " Random walks on graphs",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C82",
	"title": " Small world graphs, complex networks [See also 90Bxx, 91D30]",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C83",
	"title": " Graph minors",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C85",
	"title": " Graph algorithms [See also 68R10, 68W05]",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C90",
	"title": " Applications [See also 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15]",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05C99",
	"title": " None of the above, but in this section",
	"parentcode": "05Cxx",
	"level": 3
}, {
	"code": "05Dxx",
	"title": " Extremal combinatorics",
	"parentcode": "05-XX",
	"level": 2
}, {
	"code": "05D05",
	"title": " Extremal set theory",
	"parentcode": "05Dxx",
	"level": 3
}, {
	"code": "05D10",
	"title": " Ramsey theory  [See also 05C55]",
	"parentcode": "05Dxx",
	"level": 3
}, {
	"code": "05D15",
	"title": " Transversal (matching) theory",
	"parentcode": "05Dxx",
	"level": 3
}, {
	"code": "05D40",
	"title": " Probabilistic methods",
	"parentcode": "05Dxx",
	"level": 3
}, {
	"code": "05D99",
	"title": " None of the above, but in this section",
	"parentcode": "05Dxx",
	"level": 3
}, {
	"code": "05Exx",
	"title": " Algebraic combinatorics",
	"parentcode": "05-XX",
	"level": 2
}, {
	"code": "05E05",
	"title": " Symmetric functions and generalizations",
	"parentcode": "05Exx",
	"level": 3
}, {
	"code": "05E10",
	"title": " Combinatorial aspects of representation theory[See also 20C30]",
	"parentcode": "05Exx",
	"level": 3
}, {
	"code": "05E15",
	"title": " Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80]",
	"parentcode": "05Exx",
	"level": 3
}, {
	"code": "05E18",
	"title": " Group actions on combinatorial structures",
	"parentcode": "05Exx",
	"level": 3
}, {
	"code": "05E30",
	"title": " Association schemes, strongly regular graphs",
	"parentcode": "05Exx",
	"level": 3
}, {
	"code": "05E40",
	"title": " Combinatorial aspects of commutative algebra",
	"parentcode": "05Exx",
	"level": 3
}, {
	"code": "05E45",
	"title": " Combinatorial aspects of simplicial complexes",
	"parentcode": "05Exx",
	"level": 3
}, {
	"code": "05E99",
	"title": " None of the above, but in this section",
	"parentcode": "05Exx",
	"level": 3
}, {
	"code": "06-XX",
	"title": " Order, lattices, ordered algebraic structures [See also 18B35]",
	"parentcode": null,
	"level": 1
}, {
	"code": "06-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "06-XX",
	"level": 2
}, {
	"code": "06-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "06-XX",
	"level": 2
}, {
	"code": "06-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "06-XX",
	"level": 2
}, {
	"code": "06-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "06-XX",
	"level": 2
}, {
	"code": "06-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "06-XX",
	"level": 2
}, {
	"code": "06-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "06-XX",
	"level": 2
}, {
	"code": "06Axx",
	"title": " Ordered sets",
	"parentcode": "06-XX",
	"level": 2
}, {
	"code": "06A05",
	"title": " Total order",
	"parentcode": "06Axx",
	"level": 3
}, {
	"code": "06A06",
	"title": " Partial order, general",
	"parentcode": "06Axx",
	"level": 3
}, {
	"code": "06A07",
	"title": " Combinatorics of partially ordered sets",
	"parentcode": "06Axx",
	"level": 3
}, {
	"code": "06A11",
	"title": " Algebraic aspects of posets",
	"parentcode": "06Axx",
	"level": 3
}, {
	"code": "06A12",
	"title": " Semilattices [See also 20M10; for topological semilattices see 22A26]",
	"parentcode": "06Axx",
	"level": 3
}, {
	"code": "06A15",
	"title": " Galois correspondences, closure operators",
	"parentcode": "06Axx",
	"level": 3
}, {
	"code": "06A75",
	"title": " Generalizations of ordered sets",
	"parentcode": "06Axx",
	"level": 3
}, {
	"code": "06A99",
	"title": " None of the above, but in this section",
	"parentcode": "06Axx",
	"level": 3
}, {
	"code": "06Bxx",
	"title": " Lattices [See also 03G10]",
	"parentcode": "06-XX",
	"level": 2
}, {
	"code": "06B05",
	"title": " Structure theory",
	"parentcode": "06Bxx",
	"level": 3
}, {
	"code": "06B10",
	"title": " Ideals, congruence relations",
	"parentcode": "06Bxx",
	"level": 3
}, {
	"code": "06B15",
	"title": " Representation theory",
	"parentcode": "06Bxx",
	"level": 3
}, {
	"code": "06B20",
	"title": " Varieties of lattices",
	"parentcode": "06Bxx",
	"level": 3
}, {
	"code": "06B23",
	"title": " Complete lattices, completions",
	"parentcode": "06Bxx",
	"level": 3
}, {
	"code": "06B25",
	"title": " Free lattices, projective lattices, word problems [See also 03D40, 08A50, 20F10]",
	"parentcode": "06Bxx",
	"level": 3
}, {
	"code": "06B30",
	"title": " Topological lattices, order topologies [See also 06F30, 22A26, 54F05, 54H12]",
	"parentcode": "06Bxx",
	"level": 3
}, {
	"code": "06B35",
	"title": " Continuous lattices and posets, applications [See also 06B30, 06D10, 06F30, 18B35, 22A26, 68Q55]",
	"parentcode": "06Bxx",
	"level": 3
}, {
	"code": "06B75",
	"title": " Generalizations of lattices",
	"parentcode": "06Bxx",
	"level": 3
}, {
	"code": "06B99",
	"title": " None of the above, but in this section",
	"parentcode": "06Bxx",
	"level": 3
}, {
	"code": "06Cxx",
	"title": " Modular lattices, complemented lattices",
	"parentcode": "06-XX",
	"level": 2
}, {
	"code": "06C05",
	"title": " Modular lattices, Desarguesian lattices",
	"parentcode": "06Cxx",
	"level": 3
}, {
	"code": "06C10",
	"title": " Semimodular lattices, geometric lattices",
	"parentcode": "06Cxx",
	"level": 3
}, {
	"code": "06C15",
	"title": " Complemented lattices, orthocomplemented lattices and posets [See also 03G12, 81P10]",
	"parentcode": "06Cxx",
	"level": 3
}, {
	"code": "06C20",
	"title": " Complemented modular lattices, continuous geometries",
	"parentcode": "06Cxx",
	"level": 3
}, {
	"code": "06C99",
	"title": " None of the above, but in this section",
	"parentcode": "06Cxx",
	"level": 3
}, {
	"code": "06Dxx",
	"title": " Distributive lattices",
	"parentcode": "06-XX",
	"level": 2
}, {
	"code": "06D05",
	"title": " Structure and representation theory",
	"parentcode": "06Dxx",
	"level": 3
}, {
	"code": "06D10",
	"title": " Complete distributivity",
	"parentcode": "06Dxx",
	"level": 3
}, {
	"code": "06D15",
	"title": " Pseudocomplemented lattices",
	"parentcode": "06Dxx",
	"level": 3
}, {
	"code": "06D20",
	"title": " Heyting algebras [See also 03G25]",
	"parentcode": "06Dxx",
	"level": 3
}, {
	"code": "06D22",
	"title": " Frames, locales {For topological questions see 54-XX}",
	"parentcode": "06Dxx",
	"level": 3
}, {
	"code": "06D25",
	"title": " Post algebras [See also 03G20]",
	"parentcode": "06Dxx",
	"level": 3
}, {
	"code": "06D30",
	"title": " De Morgan algebras, \\L ukasiewicz algebras [See also 03G20]",
	"parentcode": "06Dxx",
	"level": 3
}, {
	"code": "06D35",
	"title": " MV-algebras",
	"parentcode": "06Dxx",
	"level": 3
}, {
	"code": "06D50",
	"title": " Lattices and duality",
	"parentcode": "06Dxx",
	"level": 3
}, {
	"code": "06D72",
	"title": " Fuzzy lattices (soft algebras) and related topics",
	"parentcode": "06Dxx",
	"level": 3
}, {
	"code": "06D75",
	"title": " Other generalizations of distributive lattices",
	"parentcode": "06Dxx",
	"level": 3
}, {
	"code": "06D99",
	"title": " None of the above, but in this section",
	"parentcode": "06Dxx",
	"level": 3
}, {
	"code": "06Exx",
	"title": " Boolean algebras (Boolean rings) [See also 03G05]",
	"parentcode": "06-XX",
	"level": 2
}, {
	"code": "06E05",
	"title": " Structure theory",
	"parentcode": "06Exx",
	"level": 3
}, {
	"code": "06E10",
	"title": " Chain conditions, complete algebras",
	"parentcode": "06Exx",
	"level": 3
}, {
	"code": "06E15",
	"title": " Stone spaces (Boolean spaces) and related structures",
	"parentcode": "06Exx",
	"level": 3
}, {
	"code": "06E20",
	"title": " Ring-theoretic properties [See also 16E50, 16G30]",
	"parentcode": "06Exx",
	"level": 3
}, {
	"code": "06E25",
	"title": " Boolean algebras with additional operations (diagonalizable algebras, etc.) [See also 03G25, 03F45]",
	"parentcode": "06Exx",
	"level": 3
}, {
	"code": "06E30",
	"title": " Boolean functions [See also 94C10]",
	"parentcode": "06Exx",
	"level": 3
}, {
	"code": "06E75",
	"title": " Generalizations of Boolean algebras",
	"parentcode": "06Exx",
	"level": 3
}, {
	"code": "06E99",
	"title": " None of the above, but in this section",
	"parentcode": "06Exx",
	"level": 3
}, {
	"code": "06Fxx",
	"title": " Ordered structures",
	"parentcode": "06-XX",
	"level": 2
}, {
	"code": "06F05",
	"title": " Ordered semigroups and monoids [See also 20Mxx]",
	"parentcode": "06Fxx",
	"level": 3
}, {
	"code": "06F07",
	"title": " Quantales",
	"parentcode": "06Fxx",
	"level": 3
}, {
	"code": "06F10",
	"title": " Noether lattices",
	"parentcode": "06Fxx",
	"level": 3
}, {
	"code": "06F15",
	"title": " Ordered groups [See also 20F60]",
	"parentcode": "06Fxx",
	"level": 3
}, {
	"code": "06F20",
	"title": " Ordered abelian groups, Riesz groups, ordered linear spaces [See also 46A40]",
	"parentcode": "06Fxx",
	"level": 3
}, {
	"code": "06F25",
	"title": " Ordered rings, algebras, modules {For ordered fields, see 12J15; see also 13J25, 16W80}",
	"parentcode": "06Fxx",
	"level": 3
}, {
	"code": "06F30",
	"title": " Topological lattices, order topologies [See also 06B30, 22A26, 54F05, 54H12]",
	"parentcode": "06Fxx",
	"level": 3
}, {
	"code": "06F35",
	"title": " BCK-algebras, BCI-algebras [See also 03G25]",
	"parentcode": "06Fxx",
	"level": 3
}, {
	"code": "06F99",
	"title": " None of the above, but in this section",
	"parentcode": "06Fxx",
	"level": 3
}, {
	"code": "08-XX",
	"title": " General algebraic systems",
	"parentcode": null,
	"level": 1
}, {
	"code": "08-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "08-XX",
	"level": 2
}, {
	"code": "08-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "08-XX",
	"level": 2
}, {
	"code": "08-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "08-XX",
	"level": 2
}, {
	"code": "08-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "08-XX",
	"level": 2
}, {
	"code": "08-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "08-XX",
	"level": 2
}, {
	"code": "08-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "08-XX",
	"level": 2
}, {
	"code": "08Axx",
	"title": " Algebraic structures [See also 03C05]",
	"parentcode": "08-XX",
	"level": 2
}, {
	"code": "08A02",
	"title": " Relational systems, laws of composition",
	"parentcode": "08Axx",
	"level": 3
}, {
	"code": "08A05",
	"title": " Structure theory",
	"parentcode": "08Axx",
	"level": 3
}, {
	"code": "08A30",
	"title": " Subalgebras, congruence relations",
	"parentcode": "08Axx",
	"level": 3
}, {
	"code": "08A35",
	"title": " Automorphisms, endomorphisms",
	"parentcode": "08Axx",
	"level": 3
}, {
	"code": "08A40",
	"title": " Operations, polynomials, primal algebras",
	"parentcode": "08Axx",
	"level": 3
}, {
	"code": "08A45",
	"title": " Equational compactness",
	"parentcode": "08Axx",
	"level": 3
}, {
	"code": "08A50",
	"title": " Word problems [See also 03D40, 06B25, 20F10, 68R15]",
	"parentcode": "08Axx",
	"level": 3
}, {
	"code": "08A55",
	"title": " Partial algebras",
	"parentcode": "08Axx",
	"level": 3
}, {
	"code": "08A60",
	"title": " Unary algebras",
	"parentcode": "08Axx",
	"level": 3
}, {
	"code": "08A62",
	"title": " Finitary algebras",
	"parentcode": "08Axx",
	"level": 3
}, {
	"code": "08A65",
	"title": " Infinitary algebras",
	"parentcode": "08Axx",
	"level": 3
}, {
	"code": "08A68",
	"title": " Heterogeneous algebras",
	"parentcode": "08Axx",
	"level": 3
}, {
	"code": "08A70",
	"title": " Applications of universal algebra in computer science",
	"parentcode": "08Axx",
	"level": 3
}, {
	"code": "08A72",
	"title": " Fuzzy algebraic structures",
	"parentcode": "08Axx",
	"level": 3
}, {
	"code": "08A99",
	"title": " None of the above, but in this section",
	"parentcode": "08Axx",
	"level": 3
}, {
	"code": "08Bxx",
	"title": " Varieties [See also 03C05]",
	"parentcode": "08-XX",
	"level": 2
}, {
	"code": "08B05",
	"title": " Equational logic, Mal′cev (Mal′tsev) conditions",
	"parentcode": "08Bxx",
	"level": 3
}, {
	"code": "08B10",
	"title": " Congruence modularity, congruence distributivity",
	"parentcode": "08Bxx",
	"level": 3
}, {
	"code": "08B15",
	"title": " Lattices of varieties",
	"parentcode": "08Bxx",
	"level": 3
}, {
	"code": "08B20",
	"title": " Free algebras",
	"parentcode": "08Bxx",
	"level": 3
}, {
	"code": "08B25",
	"title": " Products, amalgamated products, and other kinds of limits and colimits [See also 18A30]",
	"parentcode": "08Bxx",
	"level": 3
}, {
	"code": "08B26",
	"title": " Subdirect products and subdirect irreducibility",
	"parentcode": "08Bxx",
	"level": 3
}, {
	"code": "08B30",
	"title": " Injectives, projectives",
	"parentcode": "08Bxx",
	"level": 3
}, {
	"code": "08B99",
	"title": " None of the above, but in this section",
	"parentcode": "08Bxx",
	"level": 3
}, {
	"code": "08Cxx",
	"title": " Other classes of algebras",
	"parentcode": "08-XX",
	"level": 2
}, {
	"code": "08C05",
	"title": " Categories of algebras [See also 18C05]",
	"parentcode": "08Cxx",
	"level": 3
}, {
	"code": "08C10",
	"title": " Axiomatic model classes [See also 03Cxx, in particular 03C60]",
	"parentcode": "08Cxx",
	"level": 3
}, {
	"code": "08C15",
	"title": " Quasivarieties",
	"parentcode": "08Cxx",
	"level": 3
}, {
	"code": "08C20",
	"title": " Natural dualities for classes of algebras [See also 06E15, 18A40, 22A30]",
	"parentcode": "08Cxx",
	"level": 3
}, {
	"code": "08C99",
	"title": " None of the above, but in this section",
	"parentcode": "08Cxx",
	"level": 3
}, {
	"code": "11-XX",
	"title": " Number theory",
	"parentcode": null,
	"level": 1
}, {
	"code": "11-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11Axx",
	"title": " Elementary number theory {For analogues in number fields, see 11R04}",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11A05",
	"title": " Multiplicative structure; Euclidean algorithm; greatest common divisors",
	"parentcode": "11Axx",
	"level": 3
}, {
	"code": "11A07",
	"title": " Congruences; primitive roots; residue systems",
	"parentcode": "11Axx",
	"level": 3
}, {
	"code": "11A15",
	"title": " Power residues, reciprocity",
	"parentcode": "11Axx",
	"level": 3
}, {
	"code": "11A25",
	"title": " Arithmetic functions; related numbers; inversion formulas",
	"parentcode": "11Axx",
	"level": 3
}, {
	"code": "11A41",
	"title": " Primes",
	"parentcode": "11Axx",
	"level": 3
}, {
	"code": "11A51",
	"title": " Factorization; primality",
	"parentcode": "11Axx",
	"level": 3
}, {
	"code": "11A55",
	"title": " Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15]",
	"parentcode": "11Axx",
	"level": 3
}, {
	"code": "11A63",
	"title": " Radix representation; digital problems {For metric results, see 11K16}",
	"parentcode": "11Axx",
	"level": 3
}, {
	"code": "11A67",
	"title": " Other representations",
	"parentcode": "11Axx",
	"level": 3
}, {
	"code": "11A99",
	"title": " None of the above, but in this section",
	"parentcode": "11Axx",
	"level": 3
}, {
	"code": "11Bxx",
	"title": " Sequences and sets",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11B05",
	"title": " Density, gaps, topology",
	"parentcode": "11Bxx",
	"level": 3
}, {
	"code": "11B13",
	"title": " Additive bases, including sumsets [See also 05B10]",
	"parentcode": "11Bxx",
	"level": 3
}, {
	"code": "11B25",
	"title": " Arithmetic progressions [See also 11N13]",
	"parentcode": "11Bxx",
	"level": 3
}, {
	"code": "11B30",
	"title": " Arithmetic combinatorics; higher degree uniformity",
	"parentcode": "11Bxx",
	"level": 3
}, {
	"code": "11B34",
	"title": " Representation functions",
	"parentcode": "11Bxx",
	"level": 3
}, {
	"code": "11B37",
	"title": " Recurrences {For applications to special functions, see 33-XX}",
	"parentcode": "11Bxx",
	"level": 3
}, {
	"code": "11B39",
	"title": " Fibonacci and Lucas numbers and polynomials and generalizations",
	"parentcode": "11Bxx",
	"level": 3
}, {
	"code": "11B50",
	"title": " Sequences (mod $m$)",
	"parentcode": "11Bxx",
	"level": 3
}, {
	"code": "11B57",
	"title": " Farey sequences; the sequences ${1^k, 2^k, \\cdots}$",
	"parentcode": "11Bxx",
	"level": 3
}, {
	"code": "11B65",
	"title": " Binomial coefficients; factorials; $q$-identities [See also 05A10, 05A30]",
	"parentcode": "11Bxx",
	"level": 3
}, {
	"code": "11B68",
	"title": " Bernoulli and Euler numbers and polynomials",
	"parentcode": "11Bxx",
	"level": 3
}, {
	"code": "11B73",
	"title": " Bell and Stirling numbers",
	"parentcode": "11Bxx",
	"level": 3
}, {
	"code": "11B75",
	"title": " Other combinatorial number theory",
	"parentcode": "11Bxx",
	"level": 3
}, {
	"code": "11B83",
	"title": " Special sequences and polynomials",
	"parentcode": "11Bxx",
	"level": 3
}, {
	"code": "11B85",
	"title": " Automata sequences",
	"parentcode": "11Bxx",
	"level": 3
}, {
	"code": "11B99",
	"title": " None of the above, but in this section",
	"parentcode": "11Bxx",
	"level": 3
}, {
	"code": "11Cxx",
	"title": " Polynomials and matrices",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11C08",
	"title": " Polynomials [See also 13F20]",
	"parentcode": "11Cxx",
	"level": 3
}, {
	"code": "11C20",
	"title": " Matrices, determinants [See also 15B36]",
	"parentcode": "11Cxx",
	"level": 3
}, {
	"code": "11C99",
	"title": " None of the above, but in this section",
	"parentcode": "11Cxx",
	"level": 3
}, {
	"code": "11Dxx",
	"title": " Diophantine equations [See also 11Gxx, 14Gxx]",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11D04",
	"title": " Linear equations",
	"parentcode": "11Dxx",
	"level": 3
}, {
	"code": "11D07",
	"title": " The Frobenius problem",
	"parentcode": "11Dxx",
	"level": 3
}, {
	"code": "11D09",
	"title": " Quadratic and bilinear equations",
	"parentcode": "11Dxx",
	"level": 3
}, {
	"code": "11D25",
	"title": " Cubic and quartic equations",
	"parentcode": "11Dxx",
	"level": 3
}, {
	"code": "11D41",
	"title": " Higher degree equations; Fermat's equation",
	"parentcode": "11Dxx",
	"level": 3
}, {
	"code": "11D45",
	"title": " Counting solutions of Diophantine equations",
	"parentcode": "11Dxx",
	"level": 3
}, {
	"code": "11D57",
	"title": " Multiplicative and norm form equations",
	"parentcode": "11Dxx",
	"level": 3
}, {
	"code": "11D59",
	"title": " Thue-Mahler equations",
	"parentcode": "11Dxx",
	"level": 3
}, {
	"code": "11D61",
	"title": " Exponential equations",
	"parentcode": "11Dxx",
	"level": 3
}, {
	"code": "11D68",
	"title": " Rational numbers as sums of fractions",
	"parentcode": "11Dxx",
	"level": 3
}, {
	"code": "11D72",
	"title": " Equations in many variables [See also 11P55]",
	"parentcode": "11Dxx",
	"level": 3
}, {
	"code": "11D75",
	"title": " Diophantine inequalities [See also 11J25]",
	"parentcode": "11Dxx",
	"level": 3
}, {
	"code": "11D79",
	"title": " Congruences in many variables",
	"parentcode": "11Dxx",
	"level": 3
}, {
	"code": "11D85",
	"title": " Representation problems [See also 11P55]",
	"parentcode": "11Dxx",
	"level": 3
}, {
	"code": "11D88",
	"title": " $p$-adic and power series fields",
	"parentcode": "11Dxx",
	"level": 3
}, {
	"code": "11D99",
	"title": " None of the above, but in this section",
	"parentcode": "11Dxx",
	"level": 3
}, {
	"code": "11Exx",
	"title": " Forms and linear algebraic groups [See also 19Gxx] {For quadratic forms in linear algebra, see 15A63}",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11E04",
	"title": " Quadratic forms over general fields",
	"parentcode": "11Exx",
	"level": 3
}, {
	"code": "11E08",
	"title": " Quadratic forms over local rings and fields",
	"parentcode": "11Exx",
	"level": 3
}, {
	"code": "11E10",
	"title": " Forms over real fields",
	"parentcode": "11Exx",
	"level": 3
}, {
	"code": "11E12",
	"title": " Quadratic forms over global rings and fields",
	"parentcode": "11Exx",
	"level": 3
}, {
	"code": "11E16",
	"title": " General binary quadratic forms",
	"parentcode": "11Exx",
	"level": 3
}, {
	"code": "11E20",
	"title": " General ternary and quaternary quadratic forms; forms of more than two variables",
	"parentcode": "11Exx",
	"level": 3
}, {
	"code": "11E25",
	"title": " Sums of squares and representations by other particular quadratic forms",
	"parentcode": "11Exx",
	"level": 3
}, {
	"code": "11E39",
	"title": " Bilinear and Hermitian forms",
	"parentcode": "11Exx",
	"level": 3
}, {
	"code": "11E41",
	"title": " Class numbers of quadratic and Hermitian forms",
	"parentcode": "11Exx",
	"level": 3
}, {
	"code": "11E45",
	"title": " Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)",
	"parentcode": "11Exx",
	"level": 3
}, {
	"code": "11E57",
	"title": " Classical groups [See also 14Lxx, 20Gxx]",
	"parentcode": "11Exx",
	"level": 3
}, {
	"code": "11E70",
	"title": " $K$-theory of quadratic and Hermitian forms",
	"parentcode": "11Exx",
	"level": 3
}, {
	"code": "11E72",
	"title": " Galois cohomology of linear algebraic groups [See also 20G10]",
	"parentcode": "11Exx",
	"level": 3
}, {
	"code": "11E76",
	"title": " Forms of degree higher than two",
	"parentcode": "11Exx",
	"level": 3
}, {
	"code": "11E81",
	"title": " Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24]",
	"parentcode": "11Exx",
	"level": 3
}, {
	"code": "11E88",
	"title": " Quadratic spaces; Clifford algebras [See also 15A63, 15A66]",
	"parentcode": "11Exx",
	"level": 3
}, {
	"code": "11E95",
	"title": " $p$-adic theory",
	"parentcode": "11Exx",
	"level": 3
}, {
	"code": "11E99",
	"title": " None of the above, but in this section",
	"parentcode": "11Exx",
	"level": 3
}, {
	"code": "11Fxx",
	"title": " Discontinuous groups and automorphic forms [See also 11R39, 11S37, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx] {For relations with quadratic forms, see 11E45}",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11F03",
	"title": " Modular and automorphic functions",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F06",
	"title": " Structure of modular groups and generalizations; arithmetic groups [See also 20H05, 20H10, 22E40]",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F11",
	"title": " Holomorphic modular forms of integral weight",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F12",
	"title": " Automorphic forms, one variable",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F20",
	"title": " Dedekind eta function, Dedekind sums",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F22",
	"title": " Relationship to Lie algebras and finite simple groups",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F23",
	"title": " Relations with algebraic geometry and topology",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F25",
	"title": " Hecke-Petersson operators, differential operators (one variable)",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F27",
	"title": " Theta series; Weil representation; theta correspondences",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F30",
	"title": " Fourier coefficients of automorphic forms",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F32",
	"title": " Modular correspondences, etc.",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F33",
	"title": " Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50]",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F37",
	"title": " Forms of half-integer weight; nonholomorphic modular forms",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F41",
	"title": " Automorphic forms on ${\\rm GL}(2)$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F46",
	"title": " Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F50",
	"title": " Jacobi forms",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F52",
	"title": " Modular forms associated to Drinfel'd modules",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F55",
	"title": " Other groups and their modular and automorphic forms (several variables)",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F60",
	"title": " Hecke-Petersson operators, differential operators (several variables)",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F66",
	"title": " Langlands $L$-functions; one variable Dirichlet series and functional equations",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F67",
	"title": " Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F68",
	"title": " Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F70",
	"title": " Representation-theoretic methods; automorphic representations over local and global fields",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F72",
	"title": " Spectral theory; Selberg trace formula",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F75",
	"title": " Cohomology of arithmetic groups",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F80",
	"title": " Galois representations",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F85",
	"title": " $p$-adic theory, local fields [See also 14G20, 22E50]",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11F99",
	"title": " None of the above, but in this section",
	"parentcode": "11Fxx",
	"level": 3
}, {
	"code": "11Gxx",
	"title": " Arithmetic algebraic geometry (Diophantine geometry) [See also 11Dxx, 14Gxx, 14Kxx]",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11G05",
	"title": " Elliptic curves over global fields [See also 14H52]",
	"parentcode": "11Gxx",
	"level": 3
}, {
	"code": "11G07",
	"title": " Elliptic curves over local fields [See also 14G20, 14H52]",
	"parentcode": "11Gxx",
	"level": 3
}, {
	"code": "11G09",
	"title": " Drinfel'd modules; higher-dimensional motives, etc. [See also 14L05]",
	"parentcode": "11Gxx",
	"level": 3
}, {
	"code": "11G10",
	"title": " Abelian varieties of dimension $> 1$ [See also 14Kxx]",
	"parentcode": "11Gxx",
	"level": 3
}, {
	"code": "11G15",
	"title": " Complex multiplication and moduli of abelian varieties [See also 14K22]",
	"parentcode": "11Gxx",
	"level": 3
}, {
	"code": "11G16",
	"title": " Elliptic and modular units [See also 11R27]",
	"parentcode": "11Gxx",
	"level": 3
}, {
	"code": "11G18",
	"title": " Arithmetic aspects of modular and Shimura varieties [See also 14G35]",
	"parentcode": "11Gxx",
	"level": 3
}, {
	"code": "11G20",
	"title": " Curves over finite and local fields [See also 14H25]",
	"parentcode": "11Gxx",
	"level": 3
}, {
	"code": "11G25",
	"title": " Varieties over finite and local fields [See also 14G15, 14G20]",
	"parentcode": "11Gxx",
	"level": 3
}, {
	"code": "11G30",
	"title": " Curves of arbitrary genus or genus $\\ne 1$ over global fields [See also 14H25]",
	"parentcode": "11Gxx",
	"level": 3
}, {
	"code": "11G32",
	"title": " Dessins d'enfants, Belyĭ theory",
	"parentcode": "11Gxx",
	"level": 3
}, {
	"code": "11G35",
	"title": " Varieties over global fields [See also 14G25]",
	"parentcode": "11Gxx",
	"level": 3
}, {
	"code": "11G40",
	"title": " $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]",
	"parentcode": "11Gxx",
	"level": 3
}, {
	"code": "11G42",
	"title": " Arithmetic mirror symmetry [See also 14J33]",
	"parentcode": "11Gxx",
	"level": 3
}, {
	"code": "11G45",
	"title": " Geometric class field theory [See also 11R37, 14C35, 19F05]",
	"parentcode": "11Gxx",
	"level": 3
}, {
	"code": "11G50",
	"title": " Heights [See also 14G40, 37P30]",
	"parentcode": "11Gxx",
	"level": 3
}, {
	"code": "11G55",
	"title": " Polylogarithms and relations with $K$-theory",
	"parentcode": "11Gxx",
	"level": 3
}, {
	"code": "11G99",
	"title": " None of the above, but in this section",
	"parentcode": "11Gxx",
	"level": 3
}, {
	"code": "11Hxx",
	"title": " Geometry of numbers {For applications in coding theory, see 94B75}",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11H06",
	"title": " Lattices and convex bodies [See also 11P21, 52C05, 52C07]",
	"parentcode": "11Hxx",
	"level": 3
}, {
	"code": "11H16",
	"title": " Nonconvex bodies",
	"parentcode": "11Hxx",
	"level": 3
}, {
	"code": "11H31",
	"title": " Lattice packing and covering [See also 05B40, 52C15, 52C17]",
	"parentcode": "11Hxx",
	"level": 3
}, {
	"code": "11H46",
	"title": " Products of linear forms",
	"parentcode": "11Hxx",
	"level": 3
}, {
	"code": "11H50",
	"title": " Minima of forms",
	"parentcode": "11Hxx",
	"level": 3
}, {
	"code": "11H55",
	"title": " Quadratic forms (reduction theory, extreme forms, etc.)",
	"parentcode": "11Hxx",
	"level": 3
}, {
	"code": "11H56",
	"title": " Automorphism groups of lattices",
	"parentcode": "11Hxx",
	"level": 3
}, {
	"code": "11H60",
	"title": " Mean value and transfer theorems",
	"parentcode": "11Hxx",
	"level": 3
}, {
	"code": "11H71",
	"title": " Relations with coding theory",
	"parentcode": "11Hxx",
	"level": 3
}, {
	"code": "11H99",
	"title": " None of the above, but in this section",
	"parentcode": "11Hxx",
	"level": 3
}, {
	"code": "11Jxx",
	"title": " Diophantine approximation, transcendental number theory [See also 11K60]",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11J04",
	"title": " Homogeneous approximation to one number",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J06",
	"title": " Markov and Lagrange spectra and generalizations",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J13",
	"title": " Simultaneous homogeneous approximation, linear forms",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J17",
	"title": " Approximation by numbers from a fixed field",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J20",
	"title": " Inhomogeneous linear forms",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J25",
	"title": " Diophantine inequalities [See also 11D75]",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J54",
	"title": " Small fractional parts of polynomials and generalizations",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J61",
	"title": " Approximation in non-Archimedean valuations",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J68",
	"title": " Approximation to algebraic numbers",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J70",
	"title": " Continued fractions and generalizations [See also 11A55, 11K50]",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J71",
	"title": " Distribution modulo one [See also 11K06]",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J72",
	"title": " Irrationality; linear independence over a field",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J81",
	"title": " Transcendence (general theory)",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J82",
	"title": " Measures of irrationality and of transcendence",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J83",
	"title": " Metric theory",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J85",
	"title": " Algebraic independence; Gel'fond's method",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J86",
	"title": " Linear forms in logarithms; Baker's method",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J87",
	"title": " Schmidt Subspace Theorem and applications",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J89",
	"title": " Transcendence theory of elliptic and abelian functions",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J91",
	"title": " Transcendence theory of other special functions",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J93",
	"title": " Transcendence theory of Drinfel'd and $t$-modules",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J95",
	"title": " Results involving abelian varieties",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J97",
	"title": " Analogues of methods in Nevanlinna theory (work of Vojta et al.)",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11J99",
	"title": " None of the above, but in this section",
	"parentcode": "11Jxx",
	"level": 3
}, {
	"code": "11Kxx",
	"title": " Probabilistic theory",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11K06",
	"title": " General theory of distribution modulo $1$ [See also 11J71]",
	"parentcode": "11Kxx",
	"level": 3
}, {
	"code": "11K16",
	"title": " Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. [See also 11A63]",
	"parentcode": "11Kxx",
	"level": 3
}, {
	"code": "11K31",
	"title": " Special sequences",
	"parentcode": "11Kxx",
	"level": 3
}, {
	"code": "11K36",
	"title": " Well-distributed sequences and other variations",
	"parentcode": "11Kxx",
	"level": 3
}, {
	"code": "11K38",
	"title": " Irregularities of distribution, discrepancy [See also 11Nxx]",
	"parentcode": "11Kxx",
	"level": 3
}, {
	"code": "11K41",
	"title": " Continuous, $p$-adic and abstract analogues",
	"parentcode": "11Kxx",
	"level": 3
}, {
	"code": "11K45",
	"title": " Pseudo-random numbers; Monte Carlo methods",
	"parentcode": "11Kxx",
	"level": 3
}, {
	"code": "11K50",
	"title": " Metric theory of continued fractions [See also 11A55, 11J70]",
	"parentcode": "11Kxx",
	"level": 3
}, {
	"code": "11K55",
	"title": " Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx]",
	"parentcode": "11Kxx",
	"level": 3
}, {
	"code": "11K60",
	"title": " Diophantine approximation [See also 11Jxx]",
	"parentcode": "11Kxx",
	"level": 3
}, {
	"code": "11K65",
	"title": " Arithmetic functions [See also 11Nxx]",
	"parentcode": "11Kxx",
	"level": 3
}, {
	"code": "11K70",
	"title": " Harmonic analysis and almost periodicity",
	"parentcode": "11Kxx",
	"level": 3
}, {
	"code": "11K99",
	"title": " None of the above, but in this section",
	"parentcode": "11Kxx",
	"level": 3
}, {
	"code": "11Lxx",
	"title": " Exponential sums and character sums {For finite fields, see 11Txx}",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11L03",
	"title": " Trigonometric and exponential sums, general",
	"parentcode": "11Lxx",
	"level": 3
}, {
	"code": "11L05",
	"title": " Gauss and Kloosterman sums; generalizations",
	"parentcode": "11Lxx",
	"level": 3
}, {
	"code": "11L07",
	"title": " Estimates on exponential sums",
	"parentcode": "11Lxx",
	"level": 3
}, {
	"code": "11L10",
	"title": " Jacobsthal and Brewer sums; other complete character sums",
	"parentcode": "11Lxx",
	"level": 3
}, {
	"code": "11L15",
	"title": " Weyl sums",
	"parentcode": "11Lxx",
	"level": 3
}, {
	"code": "11L20",
	"title": " Sums over primes",
	"parentcode": "11Lxx",
	"level": 3
}, {
	"code": "11L26",
	"title": " Sums over arbitrary intervals",
	"parentcode": "11Lxx",
	"level": 3
}, {
	"code": "11L40",
	"title": " Estimates on character sums",
	"parentcode": "11Lxx",
	"level": 3
}, {
	"code": "11L99",
	"title": " None of the above, but in this section",
	"parentcode": "11Lxx",
	"level": 3
}, {
	"code": "11Mxx",
	"title": " Zeta and $L$-functions",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11M06",
	"title": " $\\zeta (s)$ and $L(s, \\chi)$",
	"parentcode": "11Mxx",
	"level": 3
}, {
	"code": "11M20",
	"title": " Real zeros of $L(s, \\chi)$; results on $L(1, \\chi)$",
	"parentcode": "11Mxx",
	"level": 3
}, {
	"code": "11M26",
	"title": " Nonreal zeros of $\\zeta (s)$ and $L(s, \\chi)$; Riemann and other hypotheses",
	"parentcode": "11Mxx",
	"level": 3
}, {
	"code": "11M32",
	"title": " Multiple Dirichlet series and zeta functions and multizeta values",
	"parentcode": "11Mxx",
	"level": 3
}, {
	"code": "11M35",
	"title": " Hurwitz and Lerch zeta functions",
	"parentcode": "11Mxx",
	"level": 3
}, {
	"code": "11M36",
	"title": " Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas",
	"parentcode": "11Mxx",
	"level": 3
}, {
	"code": "11M38",
	"title": " Zeta and $L$-functions in characteristic $p$",
	"parentcode": "11Mxx",
	"level": 3
}, {
	"code": "11M41",
	"title": " Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}",
	"parentcode": "11Mxx",
	"level": 3
}, {
	"code": "11M45",
	"title": " Tauberian theorems [See also 40E05]",
	"parentcode": "11Mxx",
	"level": 3
}, {
	"code": "11M50",
	"title": " Relations with random matrices",
	"parentcode": "11Mxx",
	"level": 3
}, {
	"code": "11M55",
	"title": " Relations with noncommutative geometry",
	"parentcode": "11Mxx",
	"level": 3
}, {
	"code": "11M99",
	"title": " None of the above, but in this section",
	"parentcode": "11Mxx",
	"level": 3
}, {
	"code": "11Nxx",
	"title": " Multiplicative number theory",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11N05",
	"title": " Distribution of primes",
	"parentcode": "11Nxx",
	"level": 3
}, {
	"code": "11N13",
	"title": " Primes in progressions [See also 11B25]",
	"parentcode": "11Nxx",
	"level": 3
}, {
	"code": "11N25",
	"title": " Distribution of integers with specified multiplicative constraints",
	"parentcode": "11Nxx",
	"level": 3
}, {
	"code": "11N30",
	"title": " Turán theory [See also 30Bxx]",
	"parentcode": "11Nxx",
	"level": 3
}, {
	"code": "11N32",
	"title": " Primes represented by polynomials; other multiplicative structure of polynomial values",
	"parentcode": "11Nxx",
	"level": 3
}, {
	"code": "11N35",
	"title": " Sieves",
	"parentcode": "11Nxx",
	"level": 3
}, {
	"code": "11N36",
	"title": " Applications of sieve methods",
	"parentcode": "11Nxx",
	"level": 3
}, {
	"code": "11N37",
	"title": " Asymptotic results on arithmetic functions",
	"parentcode": "11Nxx",
	"level": 3
}, {
	"code": "11N45",
	"title": " Asymptotic results on counting functions for algebraic and topological structures",
	"parentcode": "11Nxx",
	"level": 3
}, {
	"code": "11N56",
	"title": " Rate of growth of arithmetic functions",
	"parentcode": "11Nxx",
	"level": 3
}, {
	"code": "11N60",
	"title": " Distribution functions associated with additive and positive multiplicative functions",
	"parentcode": "11Nxx",
	"level": 3
}, {
	"code": "11N64",
	"title": " Other results on the distribution of values or the characterization of arithmetic functions",
	"parentcode": "11Nxx",
	"level": 3
}, {
	"code": "11N69",
	"title": " Distribution of integers in special residue classes",
	"parentcode": "11Nxx",
	"level": 3
}, {
	"code": "11N75",
	"title": " Applications of automorphic functions and forms to multiplicative problems [See also 11Fxx]",
	"parentcode": "11Nxx",
	"level": 3
}, {
	"code": "11N80",
	"title": " Generalized primes and integers",
	"parentcode": "11Nxx",
	"level": 3
}, {
	"code": "11N99",
	"title": " None of the above, but in this section",
	"parentcode": "11Nxx",
	"level": 3
}, {
	"code": "11Pxx",
	"title": " Additive number theory; partitions",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11P05",
	"title": " Waring's problem and variants",
	"parentcode": "11Pxx",
	"level": 3
}, {
	"code": "11P21",
	"title": " Lattice points in specified regions",
	"parentcode": "11Pxx",
	"level": 3
}, {
	"code": "11P32",
	"title": " Goldbach-type theorems; other additive questions involving primes",
	"parentcode": "11Pxx",
	"level": 3
}, {
	"code": "11P55",
	"title": " Applications of the Hardy-Littlewood method [See also 11D85]",
	"parentcode": "11Pxx",
	"level": 3
}, {
	"code": "11P70",
	"title": " Inverse problems of additive number theory, including sumsets",
	"parentcode": "11Pxx",
	"level": 3
}, {
	"code": "11P81",
	"title": " Elementary theory of partitions [See also 05A17]",
	"parentcode": "11Pxx",
	"level": 3
}, {
	"code": "11P82",
	"title": " Analytic theory of partitions",
	"parentcode": "11Pxx",
	"level": 3
}, {
	"code": "11P83",
	"title": " Partitions; congruences and congruential restrictions",
	"parentcode": "11Pxx",
	"level": 3
}, {
	"code": "11P84",
	"title": " Partition identities; identities of Rogers-Ramanujan type",
	"parentcode": "11Pxx",
	"level": 3
}, {
	"code": "11P99",
	"title": " None of the above, but in this section",
	"parentcode": "11Pxx",
	"level": 3
}, {
	"code": "11Rxx",
	"title": " Algebraic number theory",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11R04",
	"title": " Algebraic numbers; rings of algebraic integers",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R06",
	"title": " PV-numbers and generalizations; other special algebraic numbers; Mahler measure",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R09",
	"title": " Polynomials (irreducibility, etc.)",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R11",
	"title": " Quadratic extensions",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R16",
	"title": " Cubic and quartic extensions",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R18",
	"title": " Cyclotomic extensions",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R20",
	"title": " Other abelian and metabelian extensions",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R21",
	"title": " Other number fields",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R23",
	"title": " Iwasawa theory",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R27",
	"title": " Units and factorization",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R29",
	"title": " Class numbers, class groups, discriminants",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R32",
	"title": " Galois theory",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R33",
	"title": " Integral representations related to algebraic numbers; Galois module structure of rings of integers [See also 20C10]",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R34",
	"title": " Galois cohomology [See also 12Gxx, 19A31]",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R37",
	"title": " Class field theory",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R39",
	"title": " Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55]",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R42",
	"title": " Zeta functions and $L$-functions of number fields [See also 11M41, 19F27]",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R44",
	"title": " Distribution of prime ideals [See also 11N05]",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R45",
	"title": " Density theorems",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R47",
	"title": " Other analytic theory [See also 11Nxx]",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R52",
	"title": " Quaternion and other division algebras",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R54",
	"title": " Other algebras and orders, and their zeta and $L$-functions [See also 11S45, 16Hxx, 16Kxx]",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R56",
	"title": " Adèle rings and groups",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R58",
	"title": " Arithmetic theory of algebraic function fields [See also 14-XX]",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R60",
	"title": " Cyclotomic function fields (class groups, Bernoulli objects, etc.)",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R65",
	"title": " Class groups and Picard groups of orders",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R70",
	"title": " $K$-theory of global fields [See also 19Fxx]",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R80",
	"title": " Totally real fields [See also 12J15]",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11R99",
	"title": " None of the above, but in this section",
	"parentcode": "11Rxx",
	"level": 3
}, {
	"code": "11Sxx",
	"title": " Algebraic number theory",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11S05",
	"title": " Polynomials",
	"parentcode": "11Sxx",
	"level": 3
}, {
	"code": "11S15",
	"title": " Ramification and extension theory",
	"parentcode": "11Sxx",
	"level": 3
}, {
	"code": "11S20",
	"title": " Galois theory",
	"parentcode": "11Sxx",
	"level": 3
}, {
	"code": "11S23",
	"title": " Integral representations",
	"parentcode": "11Sxx",
	"level": 3
}, {
	"code": "11S25",
	"title": " Galois cohomology [See also 12Gxx, 16H05]",
	"parentcode": "11Sxx",
	"level": 3
}, {
	"code": "11S31",
	"title": " Class field theory; $p$-adic formal groups [See also 14L05]",
	"parentcode": "11Sxx",
	"level": 3
}, {
	"code": "11S37",
	"title": " Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50]",
	"parentcode": "11Sxx",
	"level": 3
}, {
	"code": "11S40",
	"title": " Zeta functions and $L$-functions [See also 11M41, 19F27]",
	"parentcode": "11Sxx",
	"level": 3
}, {
	"code": "11S45",
	"title": " Algebras and orders, and their zeta functions [See also 11R52, 11R54, 16Hxx, 16Kxx]",
	"parentcode": "11Sxx",
	"level": 3
}, {
	"code": "11S70",
	"title": " $K$-theory of local fields [See also 19Fxx]",
	"parentcode": "11Sxx",
	"level": 3
}, {
	"code": "11S80",
	"title": " Other analytic theory (analogues of beta and gamma functions, $p$-adic integration, etc.)",
	"parentcode": "11Sxx",
	"level": 3
}, {
	"code": "11S82",
	"title": " Non-Archimedean dynamical systems [See mainly 37Pxx]",
	"parentcode": "11Sxx",
	"level": 3
}, {
	"code": "11S85",
	"title": " Other nonanalytic theory",
	"parentcode": "11Sxx",
	"level": 3
}, {
	"code": "11S90",
	"title": " Prehomogeneous vector spaces",
	"parentcode": "11Sxx",
	"level": 3
}, {
	"code": "11S99",
	"title": " None of the above, but in this section",
	"parentcode": "11Sxx",
	"level": 3
}, {
	"code": "11Txx",
	"title": " Finite fields and commutative rings (number-theoretic aspects)",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11T06",
	"title": " Polynomials",
	"parentcode": "11Txx",
	"level": 3
}, {
	"code": "11T22",
	"title": " Cyclotomy",
	"parentcode": "11Txx",
	"level": 3
}, {
	"code": "11T23",
	"title": " Exponential sums",
	"parentcode": "11Txx",
	"level": 3
}, {
	"code": "11T24",
	"title": " Other character sums and Gauss sums",
	"parentcode": "11Txx",
	"level": 3
}, {
	"code": "11T30",
	"title": " Structure theory",
	"parentcode": "11Txx",
	"level": 3
}, {
	"code": "11T55",
	"title": " Arithmetic theory of polynomial rings over finite fields",
	"parentcode": "11Txx",
	"level": 3
}, {
	"code": "11T60",
	"title": " Finite upper half-planes",
	"parentcode": "11Txx",
	"level": 3
}, {
	"code": "11T71",
	"title": " Algebraic coding theory; cryptography",
	"parentcode": "11Txx",
	"level": 3
}, {
	"code": "11T99",
	"title": " None of the above, but in this section",
	"parentcode": "11Txx",
	"level": 3
}, {
	"code": "11Uxx",
	"title": " Connections with logic",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11U05",
	"title": " Decidability [See also 03B25]",
	"parentcode": "11Uxx",
	"level": 3
}, {
	"code": "11U07",
	"title": " Ultraproducts [See also 03C20]",
	"parentcode": "11Uxx",
	"level": 3
}, {
	"code": "11U09",
	"title": " Model theory [See also 03Cxx]",
	"parentcode": "11Uxx",
	"level": 3
}, {
	"code": "11U10",
	"title": " Nonstandard arithmetic [See also 03H15]",
	"parentcode": "11Uxx",
	"level": 3
}, {
	"code": "11U99",
	"title": " None of the above, but in this section",
	"parentcode": "11Uxx",
	"level": 3
}, {
	"code": "11Yxx",
	"title": " Computational number theory [See also 11-04]",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11Y05",
	"title": " Factorization",
	"parentcode": "11Yxx",
	"level": 3
}, {
	"code": "11Y11",
	"title": " Primality",
	"parentcode": "11Yxx",
	"level": 3
}, {
	"code": "11Y16",
	"title": " Algorithms; complexity [See also 68Q25]",
	"parentcode": "11Yxx",
	"level": 3
}, {
	"code": "11Y35",
	"title": " Analytic computations",
	"parentcode": "11Yxx",
	"level": 3
}, {
	"code": "11Y40",
	"title": " Algebraic number theory computations",
	"parentcode": "11Yxx",
	"level": 3
}, {
	"code": "11Y50",
	"title": " Computer solution of Diophantine equations",
	"parentcode": "11Yxx",
	"level": 3
}, {
	"code": "11Y55",
	"title": " Calculation of integer sequences",
	"parentcode": "11Yxx",
	"level": 3
}, {
	"code": "11Y60",
	"title": " Evaluation of constants",
	"parentcode": "11Yxx",
	"level": 3
}, {
	"code": "11Y65",
	"title": " Continued fraction calculations",
	"parentcode": "11Yxx",
	"level": 3
}, {
	"code": "11Y70",
	"title": " Values of arithmetic functions; tables",
	"parentcode": "11Yxx",
	"level": 3
}, {
	"code": "11Y99",
	"title": " None of the above, but in this section",
	"parentcode": "11Yxx",
	"level": 3
}, {
	"code": "11Zxx",
	"title": " Miscellaneous applications of number theory",
	"parentcode": "11-XX",
	"level": 2
}, {
	"code": "11Z05",
	"title": " Miscellaneous applications of number theory",
	"parentcode": "11Zxx",
	"level": 3
}, {
	"code": "11Z99",
	"title": " None of the above, but in this section",
	"parentcode": "11Zxx",
	"level": 3
}, {
	"code": "12-XX",
	"title": " Field theory and polynomials",
	"parentcode": null,
	"level": 1
}, {
	"code": "12-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "12-XX",
	"level": 2
}, {
	"code": "12-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "12-XX",
	"level": 2
}, {
	"code": "12-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "12-XX",
	"level": 2
}, {
	"code": "12-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "12-XX",
	"level": 2
}, {
	"code": "12-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "12-XX",
	"level": 2
}, {
	"code": "12-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "12-XX",
	"level": 2
}, {
	"code": "12Dxx",
	"title": " Real and complex fields",
	"parentcode": "12-XX",
	"level": 2
}, {
	"code": "12D05",
	"title": " Polynomials",
	"parentcode": "12Dxx",
	"level": 3
}, {
	"code": "12D10",
	"title": " Polynomials",
	"parentcode": "12Dxx",
	"level": 3
}, {
	"code": "12D15",
	"title": " Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also 11Exx]",
	"parentcode": "12Dxx",
	"level": 3
}, {
	"code": "12D99",
	"title": " None of the above, but in this section",
	"parentcode": "12Dxx",
	"level": 3
}, {
	"code": "12Exx",
	"title": " General field theory",
	"parentcode": "12-XX",
	"level": 2
}, {
	"code": "12E05",
	"title": " Polynomials (irreducibility, etc.)",
	"parentcode": "12Exx",
	"level": 3
}, {
	"code": "12E10",
	"title": " Special polynomials",
	"parentcode": "12Exx",
	"level": 3
}, {
	"code": "12E12",
	"title": " Equations",
	"parentcode": "12Exx",
	"level": 3
}, {
	"code": "12E15",
	"title": " Skew fields, division rings [See also 11R52, 11R54, 11S45, 16Kxx]",
	"parentcode": "12Exx",
	"level": 3
}, {
	"code": "12E20",
	"title": " Finite fields (field-theoretic aspects)",
	"parentcode": "12Exx",
	"level": 3
}, {
	"code": "12E25",
	"title": " Hilbertian fields; Hilbert's irreducibility theorem",
	"parentcode": "12Exx",
	"level": 3
}, {
	"code": "12E30",
	"title": " Field arithmetic",
	"parentcode": "12Exx",
	"level": 3
}, {
	"code": "12E99",
	"title": " None of the above, but in this section",
	"parentcode": "12Exx",
	"level": 3
}, {
	"code": "12Fxx",
	"title": " Field extensions",
	"parentcode": "12-XX",
	"level": 2
}, {
	"code": "12F05",
	"title": " Algebraic extensions",
	"parentcode": "12Fxx",
	"level": 3
}, {
	"code": "12F10",
	"title": " Separable extensions, Galois theory",
	"parentcode": "12Fxx",
	"level": 3
}, {
	"code": "12F12",
	"title": " Inverse Galois theory",
	"parentcode": "12Fxx",
	"level": 3
}, {
	"code": "12F15",
	"title": " Inseparable extensions",
	"parentcode": "12Fxx",
	"level": 3
}, {
	"code": "12F20",
	"title": " Transcendental extensions",
	"parentcode": "12Fxx",
	"level": 3
}, {
	"code": "12F99",
	"title": " None of the above, but in this section",
	"parentcode": "12Fxx",
	"level": 3
}, {
	"code": "12Gxx",
	"title": " Homological methods (field theory)",
	"parentcode": "12-XX",
	"level": 2
}, {
	"code": "12G05",
	"title": " Galois cohomology [See also 14F22, 16Hxx, 16K50]",
	"parentcode": "12Gxx",
	"level": 3
}, {
	"code": "12G10",
	"title": " Cohomological dimension",
	"parentcode": "12Gxx",
	"level": 3
}, {
	"code": "12G99",
	"title": " None of the above, but in this section",
	"parentcode": "12Gxx",
	"level": 3
}, {
	"code": "12Hxx",
	"title": " Differential and difference algebra",
	"parentcode": "12-XX",
	"level": 2
}, {
	"code": "12H05",
	"title": " Differential algebra [See also 13Nxx]",
	"parentcode": "12Hxx",
	"level": 3
}, {
	"code": "12H10",
	"title": " Difference algebra [See also 39Axx]",
	"parentcode": "12Hxx",
	"level": 3
}, {
	"code": "12H20",
	"title": " Abstract differential equations [See also 34Mxx]",
	"parentcode": "12Hxx",
	"level": 3
}, {
	"code": "12H25",
	"title": " $p$-adic differential equations [See also 11S80, 14G20]",
	"parentcode": "12Hxx",
	"level": 3
}, {
	"code": "12H99",
	"title": " None of the above, but in this section",
	"parentcode": "12Hxx",
	"level": 3
}, {
	"code": "12Jxx",
	"title": " Topological fields",
	"parentcode": "12-XX",
	"level": 2
}, {
	"code": "12J05",
	"title": " Normed fields",
	"parentcode": "12Jxx",
	"level": 3
}, {
	"code": "12J10",
	"title": " Valued fields",
	"parentcode": "12Jxx",
	"level": 3
}, {
	"code": "12J12",
	"title": " Formally $p$-adic fields",
	"parentcode": "12Jxx",
	"level": 3
}, {
	"code": "12J15",
	"title": " Ordered fields",
	"parentcode": "12Jxx",
	"level": 3
}, {
	"code": "12J17",
	"title": " Topological semifields",
	"parentcode": "12Jxx",
	"level": 3
}, {
	"code": "12J20",
	"title": " General valuation theory [See also 13A18]",
	"parentcode": "12Jxx",
	"level": 3
}, {
	"code": "12J25",
	"title": " Non-Archimedean valued fields [See also 30G06, 32P05, 46S10, 47S10]",
	"parentcode": "12Jxx",
	"level": 3
}, {
	"code": "12J27",
	"title": " Krasner-Tate algebras [See mainly 32P05; see also 46S10, 47S10]",
	"parentcode": "12Jxx",
	"level": 3
}, {
	"code": "12J99",
	"title": " None of the above, but in this section",
	"parentcode": "12Jxx",
	"level": 3
}, {
	"code": "12Kxx",
	"title": " Generalizations of fields",
	"parentcode": "12-XX",
	"level": 2
}, {
	"code": "12K05",
	"title": " Near-fields [See also 16Y30]",
	"parentcode": "12Kxx",
	"level": 3
}, {
	"code": "12K10",
	"title": " Semifields [See also 16Y60]",
	"parentcode": "12Kxx",
	"level": 3
}, {
	"code": "12K99",
	"title": " None of the above, but in this section",
	"parentcode": "12Kxx",
	"level": 3
}, {
	"code": "12Lxx",
	"title": " Connections with logic",
	"parentcode": "12-XX",
	"level": 2
}, {
	"code": "12L05",
	"title": " Decidability [See also 03B25]",
	"parentcode": "12Lxx",
	"level": 3
}, {
	"code": "12L10",
	"title": " Ultraproducts [See also 03C20]",
	"parentcode": "12Lxx",
	"level": 3
}, {
	"code": "12L12",
	"title": " Model theory [See also 03C60]",
	"parentcode": "12Lxx",
	"level": 3
}, {
	"code": "12L15",
	"title": " Nonstandard arithmetic [See also 03H15]",
	"parentcode": "12Lxx",
	"level": 3
}, {
	"code": "12L99",
	"title": " None of the above, but in this section",
	"parentcode": "12Lxx",
	"level": 3
}, {
	"code": "12Yxx",
	"title": " Computational aspects of field theory and polynomials",
	"parentcode": "12-XX",
	"level": 2
}, {
	"code": "12Y05",
	"title": " Computational aspects of field theory and polynomials",
	"parentcode": "12Yxx",
	"level": 3
}, {
	"code": "12Y99",
	"title": " None of the above, but in this section",
	"parentcode": "12Yxx",
	"level": 3
}, {
	"code": "13-XX",
	"title": " Commutative algebra",
	"parentcode": null,
	"level": 1
}, {
	"code": "13-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "13-XX",
	"level": 2
}, {
	"code": "13-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "13-XX",
	"level": 2
}, {
	"code": "13-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "13-XX",
	"level": 2
}, {
	"code": "13-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "13-XX",
	"level": 2
}, {
	"code": "13-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "13-XX",
	"level": 2
}, {
	"code": "13-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "13-XX",
	"level": 2
}, {
	"code": "13Axx",
	"title": " General commutative ring theory",
	"parentcode": "13-XX",
	"level": 2
}, {
	"code": "13A02",
	"title": " Graded rings [See also 16W50]",
	"parentcode": "13Axx",
	"level": 3
}, {
	"code": "13A05",
	"title": " Divisibility; factorizations [See also 13F15]",
	"parentcode": "13Axx",
	"level": 3
}, {
	"code": "13A15",
	"title": " Ideals; multiplicative ideal theory",
	"parentcode": "13Axx",
	"level": 3
}, {
	"code": "13A18",
	"title": " Valuations and their generalizations [See also 12J20]",
	"parentcode": "13Axx",
	"level": 3
}, {
	"code": "13A30",
	"title": " Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics",
	"parentcode": "13Axx",
	"level": 3
}, {
	"code": "13A35",
	"title": " Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$; tight closure [See also 13B22]",
	"parentcode": "13Axx",
	"level": 3
}, {
	"code": "13A50",
	"title": " Actions of groups on commutative rings; invariant theory [See also 14L24]",
	"parentcode": "13Axx",
	"level": 3
}, {
	"code": "13A99",
	"title": " None of the above, but in this section",
	"parentcode": "13Axx",
	"level": 3
}, {
	"code": "13Bxx",
	"title": " Ring extensions and related topics",
	"parentcode": "13-XX",
	"level": 2
}, {
	"code": "13B02",
	"title": " Extension theory",
	"parentcode": "13Bxx",
	"level": 3
}, {
	"code": "13B05",
	"title": " Galois theory",
	"parentcode": "13Bxx",
	"level": 3
}, {
	"code": "13B10",
	"title": " Morphisms",
	"parentcode": "13Bxx",
	"level": 3
}, {
	"code": "13B21",
	"title": " Integral dependence; going up, going down",
	"parentcode": "13Bxx",
	"level": 3
}, {
	"code": "13B22",
	"title": " Integral closure of rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.)",
	"parentcode": "13Bxx",
	"level": 3
}, {
	"code": "13B25",
	"title": " Polynomials over commutative rings [See also 11C08, 11T06, 13F20, 13M10]",
	"parentcode": "13Bxx",
	"level": 3
}, {
	"code": "13B30",
	"title": " Rings of fractions and localization [See also 16S85]",
	"parentcode": "13Bxx",
	"level": 3
}, {
	"code": "13B35",
	"title": " Completion [See also 13J10]",
	"parentcode": "13Bxx",
	"level": 3
}, {
	"code": "13B40",
	"title": " Étale and flat extensions; Henselization; Artin approximation [See also 13J15, 14B12, 14B25]",
	"parentcode": "13Bxx",
	"level": 3
}, {
	"code": "13B99",
	"title": " None of the above, but in this section",
	"parentcode": "13Bxx",
	"level": 3
}, {
	"code": "13Cxx",
	"title": " Theory of modules and ideals",
	"parentcode": "13-XX",
	"level": 2
}, {
	"code": "13C05",
	"title": " Structure, classification theorems",
	"parentcode": "13Cxx",
	"level": 3
}, {
	"code": "13C10",
	"title": " Projective and free modules and ideals [See also 19A13]",
	"parentcode": "13Cxx",
	"level": 3
}, {
	"code": "13C11",
	"title": " Injective and flat modules and ideals",
	"parentcode": "13Cxx",
	"level": 3
}, {
	"code": "13C12",
	"title": " Torsion modules and ideals",
	"parentcode": "13Cxx",
	"level": 3
}, {
	"code": "13C13",
	"title": " Other special types",
	"parentcode": "13Cxx",
	"level": 3
}, {
	"code": "13C14",
	"title": " Cohen-Macaulay modules [See also 13H10]",
	"parentcode": "13Cxx",
	"level": 3
}, {
	"code": "13C15",
	"title": " Dimension theory, depth, related rings (catenary, etc.)",
	"parentcode": "13Cxx",
	"level": 3
}, {
	"code": "13C20",
	"title": " Class groups [See also 11R29]",
	"parentcode": "13Cxx",
	"level": 3
}, {
	"code": "13C40",
	"title": " Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12]",
	"parentcode": "13Cxx",
	"level": 3
}, {
	"code": "13C60",
	"title": " Module categories",
	"parentcode": "13Cxx",
	"level": 3
}, {
	"code": "13C99",
	"title": " None of the above, but in this section",
	"parentcode": "13Cxx",
	"level": 3
}, {
	"code": "13Dxx",
	"title": " Homological methods {For noncommutative rings, see 16Exx; for general categories, see 18Gxx}",
	"parentcode": "13-XX",
	"level": 2
}, {
	"code": "13D02",
	"title": " Syzygies,  resolutions, complexes",
	"parentcode": "13Dxx",
	"level": 3
}, {
	"code": "13D03",
	"title": " (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)",
	"parentcode": "13Dxx",
	"level": 3
}, {
	"code": "13D05",
	"title": " Homological dimension",
	"parentcode": "13Dxx",
	"level": 3
}, {
	"code": "13D07",
	"title": " Homological functors on modules (Tor, Ext, etc.)",
	"parentcode": "13Dxx",
	"level": 3
}, {
	"code": "13D09",
	"title": " Derived categories",
	"parentcode": "13Dxx",
	"level": 3
}, {
	"code": "13D10",
	"title": " Deformations and infinitesimal methods [See also 14B10, 14B12, 14D15, 32Gxx]",
	"parentcode": "13Dxx",
	"level": 3
}, {
	"code": "13D15",
	"title": " Grothendieck groups, $K$-theory [See also 14C35, 18F30, 19Axx, 19D50]",
	"parentcode": "13Dxx",
	"level": 3
}, {
	"code": "13D22",
	"title": " Homological conjectures (intersection theorems)",
	"parentcode": "13Dxx",
	"level": 3
}, {
	"code": "13D30",
	"title": " Torsion theory [See also 13C12, 18E40]",
	"parentcode": "13Dxx",
	"level": 3
}, {
	"code": "13D40",
	"title": " Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series",
	"parentcode": "13Dxx",
	"level": 3
}, {
	"code": "13D45",
	"title": " Local cohomology [See also 14B15]",
	"parentcode": "13Dxx",
	"level": 3
}, {
	"code": "13D99",
	"title": " None of the above, but in this section",
	"parentcode": "13Dxx",
	"level": 3
}, {
	"code": "13Exx",
	"title": " Chain conditions, finiteness conditions",
	"parentcode": "13-XX",
	"level": 2
}, {
	"code": "13E05",
	"title": " Noetherian rings and modules",
	"parentcode": "13Exx",
	"level": 3
}, {
	"code": "13E10",
	"title": " Artinian rings and modules, finite-dimensional algebras",
	"parentcode": "13Exx",
	"level": 3
}, {
	"code": "13E15",
	"title": " Rings and modules of finite generation or presentation; number of generators",
	"parentcode": "13Exx",
	"level": 3
}, {
	"code": "13E99",
	"title": " None of the above, but in this section",
	"parentcode": "13Exx",
	"level": 3
}, {
	"code": "13Fxx",
	"title": " Arithmetic rings and other special rings",
	"parentcode": "13-XX",
	"level": 2
}, {
	"code": "13F05",
	"title": " Dedekind, Prüfer, Krull and Mori rings and their generalizations",
	"parentcode": "13Fxx",
	"level": 3
}, {
	"code": "13F07",
	"title": " Euclidean rings and generalizations",
	"parentcode": "13Fxx",
	"level": 3
}, {
	"code": "13F10",
	"title": " Principal ideal rings",
	"parentcode": "13Fxx",
	"level": 3
}, {
	"code": "13F15",
	"title": " Rings defined by factorization properties (e.g., atomic, factorial, half-factorial) [See also 13A05, 14M05]",
	"parentcode": "13Fxx",
	"level": 3
}, {
	"code": "13F20",
	"title": " Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]",
	"parentcode": "13Fxx",
	"level": 3
}, {
	"code": "13F25",
	"title": " Formal power series rings [See also 13J05]",
	"parentcode": "13Fxx",
	"level": 3
}, {
	"code": "13F30",
	"title": " Valuation rings [See also 13A18]",
	"parentcode": "13Fxx",
	"level": 3
}, {
	"code": "13F35",
	"title": " Witt vectors and related rings",
	"parentcode": "13Fxx",
	"level": 3
}, {
	"code": "13F40",
	"title": " Excellent rings",
	"parentcode": "13Fxx",
	"level": 3
}, {
	"code": "13F45",
	"title": " Seminormal rings",
	"parentcode": "13Fxx",
	"level": 3
}, {
	"code": "13F50",
	"title": " Rings with straightening laws, Hodge algebras",
	"parentcode": "13Fxx",
	"level": 3
}, {
	"code": "13F55",
	"title": " Stanley-Reisner face rings; simplicial complexes [See also 55U10]",
	"parentcode": "13Fxx",
	"level": 3
}, {
	"code": "13F60",
	"title": " Cluster algebras",
	"parentcode": "13Fxx",
	"level": 3
}, {
	"code": "13F99",
	"title": " None of the above, but in this section",
	"parentcode": "13Fxx",
	"level": 3
}, {
	"code": "13Gxx",
	"title": " Integral domains",
	"parentcode": "13-XX",
	"level": 2
}, {
	"code": "13G05",
	"title": " Integral domains",
	"parentcode": "13Gxx",
	"level": 3
}, {
	"code": "13G99",
	"title": " None of the above, but in this section",
	"parentcode": "13Gxx",
	"level": 3
}, {
	"code": "13Hxx",
	"title": " Local rings and semilocal rings",
	"parentcode": "13-XX",
	"level": 2
}, {
	"code": "13H05",
	"title": " Regular local rings",
	"parentcode": "13Hxx",
	"level": 3
}, {
	"code": "13H10",
	"title": " Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]",
	"parentcode": "13Hxx",
	"level": 3
}, {
	"code": "13H15",
	"title": " Multiplicity theory and related topics [See also 14C17]",
	"parentcode": "13Hxx",
	"level": 3
}, {
	"code": "13H99",
	"title": " None of the above, but in this section",
	"parentcode": "13Hxx",
	"level": 3
}, {
	"code": "13Jxx",
	"title": " Topological rings and modules [See also 16W60, 16W80]",
	"parentcode": "13-XX",
	"level": 2
}, {
	"code": "13J05",
	"title": " Power series rings [See also 13F25]",
	"parentcode": "13Jxx",
	"level": 3
}, {
	"code": "13J07",
	"title": " Analytical algebras and rings [See also 32B05]",
	"parentcode": "13Jxx",
	"level": 3
}, {
	"code": "13J10",
	"title": " Complete rings, completion [See also 13B35]",
	"parentcode": "13Jxx",
	"level": 3
}, {
	"code": "13J15",
	"title": " Henselian rings [See also 13B40]",
	"parentcode": "13Jxx",
	"level": 3
}, {
	"code": "13J20",
	"title": " Global topological rings",
	"parentcode": "13Jxx",
	"level": 3
}, {
	"code": "13J25",
	"title": " Ordered rings [See also 06F25]",
	"parentcode": "13Jxx",
	"level": 3
}, {
	"code": "13J30",
	"title": " Real algebra [See also 12D15, 14Pxx]",
	"parentcode": "13Jxx",
	"level": 3
}, {
	"code": "13J99",
	"title": " None of the above, but in this section",
	"parentcode": "13Jxx",
	"level": 3
}, {
	"code": "13Lxx",
	"title": " Applications of logic to commutative algebra [See also 03Cxx, 03Hxx]",
	"parentcode": "13-XX",
	"level": 2
}, {
	"code": "13L05",
	"title": " Applications of logic to commutative algebra [See also 03Cxx, 03Hxx]",
	"parentcode": "13Lxx",
	"level": 3
}, {
	"code": "13L99",
	"title": " None of the above, but in this section",
	"parentcode": "13Lxx",
	"level": 3
}, {
	"code": "13Mxx",
	"title": " Finite commutative rings {For number-theoretic aspects, see 11Txx}",
	"parentcode": "13-XX",
	"level": 2
}, {
	"code": "13M05",
	"title": " Structure",
	"parentcode": "13Mxx",
	"level": 3
}, {
	"code": "13M10",
	"title": " Polynomials",
	"parentcode": "13Mxx",
	"level": 3
}, {
	"code": "13M99",
	"title": " None of the above, but in this section",
	"parentcode": "13Mxx",
	"level": 3
}, {
	"code": "13Nxx",
	"title": " Differential algebra [See also 12H05, 14F10]",
	"parentcode": "13-XX",
	"level": 2
}, {
	"code": "13N05",
	"title": " Modules of differentials",
	"parentcode": "13Nxx",
	"level": 3
}, {
	"code": "13N10",
	"title": " Rings of differential operators and their modules [See also 16S32, 32C38]",
	"parentcode": "13Nxx",
	"level": 3
}, {
	"code": "13N15",
	"title": " Derivations",
	"parentcode": "13Nxx",
	"level": 3
}, {
	"code": "13N99",
	"title": " None of the above, but in this section",
	"parentcode": "13Nxx",
	"level": 3
}, {
	"code": "13Pxx",
	"title": " Computational aspects and applications [See also 14Qxx, 68W30]",
	"parentcode": "13-XX",
	"level": 2
}, {
	"code": "13P05",
	"title": " Polynomials, factorization [See also 12Y05]",
	"parentcode": "13Pxx",
	"level": 3
}, {
	"code": "13P10",
	"title": " Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)",
	"parentcode": "13Pxx",
	"level": 3
}, {
	"code": "13P15",
	"title": " Solving polynomial systems; resultants",
	"parentcode": "13Pxx",
	"level": 3
}, {
	"code": "13P20",
	"title": " Computational homological algebra [See also  13Dxx]",
	"parentcode": "13Pxx",
	"level": 3
}, {
	"code": "13P25",
	"title": " Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)",
	"parentcode": "13Pxx",
	"level": 3
}, {
	"code": "13P99",
	"title": " None of the above, but in this section",
	"parentcode": "13Pxx",
	"level": 3
}, {
	"code": "14-XX",
	"title": " Algebraic geometry",
	"parentcode": null,
	"level": 1
}, {
	"code": "14-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14Axx",
	"title": " Foundations",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14A05",
	"title": " Relevant commutative algebra [See also 13-XX]",
	"parentcode": "14Axx",
	"level": 3
}, {
	"code": "14A10",
	"title": " Varieties and morphisms",
	"parentcode": "14Axx",
	"level": 3
}, {
	"code": "14A15",
	"title": " Schemes and morphisms",
	"parentcode": "14Axx",
	"level": 3
}, {
	"code": "14A20",
	"title": " Generalizations (algebraic spaces, stacks)",
	"parentcode": "14Axx",
	"level": 3
}, {
	"code": "14A22",
	"title": " Noncommutative algebraic geometry [See also 16S38]",
	"parentcode": "14Axx",
	"level": 3
}, {
	"code": "14A25",
	"title": " Elementary questions",
	"parentcode": "14Axx",
	"level": 3
}, {
	"code": "14A99",
	"title": " None of the above, but in this section",
	"parentcode": "14Axx",
	"level": 3
}, {
	"code": "14Bxx",
	"title": " Local theory",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14B05",
	"title": " Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]",
	"parentcode": "14Bxx",
	"level": 3
}, {
	"code": "14B07",
	"title": " Deformations of singularities [See also 14D15, 32S30]",
	"parentcode": "14Bxx",
	"level": 3
}, {
	"code": "14B10",
	"title": " Infinitesimal methods [See also 13D10]",
	"parentcode": "14Bxx",
	"level": 3
}, {
	"code": "14B12",
	"title": " Local deformation theory, Artin approximation, etc. [See also 13B40, 13D10]",
	"parentcode": "14Bxx",
	"level": 3
}, {
	"code": "14B15",
	"title": " Local cohomology [See also 13D45, 32C36]",
	"parentcode": "14Bxx",
	"level": 3
}, {
	"code": "14B20",
	"title": " Formal neighborhoods",
	"parentcode": "14Bxx",
	"level": 3
}, {
	"code": "14B25",
	"title": " Local structure of morphisms",
	"parentcode": "14Bxx",
	"level": 3
}, {
	"code": "14B99",
	"title": " None of the above, but in this section",
	"parentcode": "14Bxx",
	"level": 3
}, {
	"code": "14Cxx",
	"title": " Cycles and subschemes",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14C05",
	"title": " Parametrization (Chow and Hilbert schemes)",
	"parentcode": "14Cxx",
	"level": 3
}, {
	"code": "14C15",
	"title": " (Equivariant) Chow groups and rings; motives",
	"parentcode": "14Cxx",
	"level": 3
}, {
	"code": "14C17",
	"title": " Intersection theory, characteristic classes, intersection multiplicities [See also 13H15]",
	"parentcode": "14Cxx",
	"level": 3
}, {
	"code": "14C20",
	"title": " Divisors, linear systems, invertible sheaves",
	"parentcode": "14Cxx",
	"level": 3
}, {
	"code": "14C21",
	"title": " Pencils, nets, webs [See also 53A60]",
	"parentcode": "14Cxx",
	"level": 3
}, {
	"code": "14C22",
	"title": " Picard groups",
	"parentcode": "14Cxx",
	"level": 3
}, {
	"code": "14C25",
	"title": " Algebraic cycles",
	"parentcode": "14Cxx",
	"level": 3
}, {
	"code": "14C30",
	"title": " Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture",
	"parentcode": "14Cxx",
	"level": 3
}, {
	"code": "14C34",
	"title": " Torelli problem [See also 32G20]",
	"parentcode": "14Cxx",
	"level": 3
}, {
	"code": "14C35",
	"title": " Applications of methods of algebraic $K$-theory [See also 19Exx]",
	"parentcode": "14Cxx",
	"level": 3
}, {
	"code": "14C40",
	"title": " Riemann-Roch theorems [See also 19E20, 19L10]",
	"parentcode": "14Cxx",
	"level": 3
}, {
	"code": "14C99",
	"title": " None of the above, but in this section",
	"parentcode": "14Cxx",
	"level": 3
}, {
	"code": "14Dxx",
	"title": " Families, fibrations",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14D05",
	"title": " Structure of families (Picard-Lefschetz, monodromy, etc.)",
	"parentcode": "14Dxx",
	"level": 3
}, {
	"code": "14D06",
	"title": " Fibrations, degenerations",
	"parentcode": "14Dxx",
	"level": 3
}, {
	"code": "14D07",
	"title": " Variation of Hodge structures [See also 32G20]",
	"parentcode": "14Dxx",
	"level": 3
}, {
	"code": "14D10",
	"title": " Arithmetic ground fields (finite, local, global)",
	"parentcode": "14Dxx",
	"level": 3
}, {
	"code": "14D15",
	"title": " Formal methods; deformations [See also 13D10, 14B07, 32Gxx]",
	"parentcode": "14Dxx",
	"level": 3
}, {
	"code": "14D20",
	"title": " Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}",
	"parentcode": "14Dxx",
	"level": 3
}, {
	"code": "14D21",
	"title": " Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)[See also 32L25,  81Txx]",
	"parentcode": "14Dxx",
	"level": 3
}, {
	"code": "14D22",
	"title": " Fine and coarse moduli spaces",
	"parentcode": "14Dxx",
	"level": 3
}, {
	"code": "14D23",
	"title": " Stacks and moduli problems",
	"parentcode": "14Dxx",
	"level": 3
}, {
	"code": "14D24",
	"title": " Geometric Langlands program",
	"parentcode": "14Dxx",
	"level": 3
}, {
	"code": "14D99",
	"title": " None of the above, but in this section",
	"parentcode": "14Dxx",
	"level": 3
}, {
	"code": "14Exx",
	"title": " Birational geometry",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14E05",
	"title": " Rational and birational maps",
	"parentcode": "14Exx",
	"level": 3
}, {
	"code": "14E07",
	"title": " Birational automorphisms, Cremona group and generalizations",
	"parentcode": "14Exx",
	"level": 3
}, {
	"code": "14E08",
	"title": " Rationality questions [See also 14M20]",
	"parentcode": "14Exx",
	"level": 3
}, {
	"code": "14E15",
	"title": " Global theory and resolution of singularities [See also 14B05, 32S20, 32S45]",
	"parentcode": "14Exx",
	"level": 3
}, {
	"code": "14E16",
	"title": " McKay correspondence",
	"parentcode": "14Exx",
	"level": 3
}, {
	"code": "14E18",
	"title": " Arcs and motivic integration",
	"parentcode": "14Exx",
	"level": 3
}, {
	"code": "14E20",
	"title": " Coverings [See also 14H30]",
	"parentcode": "14Exx",
	"level": 3
}, {
	"code": "14E22",
	"title": " Ramification problems [See also 11S15]",
	"parentcode": "14Exx",
	"level": 3
}, {
	"code": "14E25",
	"title": " Embeddings",
	"parentcode": "14Exx",
	"level": 3
}, {
	"code": "14E30",
	"title": " Minimal model program (Mori theory, extremal rays)",
	"parentcode": "14Exx",
	"level": 3
}, {
	"code": "14E99",
	"title": " None of the above, but in this section",
	"parentcode": "14Exx",
	"level": 3
}, {
	"code": "14Fxx",
	"title": " (Co)homology theory [See also 13Dxx]",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14F05",
	"title": " Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]",
	"parentcode": "14Fxx",
	"level": 3
}, {
	"code": "14F10",
	"title": " Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials [See also 13Nxx, 32C38]",
	"parentcode": "14Fxx",
	"level": 3
}, {
	"code": "14F17",
	"title": " Vanishing theorems [See also 32L20]",
	"parentcode": "14Fxx",
	"level": 3
}, {
	"code": "14F18",
	"title": " Multiplier ideals",
	"parentcode": "14Fxx",
	"level": 3
}, {
	"code": "14F20",
	"title": " Étale and other Grothendieck topologies and (co)homologies",
	"parentcode": "14Fxx",
	"level": 3
}, {
	"code": "14F22",
	"title": " Brauer groups of schemes [See also 12G05, 16K50]",
	"parentcode": "14Fxx",
	"level": 3
}, {
	"code": "14F25",
	"title": " Classical real and complex (co)homology",
	"parentcode": "14Fxx",
	"level": 3
}, {
	"code": "14F30",
	"title": " $p$-adic cohomology, crystalline cohomology",
	"parentcode": "14Fxx",
	"level": 3
}, {
	"code": "14F35",
	"title": " Homotopy theory; fundamental groups [See also 14H30]",
	"parentcode": "14Fxx",
	"level": 3
}, {
	"code": "14F40",
	"title": " de Rham cohomology [See also 14C30, 32C35, 32L10]",
	"parentcode": "14Fxx",
	"level": 3
}, {
	"code": "14F42",
	"title": " Motivic cohomology; motivic homotopy theory  [See also 19E15]",
	"parentcode": "14Fxx",
	"level": 3
}, {
	"code": "14F43",
	"title": " Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)",
	"parentcode": "14Fxx",
	"level": 3
}, {
	"code": "14F45",
	"title": " Topological properties",
	"parentcode": "14Fxx",
	"level": 3
}, {
	"code": "14F99",
	"title": " None of the above, but in this section",
	"parentcode": "14Fxx",
	"level": 3
}, {
	"code": "14Gxx",
	"title": " Arithmetic problems. Diophantine geometry [See also 11Dxx, 11Gxx]",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14G05",
	"title": " Rational points",
	"parentcode": "14Gxx",
	"level": 3
}, {
	"code": "14G10",
	"title": " Zeta-functions and related questions [See also 11G40] (Birch-Swinnerton-Dyer conjecture)",
	"parentcode": "14Gxx",
	"level": 3
}, {
	"code": "14G15",
	"title": " Finite ground fields",
	"parentcode": "14Gxx",
	"level": 3
}, {
	"code": "14G17",
	"title": " Positive characteristic ground fields",
	"parentcode": "14Gxx",
	"level": 3
}, {
	"code": "14G20",
	"title": " Local ground fields",
	"parentcode": "14Gxx",
	"level": 3
}, {
	"code": "14G22",
	"title": " Rigid analytic geometry",
	"parentcode": "14Gxx",
	"level": 3
}, {
	"code": "14G25",
	"title": " Global ground fields",
	"parentcode": "14Gxx",
	"level": 3
}, {
	"code": "14G27",
	"title": " Other nonalgebraically closed ground fields",
	"parentcode": "14Gxx",
	"level": 3
}, {
	"code": "14G32",
	"title": " Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)",
	"parentcode": "14Gxx",
	"level": 3
}, {
	"code": "14G35",
	"title": " Modular and Shimura varieties [See also 11F41, 11F46, 11G18]",
	"parentcode": "14Gxx",
	"level": 3
}, {
	"code": "14G40",
	"title": " Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30]",
	"parentcode": "14Gxx",
	"level": 3
}, {
	"code": "14G50",
	"title": " Applications to coding theory and cryptography [See also 94A60, 94B27, 94B40]",
	"parentcode": "14Gxx",
	"level": 3
}, {
	"code": "14G99",
	"title": " None of the above, but in this section",
	"parentcode": "14Gxx",
	"level": 3
}, {
	"code": "14Hxx",
	"title": " Curves",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14H05",
	"title": " Algebraic functions; function fields [See also 11R58]",
	"parentcode": "14Hxx",
	"level": 3
}, {
	"code": "14H10",
	"title": " Families, moduli (algebraic)",
	"parentcode": "14Hxx",
	"level": 3
}, {
	"code": "14H15",
	"title": " Families, moduli (analytic) [See also 30F10, 32G15]",
	"parentcode": "14Hxx",
	"level": 3
}, {
	"code": "14H20",
	"title": " Singularities, local rings [See also 13Hxx, 14B05]",
	"parentcode": "14Hxx",
	"level": 3
}, {
	"code": "14H25",
	"title": " Arithmetic ground fields [See also 11Dxx, 11G05, 14Gxx]",
	"parentcode": "14Hxx",
	"level": 3
}, {
	"code": "14H30",
	"title": " Coverings, fundamental group [See also 14E20, 14F35]",
	"parentcode": "14Hxx",
	"level": 3
}, {
	"code": "14H37",
	"title": " Automorphisms",
	"parentcode": "14Hxx",
	"level": 3
}, {
	"code": "14H40",
	"title": " Jacobians, Prym varieties [See also 32G20]",
	"parentcode": "14Hxx",
	"level": 3
}, {
	"code": "14H42",
	"title": " Theta functions; Schottky problem [See also 14K25, 32G20]",
	"parentcode": "14Hxx",
	"level": 3
}, {
	"code": "14H45",
	"title": " Special curves and curves of low genus",
	"parentcode": "14Hxx",
	"level": 3
}, {
	"code": "14H50",
	"title": " Plane and space curves",
	"parentcode": "14Hxx",
	"level": 3
}, {
	"code": "14H51",
	"title": " Special divisors (gonality, Brill-Noether theory)",
	"parentcode": "14Hxx",
	"level": 3
}, {
	"code": "14H52",
	"title": " Elliptic curves [See also 11G05, 11G07, 14Kxx]",
	"parentcode": "14Hxx",
	"level": 3
}, {
	"code": "14H55",
	"title": " Riemann surfaces;  Weierstrass points; gap sequences [See also 30Fxx]",
	"parentcode": "14Hxx",
	"level": 3
}, {
	"code": "14H57",
	"title": " Dessins d'enfants theory {For arithmetic aspects, see 11G32}",
	"parentcode": "14Hxx",
	"level": 3
}, {
	"code": "14H60",
	"title": " Vector bundles on curves and their moduli [See also 14D20, 14F05]",
	"parentcode": "14Hxx",
	"level": 3
}, {
	"code": "14H70",
	"title": " Relationships with integrable systems",
	"parentcode": "14Hxx",
	"level": 3
}, {
	"code": "14H81",
	"title": " Relationships with physics",
	"parentcode": "14Hxx",
	"level": 3
}, {
	"code": "14H99",
	"title": " None of the above, but in this section",
	"parentcode": "14Hxx",
	"level": 3
}, {
	"code": "14Jxx",
	"title": " Surfaces and higher-dimensional varieties {For analytic theory, see 32Jxx}",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14J10",
	"title": " Families, moduli, classification",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14J15",
	"title": " Moduli, classification",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14J17",
	"title": " Singularities [See also 14B05, 14E15]",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14J20",
	"title": " Arithmetic ground fields [See also 11Dxx, 11G25, 11G35, 14Gxx]",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14J25",
	"title": " Special surfaces {For Hilbert modular surfaces, see 14G35}",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14J26",
	"title": " Rational and ruled surfaces",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14J27",
	"title": " Elliptic surfaces",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14J28",
	"title": " $K3$ surfaces and Enriques surfaces",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14J29",
	"title": " Surfaces of general type",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14J30",
	"title": " $3$-folds [See also 32Q25]",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14J32",
	"title": " Calabi-Yau manifolds",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14J33",
	"title": " Mirror symmetry [See also 11G42, 53D37]",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14J35",
	"title": " $4$-folds",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14J40",
	"title": " $n$-folds ($n>4$)",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14J45",
	"title": " Fano varieties",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14J50",
	"title": " Automorphisms of surfaces and higher-dimensional varieties",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14J60",
	"title": " Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14J70",
	"title": " Hypersurfaces",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14J80",
	"title": " Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14J81",
	"title": " Relationships with physics",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14J99",
	"title": " None of the above, but in this section",
	"parentcode": "14Jxx",
	"level": 3
}, {
	"code": "14Kxx",
	"title": " Abelian varieties and schemes",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14K02",
	"title": " Isogeny",
	"parentcode": "14Kxx",
	"level": 3
}, {
	"code": "14K05",
	"title": " Algebraic theory",
	"parentcode": "14Kxx",
	"level": 3
}, {
	"code": "14K10",
	"title": " Algebraic moduli, classification [See also 11G15]",
	"parentcode": "14Kxx",
	"level": 3
}, {
	"code": "14K12",
	"title": " Subvarieties",
	"parentcode": "14Kxx",
	"level": 3
}, {
	"code": "14K15",
	"title": " Arithmetic ground fields [See also 11Dxx, 11Fxx, 11G10, 14Gxx]",
	"parentcode": "14Kxx",
	"level": 3
}, {
	"code": "14K20",
	"title": " Analytic theory; abelian integrals and differentials",
	"parentcode": "14Kxx",
	"level": 3
}, {
	"code": "14K22",
	"title": " Complex multiplication [See also 11G15]",
	"parentcode": "14Kxx",
	"level": 3
}, {
	"code": "14K25",
	"title": " Theta functions [See also 14H42]",
	"parentcode": "14Kxx",
	"level": 3
}, {
	"code": "14K30",
	"title": " Picard schemes, higher Jacobians [See also 14H40, 32G20]",
	"parentcode": "14Kxx",
	"level": 3
}, {
	"code": "14K99",
	"title": " None of the above, but in this section",
	"parentcode": "14Kxx",
	"level": 3
}, {
	"code": "14Lxx",
	"title": " Algebraic groups {For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45}",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14L05",
	"title": " Formal groups, $p$-divisible groups [See also 55N22]",
	"parentcode": "14Lxx",
	"level": 3
}, {
	"code": "14L10",
	"title": " Group varieties",
	"parentcode": "14Lxx",
	"level": 3
}, {
	"code": "14L15",
	"title": " Group schemes",
	"parentcode": "14Lxx",
	"level": 3
}, {
	"code": "14L17",
	"title": " Affine algebraic groups, hyperalgebra constructions [See also 17B45, 18D35]",
	"parentcode": "14Lxx",
	"level": 3
}, {
	"code": "14L24",
	"title": " Geometric invariant theory [See also 13A50]",
	"parentcode": "14Lxx",
	"level": 3
}, {
	"code": "14L30",
	"title": " Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]",
	"parentcode": "14Lxx",
	"level": 3
}, {
	"code": "14L35",
	"title": " Classical groups (geometric aspects) [See also 20Gxx, 51N30]",
	"parentcode": "14Lxx",
	"level": 3
}, {
	"code": "14L40",
	"title": " Other algebraic groups (geometric aspects)",
	"parentcode": "14Lxx",
	"level": 3
}, {
	"code": "14L99",
	"title": " None of the above, but in this section",
	"parentcode": "14Lxx",
	"level": 3
}, {
	"code": "14Mxx",
	"title": " Special varieties",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14M05",
	"title": " Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F15, 13F45, 13H10]",
	"parentcode": "14Mxx",
	"level": 3
}, {
	"code": "14M06",
	"title": " Linkage [See also 13C40]",
	"parentcode": "14Mxx",
	"level": 3
}, {
	"code": "14M07",
	"title": " Low codimension problems",
	"parentcode": "14Mxx",
	"level": 3
}, {
	"code": "14M10",
	"title": " Complete intersections [See also 13C40]",
	"parentcode": "14Mxx",
	"level": 3
}, {
	"code": "14M12",
	"title": " Determinantal varieties [See also 13C40]",
	"parentcode": "14Mxx",
	"level": 3
}, {
	"code": "14M15",
	"title": " Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]",
	"parentcode": "14Mxx",
	"level": 3
}, {
	"code": "14M17",
	"title": " Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]",
	"parentcode": "14Mxx",
	"level": 3
}, {
	"code": "14M20",
	"title": " Rational and unirational varieties [See also 14E08]",
	"parentcode": "14Mxx",
	"level": 3
}, {
	"code": "14M22",
	"title": " Rationally connected varieties",
	"parentcode": "14Mxx",
	"level": 3
}, {
	"code": "14M25",
	"title": " Toric varieties, Newton polyhedra [See also 52B20]",
	"parentcode": "14Mxx",
	"level": 3
}, {
	"code": "14M27",
	"title": " Compactifications; symmetric and spherical varieties",
	"parentcode": "14Mxx",
	"level": 3
}, {
	"code": "14M30",
	"title": " Supervarieties [See also 32C11, 58A50]",
	"parentcode": "14Mxx",
	"level": 3
}, {
	"code": "14M99",
	"title": " None of the above, but in this section",
	"parentcode": "14Mxx",
	"level": 3
}, {
	"code": "14Nxx",
	"title": " Projective and enumerative geometry [See also 51-XX]",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14N05",
	"title": " Projective techniques [See also 51N35]",
	"parentcode": "14Nxx",
	"level": 3
}, {
	"code": "14N10",
	"title": " Enumerative problems (combinatorial problems)",
	"parentcode": "14Nxx",
	"level": 3
}, {
	"code": "14N15",
	"title": " Classical problems, Schubert calculus",
	"parentcode": "14Nxx",
	"level": 3
}, {
	"code": "14N20",
	"title": " Configurations and arrangements of linear subspaces",
	"parentcode": "14Nxx",
	"level": 3
}, {
	"code": "14N25",
	"title": " Varieties of low degree",
	"parentcode": "14Nxx",
	"level": 3
}, {
	"code": "14N30",
	"title": " Adjunction problems",
	"parentcode": "14Nxx",
	"level": 3
}, {
	"code": "14N35",
	"title": " Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]",
	"parentcode": "14Nxx",
	"level": 3
}, {
	"code": "14N99",
	"title": " None of the above, but in this section",
	"parentcode": "14Nxx",
	"level": 3
}, {
	"code": "14Pxx",
	"title": " Real algebraic and real analytic geometry",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14P05",
	"title": " Real algebraic sets [See also 12D15, 13J30]",
	"parentcode": "14Pxx",
	"level": 3
}, {
	"code": "14P10",
	"title": " Semialgebraic sets and related spaces",
	"parentcode": "14Pxx",
	"level": 3
}, {
	"code": "14P15",
	"title": " Real analytic and semianalytic sets [See also 32B20, 32C05]",
	"parentcode": "14Pxx",
	"level": 3
}, {
	"code": "14P20",
	"title": " Nash functions and manifolds [See also 32C07, 58A07]",
	"parentcode": "14Pxx",
	"level": 3
}, {
	"code": "14P25",
	"title": " Topology of real algebraic varieties",
	"parentcode": "14Pxx",
	"level": 3
}, {
	"code": "14P99",
	"title": " None of the above, but in this section",
	"parentcode": "14Pxx",
	"level": 3
}, {
	"code": "14Qxx",
	"title": " Computational aspects in algebraic geometry [See also 12Y05, 13Pxx, 68W30]",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14Q05",
	"title": " Curves",
	"parentcode": "14Qxx",
	"level": 3
}, {
	"code": "14Q10",
	"title": " Surfaces, hypersurfaces",
	"parentcode": "14Qxx",
	"level": 3
}, {
	"code": "14Q15",
	"title": " Higher-dimensional varieties",
	"parentcode": "14Qxx",
	"level": 3
}, {
	"code": "14Q20",
	"title": " Effectivity, complexity",
	"parentcode": "14Qxx",
	"level": 3
}, {
	"code": "14Q99",
	"title": " None of the above, but in this section",
	"parentcode": "14Qxx",
	"level": 3
}, {
	"code": "14Rxx",
	"title": " Affine geometry",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14R05",
	"title": " Classification of affine varieties",
	"parentcode": "14Rxx",
	"level": 3
}, {
	"code": "14R10",
	"title": " Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)",
	"parentcode": "14Rxx",
	"level": 3
}, {
	"code": "14R15",
	"title": " Jacobian problem [See also 13F20]",
	"parentcode": "14Rxx",
	"level": 3
}, {
	"code": "14R20",
	"title": " Group actions on affine varieties [See also 13A50, 14L30]",
	"parentcode": "14Rxx",
	"level": 3
}, {
	"code": "14R25",
	"title": " Affine fibrations [See also 14D06]",
	"parentcode": "14Rxx",
	"level": 3
}, {
	"code": "14R99",
	"title": " None of the above, but in this section",
	"parentcode": "14Rxx",
	"level": 3
}, {
	"code": "14Txx",
	"title": " Tropical geometry [See also 12K10, 14M25, 14N10, 52B20]",
	"parentcode": "14-XX",
	"level": 2
}, {
	"code": "14T05",
	"title": " Tropical geometry [See also 12K10, 14M25, 14N10, 52B20]",
	"parentcode": "14Txx",
	"level": 3
}, {
	"code": "14T99",
	"title": " None of the above, but in this section",
	"parentcode": "14Txx",
	"level": 3
}, {
	"code": "15-XX",
	"title": " Linear and multilinear algebra; matrix theory",
	"parentcode": null,
	"level": 1
}, {
	"code": "15-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "15-XX",
	"level": 2
}, {
	"code": "15-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "15-XX",
	"level": 2
}, {
	"code": "15-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "15-XX",
	"level": 2
}, {
	"code": "15-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "15-XX",
	"level": 2
}, {
	"code": "15-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "15-XX",
	"level": 2
}, {
	"code": "15-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "15-XX",
	"level": 2
}, {
	"code": "15Axx",
	"title": " Basic linear algebra",
	"parentcode": "15-XX",
	"level": 2
}, {
	"code": "15A03",
	"title": " Vector spaces, linear dependence, rank",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A04",
	"title": " Linear transformations, semilinear transformations",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A06",
	"title": " Linear equations",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A09",
	"title": " Matrix inversion, generalized inverses",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A12",
	"title": " Conditioning of matrices [See also 65F35]",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A15",
	"title": " Determinants, permanents, other special matrix functions [See also 19B10, 19B14]",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A16",
	"title": " Matrix exponential and similar functions of matrices",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A18",
	"title": " Eigenvalues, singular values, and eigenvectors",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A21",
	"title": " Canonical forms, reductions, classification",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A22",
	"title": " Matrix pencils [See also 47A56]",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A23",
	"title": " Factorization of matrices",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A24",
	"title": " Matrix equations and identities",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A27",
	"title": " Commutativity",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A29",
	"title": " Inverse problems",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A30",
	"title": " Algebraic systems of matrices [See also 16S50, 20Gxx, 20Hxx]",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A39",
	"title": " Linear inequalities",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A42",
	"title": " Inequalities involving eigenvalues and eigenvectors",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A45",
	"title": " Miscellaneous inequalities involving matrices",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A54",
	"title": " Matrices over function rings in one or more variables",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A60",
	"title": " Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05]",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A63",
	"title": " Quadratic and bilinear forms, inner products [See mainly 11Exx]",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A66",
	"title": " Clifford algebras, spinors",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A69",
	"title": " Multilinear algebra, tensor products",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A72",
	"title": " Vector and tensor algebra, theory of invariants [See also 13A50, 14L24]",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A75",
	"title": " Exterior algebra, Grassmann algebras",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A78",
	"title": " Other algebras built from modules",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A80",
	"title": " Max-plus and related algebras",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A83",
	"title": " Matrix completion problems",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A86",
	"title": " Linear preserver problems",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15A99",
	"title": " Miscellaneous topics",
	"parentcode": "15Axx",
	"level": 3
}, {
	"code": "15Bxx",
	"title": " Special matrices",
	"parentcode": "15-XX",
	"level": 2
}, {
	"code": "15B05",
	"title": " Toeplitz, Cauchy, and related matrices",
	"parentcode": "15Bxx",
	"level": 3
}, {
	"code": "15B10",
	"title": " Orthogonal matrices",
	"parentcode": "15Bxx",
	"level": 3
}, {
	"code": "15B15",
	"title": " Fuzzy matrices",
	"parentcode": "15Bxx",
	"level": 3
}, {
	"code": "15B33",
	"title": " Matrices over special rings (quaternions, finite fields, etc.)",
	"parentcode": "15Bxx",
	"level": 3
}, {
	"code": "15B34",
	"title": " Boolean and Hadamard matrices",
	"parentcode": "15Bxx",
	"level": 3
}, {
	"code": "15B35",
	"title": " Sign pattern matrices",
	"parentcode": "15Bxx",
	"level": 3
}, {
	"code": "15B36",
	"title": " Matrices of integers [See also 11C20]",
	"parentcode": "15Bxx",
	"level": 3
}, {
	"code": "15B48",
	"title": " Positive matrices and their generalizations; cones of matrices",
	"parentcode": "15Bxx",
	"level": 3
}, {
	"code": "15B51",
	"title": " Stochastic matrices",
	"parentcode": "15Bxx",
	"level": 3
}, {
	"code": "15B52",
	"title": " Random matrices",
	"parentcode": "15Bxx",
	"level": 3
}, {
	"code": "15B57",
	"title": " Hermitian, skew-Hermitian, and related matrices",
	"parentcode": "15Bxx",
	"level": 3
}, {
	"code": "15B99",
	"title": " None of the above, but in this section",
	"parentcode": "15Bxx",
	"level": 3
}, {
	"code": "16-XX",
	"title": " Associative rings and algebras {For the commutative case, see 13-XX}",
	"parentcode": null,
	"level": 1
}, {
	"code": "16-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16Bxx",
	"title": " General and miscellaneous",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16B50",
	"title": " Category-theoretic methods and results (except as in 16D90) [See also 18-XX]",
	"parentcode": "16Bxx",
	"level": 3
}, {
	"code": "16B70",
	"title": " Applications of logic [See also 03Cxx]",
	"parentcode": "16Bxx",
	"level": 3
}, {
	"code": "16B99",
	"title": " None of the above, but in this section",
	"parentcode": "16Bxx",
	"level": 3
}, {
	"code": "16Dxx",
	"title": " Modules, bimodules and ideals",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16D10",
	"title": " General module theory",
	"parentcode": "16Dxx",
	"level": 3
}, {
	"code": "16D20",
	"title": " Bimodules",
	"parentcode": "16Dxx",
	"level": 3
}, {
	"code": "16D25",
	"title": " Ideals",
	"parentcode": "16Dxx",
	"level": 3
}, {
	"code": "16D30",
	"title": " Infinite-dimensional simple rings (except as in 16Kxx)",
	"parentcode": "16Dxx",
	"level": 3
}, {
	"code": "16D40",
	"title": " Free, projective, and flat modules and ideals [See also 19A13]",
	"parentcode": "16Dxx",
	"level": 3
}, {
	"code": "16D50",
	"title": " Injective modules, self-injective rings [See also 16L60]",
	"parentcode": "16Dxx",
	"level": 3
}, {
	"code": "16D60",
	"title": " Simple and semisimple modules, primitive rings and ideals",
	"parentcode": "16Dxx",
	"level": 3
}, {
	"code": "16D70",
	"title": " Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation",
	"parentcode": "16Dxx",
	"level": 3
}, {
	"code": "16D80",
	"title": " Other classes of modules and ideals [See also 16G50]",
	"parentcode": "16Dxx",
	"level": 3
}, {
	"code": "16D90",
	"title": " Module categories [See also 16Gxx, 16S90]; module theory in a category-theoretic context; Morita equivalence and duality",
	"parentcode": "16Dxx",
	"level": 3
}, {
	"code": "16D99",
	"title": " None of the above, but in this section",
	"parentcode": "16Dxx",
	"level": 3
}, {
	"code": "16Exx",
	"title": " Homological methods {For commutative rings, see 13Dxx; for general categories, see 18Gxx}",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16E05",
	"title": " Syzygies, resolutions, complexes",
	"parentcode": "16Exx",
	"level": 3
}, {
	"code": "16E10",
	"title": " Homological dimension",
	"parentcode": "16Exx",
	"level": 3
}, {
	"code": "16E20",
	"title": " Grothendieck groups, $K$-theory, etc. [See also 18F30, 19Axx, 19D50]",
	"parentcode": "16Exx",
	"level": 3
}, {
	"code": "16E30",
	"title": " Homological functors on modules (Tor, Ext, etc.)",
	"parentcode": "16Exx",
	"level": 3
}, {
	"code": "16E35",
	"title": " Derived categories",
	"parentcode": "16Exx",
	"level": 3
}, {
	"code": "16E40",
	"title": " (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)",
	"parentcode": "16Exx",
	"level": 3
}, {
	"code": "16E45",
	"title": " Differential graded algebras and applications",
	"parentcode": "16Exx",
	"level": 3
}, {
	"code": "16E50",
	"title": " von Neumann regular rings and generalizations",
	"parentcode": "16Exx",
	"level": 3
}, {
	"code": "16E60",
	"title": " Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.",
	"parentcode": "16Exx",
	"level": 3
}, {
	"code": "16E65",
	"title": " Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)",
	"parentcode": "16Exx",
	"level": 3
}, {
	"code": "16E99",
	"title": " None of the above, but in this section",
	"parentcode": "16Exx",
	"level": 3
}, {
	"code": "16Gxx",
	"title": " Representation theory of rings and algebras",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16G10",
	"title": " Representations of Artinian rings",
	"parentcode": "16Gxx",
	"level": 3
}, {
	"code": "16G20",
	"title": " Representations of quivers and partially ordered sets",
	"parentcode": "16Gxx",
	"level": 3
}, {
	"code": "16G30",
	"title": " Representations of orders, lattices, algebras over commutative rings [See also 16Hxx]",
	"parentcode": "16Gxx",
	"level": 3
}, {
	"code": "16G50",
	"title": " Cohen-Macaulay modules",
	"parentcode": "16Gxx",
	"level": 3
}, {
	"code": "16G60",
	"title": " Representation type (finite, tame, wild, etc.)",
	"parentcode": "16Gxx",
	"level": 3
}, {
	"code": "16G70",
	"title": " Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers",
	"parentcode": "16Gxx",
	"level": 3
}, {
	"code": "16G99",
	"title": " None of the above, but in this section",
	"parentcode": "16Gxx",
	"level": 3
}, {
	"code": "16Hxx",
	"title": " Algebras and orders {For arithmetic aspects, see 11R52, 11R54, 11S45; for representation theory, see 16G30}",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16H05",
	"title": " Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)",
	"parentcode": "16Hxx",
	"level": 3
}, {
	"code": "16H10",
	"title": " Orders in separable algebras",
	"parentcode": "16Hxx",
	"level": 3
}, {
	"code": "16H15",
	"title": " Commutative orders",
	"parentcode": "16Hxx",
	"level": 3
}, {
	"code": "16H20",
	"title": " Lattices over orders",
	"parentcode": "16Hxx",
	"level": 3
}, {
	"code": "16H99",
	"title": " None of the above, but in this section",
	"parentcode": "16Hxx",
	"level": 3
}, {
	"code": "16Kxx",
	"title": " Division rings and semisimple Artin rings [See also 12E15, 15A30]",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16K20",
	"title": " Finite-dimensional {For crossed products, see 16S35}",
	"parentcode": "16Kxx",
	"level": 3
}, {
	"code": "16K40",
	"title": " Infinite-dimensional and general",
	"parentcode": "16Kxx",
	"level": 3
}, {
	"code": "16K50",
	"title": " Brauer groups [See also 12G05, 14F22]",
	"parentcode": "16Kxx",
	"level": 3
}, {
	"code": "16K99",
	"title": " None of the above, but in this section",
	"parentcode": "16Kxx",
	"level": 3
}, {
	"code": "16Lxx",
	"title": " Local rings and generalizations",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16L30",
	"title": " Noncommutative local and semilocal rings, perfect rings",
	"parentcode": "16Lxx",
	"level": 3
}, {
	"code": "16L60",
	"title": " Quasi-Frobenius rings [See also 16D50]",
	"parentcode": "16Lxx",
	"level": 3
}, {
	"code": "16L99",
	"title": " None of the above, but in this section",
	"parentcode": "16Lxx",
	"level": 3
}, {
	"code": "16Nxx",
	"title": " Radicals and radical properties of rings",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16N20",
	"title": " Jacobson radical, quasimultiplication",
	"parentcode": "16Nxx",
	"level": 3
}, {
	"code": "16N40",
	"title": " Nil and nilpotent radicals, sets, ideals, rings",
	"parentcode": "16Nxx",
	"level": 3
}, {
	"code": "16N60",
	"title": " Prime and semiprime rings [See also 16D60, 16U10]",
	"parentcode": "16Nxx",
	"level": 3
}, {
	"code": "16N80",
	"title": " General radicals and rings {For radicals in module categories, see 16S90}",
	"parentcode": "16Nxx",
	"level": 3
}, {
	"code": "16N99",
	"title": " None of the above, but in this section",
	"parentcode": "16Nxx",
	"level": 3
}, {
	"code": "16Pxx",
	"title": " Chain conditions, growth conditions, and other forms of finiteness",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16P10",
	"title": " Finite rings and finite-dimensional algebras {For semisimple, see 16K20; for commutative, see 11Txx, 13Mxx}",
	"parentcode": "16Pxx",
	"level": 3
}, {
	"code": "16P20",
	"title": " Artinian rings and modules",
	"parentcode": "16Pxx",
	"level": 3
}, {
	"code": "16P40",
	"title": " Noetherian rings and modules",
	"parentcode": "16Pxx",
	"level": 3
}, {
	"code": "16P50",
	"title": " Localization and Noetherian rings [See also 16U20]",
	"parentcode": "16Pxx",
	"level": 3
}, {
	"code": "16P60",
	"title": " Chain conditions on annihilators and summands",
	"parentcode": "16Pxx",
	"level": 3
}, {
	"code": "16P70",
	"title": " Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence",
	"parentcode": "16Pxx",
	"level": 3
}, {
	"code": "16P90",
	"title": " Growth rate, Gelfand-Kirillov dimension",
	"parentcode": "16Pxx",
	"level": 3
}, {
	"code": "16P99",
	"title": " None of the above, but in this section",
	"parentcode": "16Pxx",
	"level": 3
}, {
	"code": "16Rxx",
	"title": " Rings with polynomial identity",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16R10",
	"title": " $T$-ideals, identities, varieties of rings and algebras",
	"parentcode": "16Rxx",
	"level": 3
}, {
	"code": "16R20",
	"title": " Semiprime p.i. rings, rings embeddable in matrices over commutative rings",
	"parentcode": "16Rxx",
	"level": 3
}, {
	"code": "16R30",
	"title": " Trace rings and invariant theory",
	"parentcode": "16Rxx",
	"level": 3
}, {
	"code": "16R40",
	"title": " Identities other than those of matrices over commutative rings",
	"parentcode": "16Rxx",
	"level": 3
}, {
	"code": "16R50",
	"title": " Other kinds of identities (generalized polynomial, rational, involution)",
	"parentcode": "16Rxx",
	"level": 3
}, {
	"code": "16R60",
	"title": " Functional identities",
	"parentcode": "16Rxx",
	"level": 3
}, {
	"code": "16R99",
	"title": " None of the above, but in this section",
	"parentcode": "16Rxx",
	"level": 3
}, {
	"code": "16Sxx",
	"title": " Rings and algebras arising under various constructions",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16S10",
	"title": " Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)",
	"parentcode": "16Sxx",
	"level": 3
}, {
	"code": "16S15",
	"title": " Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)",
	"parentcode": "16Sxx",
	"level": 3
}, {
	"code": "16S20",
	"title": " Centralizing and normalizing extensions",
	"parentcode": "16Sxx",
	"level": 3
}, {
	"code": "16S30",
	"title": " Universal enveloping algebras of Lie algebras [See mainly 17B35]",
	"parentcode": "16Sxx",
	"level": 3
}, {
	"code": "16S32",
	"title": " Rings of differential operators [See also 13N10, 32C38]",
	"parentcode": "16Sxx",
	"level": 3
}, {
	"code": "16S34",
	"title": " Group rings [See also 20C05, 20C07], Laurent polynomial rings",
	"parentcode": "16Sxx",
	"level": 3
}, {
	"code": "16S35",
	"title": " Twisted and skew group rings, crossed products",
	"parentcode": "16Sxx",
	"level": 3
}, {
	"code": "16S36",
	"title": " Ordinary and skew polynomial rings and semigroup rings [See also 20M25]",
	"parentcode": "16Sxx",
	"level": 3
}, {
	"code": "16S37",
	"title": " Quadratic and Koszul algebras",
	"parentcode": "16Sxx",
	"level": 3
}, {
	"code": "16S38",
	"title": " Rings arising from non-commutative algebraic geometry [See also 14A22]",
	"parentcode": "16Sxx",
	"level": 3
}, {
	"code": "16S40",
	"title": " Smash products of general Hopf actions [See also 16T05]",
	"parentcode": "16Sxx",
	"level": 3
}, {
	"code": "16S50",
	"title": " Endomorphism rings; matrix rings [See also 15-XX]",
	"parentcode": "16Sxx",
	"level": 3
}, {
	"code": "16S60",
	"title": " Rings of functions, subdirect products, sheaves of rings",
	"parentcode": "16Sxx",
	"level": 3
}, {
	"code": "16S70",
	"title": " Extensions of rings by ideals",
	"parentcode": "16Sxx",
	"level": 3
}, {
	"code": "16S80",
	"title": " Deformations of rings [See also 13D10, 14D15]",
	"parentcode": "16Sxx",
	"level": 3
}, {
	"code": "16S85",
	"title": " Rings of fractions and localizations [See also 13B30]",
	"parentcode": "16Sxx",
	"level": 3
}, {
	"code": "16S90",
	"title": " Torsion theories; radicals on module categories [See also 13D30, 18E40] {For radicals of rings, see 16Nxx}",
	"parentcode": "16Sxx",
	"level": 3
}, {
	"code": "16S99",
	"title": " None of the above, but in this section",
	"parentcode": "16Sxx",
	"level": 3
}, {
	"code": "16Txx",
	"title": " Hopf algebras, quantum groups and related topics",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16T05",
	"title": " Hopf algebras and their applications [See also 16S40, 57T05]",
	"parentcode": "16Txx",
	"level": 3
}, {
	"code": "16T10",
	"title": " Bialgebras",
	"parentcode": "16Txx",
	"level": 3
}, {
	"code": "16T15",
	"title": " Coalgebras and comodules; corings",
	"parentcode": "16Txx",
	"level": 3
}, {
	"code": "16T20",
	"title": " Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50]",
	"parentcode": "16Txx",
	"level": 3
}, {
	"code": "16T25",
	"title": " Yang-Baxter equations",
	"parentcode": "16Txx",
	"level": 3
}, {
	"code": "16T30",
	"title": " Connections with combinatorics",
	"parentcode": "16Txx",
	"level": 3
}, {
	"code": "16T99",
	"title": " None of the above, but in this section",
	"parentcode": "16Txx",
	"level": 3
}, {
	"code": "16Uxx",
	"title": " Conditions on elements",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16U10",
	"title": " Integral domains",
	"parentcode": "16Uxx",
	"level": 3
}, {
	"code": "16U20",
	"title": " Ore rings, multiplicative sets, Ore localization",
	"parentcode": "16Uxx",
	"level": 3
}, {
	"code": "16U30",
	"title": " Divisibility, noncommutative UFDs",
	"parentcode": "16Uxx",
	"level": 3
}, {
	"code": "16U60",
	"title": " Units, groups of units",
	"parentcode": "16Uxx",
	"level": 3
}, {
	"code": "16U70",
	"title": " Center, normalizer (invariant elements)",
	"parentcode": "16Uxx",
	"level": 3
}, {
	"code": "16U80",
	"title": " Generalizations of commutativity",
	"parentcode": "16Uxx",
	"level": 3
}, {
	"code": "16U99",
	"title": " None of the above, but in this section",
	"parentcode": "16Uxx",
	"level": 3
}, {
	"code": "16Wxx",
	"title": " Rings and algebras with additional structure",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16W10",
	"title": " Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx]",
	"parentcode": "16Wxx",
	"level": 3
}, {
	"code": "16W20",
	"title": " Automorphisms and endomorphisms",
	"parentcode": "16Wxx",
	"level": 3
}, {
	"code": "16W22",
	"title": " Actions of groups and semigroups; invariant theory",
	"parentcode": "16Wxx",
	"level": 3
}, {
	"code": "16W25",
	"title": " Derivations, actions of Lie algebras",
	"parentcode": "16Wxx",
	"level": 3
}, {
	"code": "16W50",
	"title": " Graded rings and modules",
	"parentcode": "16Wxx",
	"level": 3
}, {
	"code": "16W55",
	"title": " “Super” (or “skew”) structure [See also 17A70, 17Bxx, 17C70] {For exterior algebras, see 15A75; for Clifford algebras, see 11E88, 15A66}",
	"parentcode": "16Wxx",
	"level": 3
}, {
	"code": "16W60",
	"title": " Valuations, completions, formal power series and related constructions [See also 13Jxx]",
	"parentcode": "16Wxx",
	"level": 3
}, {
	"code": "16W70",
	"title": " Filtered rings; filtrational and graded techniques",
	"parentcode": "16Wxx",
	"level": 3
}, {
	"code": "16W80",
	"title": " Topological and ordered rings and modules [See also 06F25, 13Jxx]",
	"parentcode": "16Wxx",
	"level": 3
}, {
	"code": "16W99",
	"title": " None of the above, but in this section",
	"parentcode": "16Wxx",
	"level": 3
}, {
	"code": "16Yxx",
	"title": " Generalizations {For nonassociative rings, see 17-XX}",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16Y30",
	"title": " Near-rings [See also 12K05]",
	"parentcode": "16Yxx",
	"level": 3
}, {
	"code": "16Y60",
	"title": " Semirings [See also 12K10]",
	"parentcode": "16Yxx",
	"level": 3
}, {
	"code": "16Y99",
	"title": " None of the above, but in this section",
	"parentcode": "16Yxx",
	"level": 3
}, {
	"code": "16Zxx",
	"title": " Computational aspects of associative rings",
	"parentcode": "16-XX",
	"level": 2
}, {
	"code": "16Z05",
	"title": " Computational aspects of associative rings [See also 68W30]",
	"parentcode": "16Zxx",
	"level": 3
}, {
	"code": "16Z99",
	"title": " None of the above, but in this section",
	"parentcode": "16Zxx",
	"level": 3
}, {
	"code": "17-XX",
	"title": " Nonassociative rings and algebras",
	"parentcode": null,
	"level": 1
}, {
	"code": "17-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "17-XX",
	"level": 2
}, {
	"code": "17-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "17-XX",
	"level": 2
}, {
	"code": "17-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "17-XX",
	"level": 2
}, {
	"code": "17-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "17-XX",
	"level": 2
}, {
	"code": "17-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "17-XX",
	"level": 2
}, {
	"code": "17-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "17-XX",
	"level": 2
}, {
	"code": "17-08",
	"title": " Computational methods",
	"parentcode": "17-XX",
	"level": 2
}, {
	"code": "17Axx",
	"title": " General nonassociative rings",
	"parentcode": "17-XX",
	"level": 2
}, {
	"code": "17A01",
	"title": " General theory",
	"parentcode": "17Axx",
	"level": 3
}, {
	"code": "17A05",
	"title": " Power-associative rings",
	"parentcode": "17Axx",
	"level": 3
}, {
	"code": "17A15",
	"title": " Noncommutative Jordan algebras",
	"parentcode": "17Axx",
	"level": 3
}, {
	"code": "17A20",
	"title": " Flexible algebras",
	"parentcode": "17Axx",
	"level": 3
}, {
	"code": "17A30",
	"title": " Algebras satisfying other identities",
	"parentcode": "17Axx",
	"level": 3
}, {
	"code": "17A32",
	"title": " Leibniz algebras",
	"parentcode": "17Axx",
	"level": 3
}, {
	"code": "17A35",
	"title": " Division algebras",
	"parentcode": "17Axx",
	"level": 3
}, {
	"code": "17A36",
	"title": " Automorphisms, derivations, other operators",
	"parentcode": "17Axx",
	"level": 3
}, {
	"code": "17A40",
	"title": " Ternary compositions",
	"parentcode": "17Axx",
	"level": 3
}, {
	"code": "17A42",
	"title": " Other $n$-ary compositions $(n \\ge 3)$",
	"parentcode": "17Axx",
	"level": 3
}, {
	"code": "17A45",
	"title": " Quadratic algebras (but not quadratic Jordan algebras)",
	"parentcode": "17Axx",
	"level": 3
}, {
	"code": "17A50",
	"title": " Free algebras",
	"parentcode": "17Axx",
	"level": 3
}, {
	"code": "17A60",
	"title": " Structure theory",
	"parentcode": "17Axx",
	"level": 3
}, {
	"code": "17A65",
	"title": " Radical theory",
	"parentcode": "17Axx",
	"level": 3
}, {
	"code": "17A70",
	"title": " Superalgebras",
	"parentcode": "17Axx",
	"level": 3
}, {
	"code": "17A75",
	"title": " Composition algebras",
	"parentcode": "17Axx",
	"level": 3
}, {
	"code": "17A80",
	"title": " Valued algebras",
	"parentcode": "17Axx",
	"level": 3
}, {
	"code": "17A99",
	"title": " None of the above, but in this section",
	"parentcode": "17Axx",
	"level": 3
}, {
	"code": "17Bxx",
	"title": " Lie algebras and Lie superalgebras {For Lie groups, see 22Exx}",
	"parentcode": "17-XX",
	"level": 2
}, {
	"code": "17B01",
	"title": " Identities, free Lie (super)algebras",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B05",
	"title": " Structure theory",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B08",
	"title": " Coadjoint orbits; nilpotent varieties",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B10",
	"title": " Representations, algebraic theory (weights)",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B15",
	"title": " Representations, analytic theory",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B20",
	"title": " Simple, semisimple, reductive (super)algebras",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B22",
	"title": " Root systems",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B25",
	"title": " Exceptional (super)algebras",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B30",
	"title": " Solvable, nilpotent (super)algebras",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B35",
	"title": " Universal enveloping (super)algebras [See also 16S30]",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B37",
	"title": " Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B40",
	"title": " Automorphisms, derivations, other operators",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B45",
	"title": " Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx]",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B50",
	"title": " Modular Lie (super)algebras",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B55",
	"title": " Homological methods in Lie (super)algebras",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B56",
	"title": " Cohomology of Lie (super)algebras",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B60",
	"title": " Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50]",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B62",
	"title": " Lie bialgebras; Lie coalgebras",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B63",
	"title": " Poisson algebras",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B65",
	"title": " Infinite-dimensional Lie (super)algebras [See also 22E65]",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B66",
	"title": " Lie algebras of vector fields and related (super) algebras",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B67",
	"title": " Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B68",
	"title": " Virasoro and related algebras",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B69",
	"title": " Vertex operators; vertex operator algebras and related structures",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B70",
	"title": " Graded Lie (super)algebras",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B75",
	"title": " Color Lie (super)algebras",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B80",
	"title": " Applications to integrable systems",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B81",
	"title": " Applications to physics",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17B99",
	"title": " None of the above, but in this section",
	"parentcode": "17Bxx",
	"level": 3
}, {
	"code": "17Cxx",
	"title": " Jordan algebras (algebras, triples and pairs)",
	"parentcode": "17-XX",
	"level": 2
}, {
	"code": "17C05",
	"title": " Identities and free Jordan structures",
	"parentcode": "17Cxx",
	"level": 3
}, {
	"code": "17C10",
	"title": " Structure theory",
	"parentcode": "17Cxx",
	"level": 3
}, {
	"code": "17C17",
	"title": " Radicals",
	"parentcode": "17Cxx",
	"level": 3
}, {
	"code": "17C20",
	"title": " Simple, semisimple algebras",
	"parentcode": "17Cxx",
	"level": 3
}, {
	"code": "17C27",
	"title": " Idempotents, Peirce decompositions",
	"parentcode": "17Cxx",
	"level": 3
}, {
	"code": "17C30",
	"title": " Associated groups, automorphisms",
	"parentcode": "17Cxx",
	"level": 3
}, {
	"code": "17C36",
	"title": " Associated manifolds",
	"parentcode": "17Cxx",
	"level": 3
}, {
	"code": "17C37",
	"title": " Associated geometries",
	"parentcode": "17Cxx",
	"level": 3
}, {
	"code": "17C40",
	"title": " Exceptional Jordan structures",
	"parentcode": "17Cxx",
	"level": 3
}, {
	"code": "17C50",
	"title": " Jordan structures associated with other structures [See also 16W10]",
	"parentcode": "17Cxx",
	"level": 3
}, {
	"code": "17C55",
	"title": " Finite-dimensional structures",
	"parentcode": "17Cxx",
	"level": 3
}, {
	"code": "17C60",
	"title": " Division algebras",
	"parentcode": "17Cxx",
	"level": 3
}, {
	"code": "17C65",
	"title": " Jordan structures on Banach spaces and algebras [See also 46H70, 46L70]",
	"parentcode": "17Cxx",
	"level": 3
}, {
	"code": "17C70",
	"title": " Super structures",
	"parentcode": "17Cxx",
	"level": 3
}, {
	"code": "17C90",
	"title": " Applications to physics",
	"parentcode": "17Cxx",
	"level": 3
}, {
	"code": "17C99",
	"title": " None of the above, but in this section",
	"parentcode": "17Cxx",
	"level": 3
}, {
	"code": "17Dxx",
	"title": " Other nonassociative rings and algebras",
	"parentcode": "17-XX",
	"level": 2
}, {
	"code": "17D05",
	"title": " Alternative rings",
	"parentcode": "17Dxx",
	"level": 3
}, {
	"code": "17D10",
	"title": " Mal'cev (Mal'tsev) rings and algebras",
	"parentcode": "17Dxx",
	"level": 3
}, {
	"code": "17D15",
	"title": " Right alternative rings",
	"parentcode": "17Dxx",
	"level": 3
}, {
	"code": "17D20",
	"title": " $(\\gamma, \\delta)$-rings, including $(1,-1)$-rings",
	"parentcode": "17Dxx",
	"level": 3
}, {
	"code": "17D25",
	"title": " Lie-admissible algebras",
	"parentcode": "17Dxx",
	"level": 3
}, {
	"code": "17D92",
	"title": " Genetic algebras",
	"parentcode": "17Dxx",
	"level": 3
}, {
	"code": "17D99",
	"title": " None of the above, but in this section",
	"parentcode": "17Dxx",
	"level": 3
}, {
	"code": "18-XX",
	"title": " Category theory; homological algebra {For commutative rings see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and 55Uxx for algebraic topology}",
	"parentcode": null,
	"level": 1
}, {
	"code": "18-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "18-XX",
	"level": 2
}, {
	"code": "18-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "18-XX",
	"level": 2
}, {
	"code": "18-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "18-XX",
	"level": 2
}, {
	"code": "18-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "18-XX",
	"level": 2
}, {
	"code": "18-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "18-XX",
	"level": 2
}, {
	"code": "18-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "18-XX",
	"level": 2
}, {
	"code": "18Axx",
	"title": " General theory of categories and functors",
	"parentcode": "18-XX",
	"level": 2
}, {
	"code": "18A05",
	"title": " Definitions, generalizations",
	"parentcode": "18Axx",
	"level": 3
}, {
	"code": "18A10",
	"title": " Graphs, diagram schemes, precategories [See especially 20L05]",
	"parentcode": "18Axx",
	"level": 3
}, {
	"code": "18A15",
	"title": " Foundations, relations to logic and deductive systems [See also 03-XX]",
	"parentcode": "18Axx",
	"level": 3
}, {
	"code": "18A20",
	"title": " Epimorphisms, monomorphisms, special classes of morphisms, null morphisms",
	"parentcode": "18Axx",
	"level": 3
}, {
	"code": "18A22",
	"title": " Special properties of functors (faithful, full, etc.)",
	"parentcode": "18Axx",
	"level": 3
}, {
	"code": "18A23",
	"title": " Natural morphisms, dinatural morphisms",
	"parentcode": "18Axx",
	"level": 3
}, {
	"code": "18A25",
	"title": " Functor categories, comma categories",
	"parentcode": "18Axx",
	"level": 3
}, {
	"code": "18A30",
	"title": " Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)",
	"parentcode": "18Axx",
	"level": 3
}, {
	"code": "18A32",
	"title": " Factorization of morphisms, substructures, quotient structures, congruences, amalgams",
	"parentcode": "18Axx",
	"level": 3
}, {
	"code": "18A35",
	"title": " Categories admitting limits (complete categories), functors preserving limits, completions",
	"parentcode": "18Axx",
	"level": 3
}, {
	"code": "18A40",
	"title": " Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)",
	"parentcode": "18Axx",
	"level": 3
}, {
	"code": "18A99",
	"title": " None of the above, but in this section",
	"parentcode": "18Axx",
	"level": 3
}, {
	"code": "18Bxx",
	"title": " Special categories",
	"parentcode": "18-XX",
	"level": 2
}, {
	"code": "18B05",
	"title": " Category of sets, characterizations [See also 03-XX]",
	"parentcode": "18Bxx",
	"level": 3
}, {
	"code": "18B10",
	"title": " Category of relations, additive relations",
	"parentcode": "18Bxx",
	"level": 3
}, {
	"code": "18B15",
	"title": " Embedding theorems, universal categories [See also 18E20]",
	"parentcode": "18Bxx",
	"level": 3
}, {
	"code": "18B20",
	"title": " Categories of machines, automata, operative categories [See also 03D05, 68Qxx]",
	"parentcode": "18Bxx",
	"level": 3
}, {
	"code": "18B25",
	"title": " Topoi [See also 03G30]",
	"parentcode": "18Bxx",
	"level": 3
}, {
	"code": "18B30",
	"title": " Categories of topological spaces and continuous mappings [See also 54-XX]",
	"parentcode": "18Bxx",
	"level": 3
}, {
	"code": "18B35",
	"title": " Preorders, orders and lattices (viewed as categories) [See also 06-XX]",
	"parentcode": "18Bxx",
	"level": 3
}, {
	"code": "18B40",
	"title": " Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also 20Axx, 20L05, 20Mxx]",
	"parentcode": "18Bxx",
	"level": 3
}, {
	"code": "18B99",
	"title": " None of the above, but in this section",
	"parentcode": "18Bxx",
	"level": 3
}, {
	"code": "18Cxx",
	"title": " Categories and theories",
	"parentcode": "18-XX",
	"level": 2
}, {
	"code": "18C05",
	"title": " Equational categories [See also 03C05, 08C05]",
	"parentcode": "18Cxx",
	"level": 3
}, {
	"code": "18C10",
	"title": " Theories (e.g. algebraic theories), structure, and semantics [See also 03G30]",
	"parentcode": "18Cxx",
	"level": 3
}, {
	"code": "18C15",
	"title": " Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples [See also 18Gxx]",
	"parentcode": "18Cxx",
	"level": 3
}, {
	"code": "18C20",
	"title": " Algebras and Kleisli categories associated with monads",
	"parentcode": "18Cxx",
	"level": 3
}, {
	"code": "18C30",
	"title": " Sketches and generalizations",
	"parentcode": "18Cxx",
	"level": 3
}, {
	"code": "18C35",
	"title": " Accessible and locally presentable categories",
	"parentcode": "18Cxx",
	"level": 3
}, {
	"code": "18C50",
	"title": " Categorical semantics of formal languages [See also 68Q55, 68Q65]",
	"parentcode": "18Cxx",
	"level": 3
}, {
	"code": "18C99",
	"title": " None of the above, but in this section",
	"parentcode": "18Cxx",
	"level": 3
}, {
	"code": "18Dxx",
	"title": " Categories with structure",
	"parentcode": "18-XX",
	"level": 2
}, {
	"code": "18D05",
	"title": " Double categories, $2$-categories, bicategories and generalizations",
	"parentcode": "18Dxx",
	"level": 3
}, {
	"code": "18D10",
	"title": " Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23]",
	"parentcode": "18Dxx",
	"level": 3
}, {
	"code": "18D15",
	"title": " Closed categories (closed monoidal and Cartesian closed categories, etc.)",
	"parentcode": "18Dxx",
	"level": 3
}, {
	"code": "18D20",
	"title": " Enriched categories (over closed or monoidal categories)",
	"parentcode": "18Dxx",
	"level": 3
}, {
	"code": "18D25",
	"title": " Strong functors, strong adjunctions",
	"parentcode": "18Dxx",
	"level": 3
}, {
	"code": "18D30",
	"title": " Fibered categories",
	"parentcode": "18Dxx",
	"level": 3
}, {
	"code": "18D35",
	"title": " Structured objects in a category (group objects, etc.)",
	"parentcode": "18Dxx",
	"level": 3
}, {
	"code": "18D50",
	"title": " Operads [See also 55P48]",
	"parentcode": "18Dxx",
	"level": 3
}, {
	"code": "18D99",
	"title": " None of the above, but in this section",
	"parentcode": "18Dxx",
	"level": 3
}, {
	"code": "18Exx",
	"title": " Abelian categories",
	"parentcode": "18-XX",
	"level": 2
}, {
	"code": "18E05",
	"title": " Preadditive, additive categories",
	"parentcode": "18Exx",
	"level": 3
}, {
	"code": "18E10",
	"title": " Exact categories, abelian categories",
	"parentcode": "18Exx",
	"level": 3
}, {
	"code": "18E15",
	"title": " Grothendieck categories",
	"parentcode": "18Exx",
	"level": 3
}, {
	"code": "18E20",
	"title": " Embedding theorems [See also 18B15]",
	"parentcode": "18Exx",
	"level": 3
}, {
	"code": "18E25",
	"title": " Derived functors and satellites",
	"parentcode": "18Exx",
	"level": 3
}, {
	"code": "18E30",
	"title": " Derived categories, triangulated categories",
	"parentcode": "18Exx",
	"level": 3
}, {
	"code": "18E35",
	"title": " Localization of categories",
	"parentcode": "18Exx",
	"level": 3
}, {
	"code": "18E40",
	"title": " Torsion theories, radicals [See also 13D30, 16S90]",
	"parentcode": "18Exx",
	"level": 3
}, {
	"code": "18E99",
	"title": " None of the above, but in this section",
	"parentcode": "18Exx",
	"level": 3
}, {
	"code": "18Fxx",
	"title": " Categories and geometry",
	"parentcode": "18-XX",
	"level": 2
}, {
	"code": "18F05",
	"title": " Local categories and functors",
	"parentcode": "18Fxx",
	"level": 3
}, {
	"code": "18F10",
	"title": " Grothendieck topologies [See also 14F20]",
	"parentcode": "18Fxx",
	"level": 3
}, {
	"code": "18F15",
	"title": " Abstract manifolds and fiber bundles [See also 55Rxx, 57Pxx]",
	"parentcode": "18Fxx",
	"level": 3
}, {
	"code": "18F20",
	"title": " Presheaves and sheaves [See also 14F05, 32C35, 32L10, 54B40, 55N30]",
	"parentcode": "18Fxx",
	"level": 3
}, {
	"code": "18F25",
	"title": " Algebraic $K$-theory and $L$-theory [See also 11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67]",
	"parentcode": "18Fxx",
	"level": 3
}, {
	"code": "18F30",
	"title": " Grothendieck groups [See also 13D15, 16E20, 19Axx]",
	"parentcode": "18Fxx",
	"level": 3
}, {
	"code": "18F99",
	"title": " None of the above, but in this section",
	"parentcode": "18Fxx",
	"level": 3
}, {
	"code": "18Gxx",
	"title": " Homological algebra [See also 13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx]",
	"parentcode": "18-XX",
	"level": 2
}, {
	"code": "18G05",
	"title": " Projectives and injectives [See also 13C10, 13C11, 16D40, 16D50]",
	"parentcode": "18Gxx",
	"level": 3
}, {
	"code": "18G10",
	"title": " Resolutions; derived functors [See also 13D02, 16E05, 18E25]",
	"parentcode": "18Gxx",
	"level": 3
}, {
	"code": "18G15",
	"title": " Ext and Tor, generalizations, Künneth formula [See also 55U25]",
	"parentcode": "18Gxx",
	"level": 3
}, {
	"code": "18G20",
	"title": " Homological dimension [See also 13D05, 16E10]",
	"parentcode": "18Gxx",
	"level": 3
}, {
	"code": "18G25",
	"title": " Relative homological algebra, projective classes",
	"parentcode": "18Gxx",
	"level": 3
}, {
	"code": "18G30",
	"title": " Simplicial sets, simplicial objects (in a category) [See also 55U10]",
	"parentcode": "18Gxx",
	"level": 3
}, {
	"code": "18G35",
	"title": " Chain complexes [See also 18E30, 55U15]",
	"parentcode": "18Gxx",
	"level": 3
}, {
	"code": "18G40",
	"title": " Spectral sequences, hypercohomology [See also 55Txx]",
	"parentcode": "18Gxx",
	"level": 3
}, {
	"code": "18G50",
	"title": " Nonabelian homological algebra",
	"parentcode": "18Gxx",
	"level": 3
}, {
	"code": "18G55",
	"title": " Homotopical algebra",
	"parentcode": "18Gxx",
	"level": 3
}, {
	"code": "18G60",
	"title": " Other (co)homology theories [See also 19D55, 46L80, 58J20, 58J22]",
	"parentcode": "18Gxx",
	"level": 3
}, {
	"code": "18G99",
	"title": " None of the above, but in this section",
	"parentcode": "18Gxx",
	"level": 3
}, {
	"code": "19-XX",
	"title": " $K$-theory [See also 16E20, 18F25]",
	"parentcode": null,
	"level": 1
}, {
	"code": "19-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "19-XX",
	"level": 2
}, {
	"code": "19-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "19-XX",
	"level": 2
}, {
	"code": "19-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "19-XX",
	"level": 2
}, {
	"code": "19-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "19-XX",
	"level": 2
}, {
	"code": "19-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "19-XX",
	"level": 2
}, {
	"code": "19-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "19-XX",
	"level": 2
}, {
	"code": "19Axx",
	"title": " Grothendieck groups and $K_0$ [See also 13D15, 18F30]",
	"parentcode": "19-XX",
	"level": 2
}, {
	"code": "19A13",
	"title": " Stability for projective modules [See also 13C10]",
	"parentcode": "19Axx",
	"level": 3
}, {
	"code": "19A15",
	"title": " Efficient generation",
	"parentcode": "19Axx",
	"level": 3
}, {
	"code": "19A22",
	"title": " Frobenius induction, Burnside and representation rings",
	"parentcode": "19Axx",
	"level": 3
}, {
	"code": "19A31",
	"title": " $K_0$ of group rings and orders",
	"parentcode": "19Axx",
	"level": 3
}, {
	"code": "19A49",
	"title": " $K_0$ of other rings",
	"parentcode": "19Axx",
	"level": 3
}, {
	"code": "19A99",
	"title": " None of the above, but in this section",
	"parentcode": "19Axx",
	"level": 3
}, {
	"code": "19Bxx",
	"title": " Whitehead groups and $K_1$",
	"parentcode": "19-XX",
	"level": 2
}, {
	"code": "19B10",
	"title": " Stable range conditions",
	"parentcode": "19Bxx",
	"level": 3
}, {
	"code": "19B14",
	"title": " Stability for linear groups",
	"parentcode": "19Bxx",
	"level": 3
}, {
	"code": "19B28",
	"title": " $K_1$ of group rings and orders [See also 57Q10]",
	"parentcode": "19Bxx",
	"level": 3
}, {
	"code": "19B37",
	"title": " Congruence subgroup problems [See also 20H05]",
	"parentcode": "19Bxx",
	"level": 3
}, {
	"code": "19B99",
	"title": " None of the above, but in this section",
	"parentcode": "19Bxx",
	"level": 3
}, {
	"code": "19Cxx",
	"title": " Steinberg groups and $K_2$",
	"parentcode": "19-XX",
	"level": 2
}, {
	"code": "19C09",
	"title": " Central extensions and Schur multipliers",
	"parentcode": "19Cxx",
	"level": 3
}, {
	"code": "19C20",
	"title": " Symbols, presentations and stability of $K_2$",
	"parentcode": "19Cxx",
	"level": 3
}, {
	"code": "19C30",
	"title": " $K_2$ and the Brauer group",
	"parentcode": "19Cxx",
	"level": 3
}, {
	"code": "19C40",
	"title": " Excision for $K_2$",
	"parentcode": "19Cxx",
	"level": 3
}, {
	"code": "19C99",
	"title": " None of the above, but in this section",
	"parentcode": "19Cxx",
	"level": 3
}, {
	"code": "19Dxx",
	"title": " Higher algebraic $K$-theory",
	"parentcode": "19-XX",
	"level": 2
}, {
	"code": "19D06",
	"title": " $Q$- and plus-constructions",
	"parentcode": "19Dxx",
	"level": 3
}, {
	"code": "19D10",
	"title": " Algebraic $K$-theory of spaces",
	"parentcode": "19Dxx",
	"level": 3
}, {
	"code": "19D23",
	"title": " Symmetric monoidal categories [See also 18D10]",
	"parentcode": "19Dxx",
	"level": 3
}, {
	"code": "19D25",
	"title": " Karoubi-Villamayor-Gersten $K$-theory",
	"parentcode": "19Dxx",
	"level": 3
}, {
	"code": "19D35",
	"title": " Negative $K$-theory, NK and Nil",
	"parentcode": "19Dxx",
	"level": 3
}, {
	"code": "19D45",
	"title": " Higher symbols, Milnor $K$-theory",
	"parentcode": "19Dxx",
	"level": 3
}, {
	"code": "19D50",
	"title": " Computations of higher $K$-theory of rings [See also 13D15, 16E20]",
	"parentcode": "19Dxx",
	"level": 3
}, {
	"code": "19D55",
	"title": " $K$-theory and homology; cyclic homology and cohomology [See also 18G60]",
	"parentcode": "19Dxx",
	"level": 3
}, {
	"code": "19D99",
	"title": " None of the above, but in this section",
	"parentcode": "19Dxx",
	"level": 3
}, {
	"code": "19Exx",
	"title": " $K$-theory in geometry",
	"parentcode": "19-XX",
	"level": 2
}, {
	"code": "19E08",
	"title": " $K$-theory of schemes [See also 14C35]",
	"parentcode": "19Exx",
	"level": 3
}, {
	"code": "19E15",
	"title": " Algebraic cycles and motivic cohomology [See also 14C25, 14C35, 14F42]",
	"parentcode": "19Exx",
	"level": 3
}, {
	"code": "19E20",
	"title": " Relations with cohomology theories [See also 14Fxx]",
	"parentcode": "19Exx",
	"level": 3
}, {
	"code": "19E99",
	"title": " None of the above, but in this section",
	"parentcode": "19Exx",
	"level": 3
}, {
	"code": "19Fxx",
	"title": " $K$-theory in number theory [See also 11R70, 11S70]",
	"parentcode": "19-XX",
	"level": 2
}, {
	"code": "19F05",
	"title": " Generalized class field theory [See also 11G45]",
	"parentcode": "19Fxx",
	"level": 3
}, {
	"code": "19F15",
	"title": " Symbols and arithmetic [See also 11R37]",
	"parentcode": "19Fxx",
	"level": 3
}, {
	"code": "19F27",
	"title": " Étale cohomology, higher regulators, zeta and $L$-functions [See also 11G40, 11R42, 11S40, 14F20, 14G10]",
	"parentcode": "19Fxx",
	"level": 3
}, {
	"code": "19F99",
	"title": " None of the above, but in this section",
	"parentcode": "19Fxx",
	"level": 3
}, {
	"code": "19Gxx",
	"title": " $K$-theory of forms [See also 11Exx]",
	"parentcode": "19-XX",
	"level": 2
}, {
	"code": "19G05",
	"title": " Stability for quadratic modules",
	"parentcode": "19Gxx",
	"level": 3
}, {
	"code": "19G12",
	"title": " Witt groups of rings [See also 11E81]",
	"parentcode": "19Gxx",
	"level": 3
}, {
	"code": "19G24",
	"title": " $L$-theory of group rings [See also 11E81]",
	"parentcode": "19Gxx",
	"level": 3
}, {
	"code": "19G38",
	"title": " Hermitian $K$-theory, relations with $K$-theory of rings",
	"parentcode": "19Gxx",
	"level": 3
}, {
	"code": "19G99",
	"title": " None of the above, but in this section",
	"parentcode": "19Gxx",
	"level": 3
}, {
	"code": "19Jxx",
	"title": " Obstructions from topology",
	"parentcode": "19-XX",
	"level": 2
}, {
	"code": "19J05",
	"title": " Finiteness and other obstructions in $K_0$",
	"parentcode": "19Jxx",
	"level": 3
}, {
	"code": "19J10",
	"title": " Whitehead (and related) torsion",
	"parentcode": "19Jxx",
	"level": 3
}, {
	"code": "19J25",
	"title": " Surgery obstructions [See also 57R67]",
	"parentcode": "19Jxx",
	"level": 3
}, {
	"code": "19J35",
	"title": " Obstructions to group actions",
	"parentcode": "19Jxx",
	"level": 3
}, {
	"code": "19J99",
	"title": " None of the above, but in this section",
	"parentcode": "19Jxx",
	"level": 3
}, {
	"code": "19Kxx",
	"title": " $K$-theory and operator algebras [See mainly 46L80, and also 46M20]",
	"parentcode": "19-XX",
	"level": 2
}, {
	"code": "19K14",
	"title": " $K_0$ as an ordered group, traces",
	"parentcode": "19Kxx",
	"level": 3
}, {
	"code": "19K33",
	"title": " EXT and $K$-homology [See also 55N22]",
	"parentcode": "19Kxx",
	"level": 3
}, {
	"code": "19K35",
	"title": " Kasparov theory ($KK$-theory) [See also 58J22]",
	"parentcode": "19Kxx",
	"level": 3
}, {
	"code": "19K56",
	"title": " Index theory [See also 58J20, 58J22]",
	"parentcode": "19Kxx",
	"level": 3
}, {
	"code": "19K99",
	"title": " None of the above, but in this section",
	"parentcode": "19Kxx",
	"level": 3
}, {
	"code": "19Lxx",
	"title": " Topological $K$-theory [See also 55N15, 55R50, 55S25]",
	"parentcode": "19-XX",
	"level": 2
}, {
	"code": "19L10",
	"title": " Riemann-Roch theorems, Chern characters",
	"parentcode": "19Lxx",
	"level": 3
}, {
	"code": "19L20",
	"title": " $J$-homomorphism, Adams operations [See also 55Q50]",
	"parentcode": "19Lxx",
	"level": 3
}, {
	"code": "19L41",
	"title": " Connective $K$-theory, cobordism [See also 55N22]",
	"parentcode": "19Lxx",
	"level": 3
}, {
	"code": "19L47",
	"title": " Equivariant $K$-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91]",
	"parentcode": "19Lxx",
	"level": 3
}, {
	"code": "19L50",
	"title": " Twisted $K$-theory; differential $K$-theory",
	"parentcode": "19Lxx",
	"level": 3
}, {
	"code": "19L64",
	"title": " Computations, geometric applications",
	"parentcode": "19Lxx",
	"level": 3
}, {
	"code": "19L99",
	"title": " None of the above, but in this section",
	"parentcode": "19Lxx",
	"level": 3
}, {
	"code": "19Mxx",
	"title": " Miscellaneous applications of $K$-theory",
	"parentcode": "19-XX",
	"level": 2
}, {
	"code": "19M05",
	"title": " Miscellaneous applications of $K$-theory",
	"parentcode": "19Mxx",
	"level": 3
}, {
	"code": "19M99",
	"title": " None of the above, but in this section",
	"parentcode": "19Mxx",
	"level": 3
}, {
	"code": "20-XX",
	"title": " Group theory and generalizations",
	"parentcode": null,
	"level": 1
}, {
	"code": "20-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "20-XX",
	"level": 2
}, {
	"code": "20-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "20-XX",
	"level": 2
}, {
	"code": "20-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "20-XX",
	"level": 2
}, {
	"code": "20-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "20-XX",
	"level": 2
}, {
	"code": "20-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "20-XX",
	"level": 2
}, {
	"code": "20-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "20-XX",
	"level": 2
}, {
	"code": "20Axx",
	"title": " Foundations",
	"parentcode": "20-XX",
	"level": 2
}, {
	"code": "20A05",
	"title": " Axiomatics and elementary properties",
	"parentcode": "20Axx",
	"level": 3
}, {
	"code": "20A10",
	"title": " Metamathematical considerations {For word problems, see 20F10}",
	"parentcode": "20Axx",
	"level": 3
}, {
	"code": "20A15",
	"title": " Applications of logic to group theory",
	"parentcode": "20Axx",
	"level": 3
}, {
	"code": "20A99",
	"title": " None of the above, but in this section",
	"parentcode": "20Axx",
	"level": 3
}, {
	"code": "20Bxx",
	"title": " Permutation groups",
	"parentcode": "20-XX",
	"level": 2
}, {
	"code": "20B05",
	"title": " General theory for finite groups",
	"parentcode": "20Bxx",
	"level": 3
}, {
	"code": "20B07",
	"title": " General theory for infinite groups",
	"parentcode": "20Bxx",
	"level": 3
}, {
	"code": "20B10",
	"title": " Characterization theorems",
	"parentcode": "20Bxx",
	"level": 3
}, {
	"code": "20B15",
	"title": " Primitive groups",
	"parentcode": "20Bxx",
	"level": 3
}, {
	"code": "20B20",
	"title": " Multiply transitive finite groups",
	"parentcode": "20Bxx",
	"level": 3
}, {
	"code": "20B22",
	"title": " Multiply transitive infinite groups",
	"parentcode": "20Bxx",
	"level": 3
}, {
	"code": "20B25",
	"title": " Finite automorphism groups of algebraic, geometric, or combinatorial structures [See also 05Bxx, 12F10, 20G40, 20H30, 51-XX]",
	"parentcode": "20Bxx",
	"level": 3
}, {
	"code": "20B27",
	"title": " Infinite automorphism groups [See also 12F10]",
	"parentcode": "20Bxx",
	"level": 3
}, {
	"code": "20B30",
	"title": " Symmetric groups",
	"parentcode": "20Bxx",
	"level": 3
}, {
	"code": "20B35",
	"title": " Subgroups of symmetric groups",
	"parentcode": "20Bxx",
	"level": 3
}, {
	"code": "20B40",
	"title": " Computational methods",
	"parentcode": "20Bxx",
	"level": 3
}, {
	"code": "20B99",
	"title": " None of the above, but in this section",
	"parentcode": "20Bxx",
	"level": 3
}, {
	"code": "20Cxx",
	"title": " Representation theory of groups [See also 19A22 (for representation rings and Burnside rings)]",
	"parentcode": "20-XX",
	"level": 2
}, {
	"code": "20C05",
	"title": " Group rings of finite groups and their modules [See also 16S34]",
	"parentcode": "20Cxx",
	"level": 3
}, {
	"code": "20C07",
	"title": " Group rings of infinite groups and their modules [See also 16S34]",
	"parentcode": "20Cxx",
	"level": 3
}, {
	"code": "20C08",
	"title": " Hecke algebras and their representations",
	"parentcode": "20Cxx",
	"level": 3
}, {
	"code": "20C10",
	"title": " Integral representations of finite groups",
	"parentcode": "20Cxx",
	"level": 3
}, {
	"code": "20C11",
	"title": " $p$-adic representations of finite groups",
	"parentcode": "20Cxx",
	"level": 3
}, {
	"code": "20C12",
	"title": " Integral representations of infinite groups",
	"parentcode": "20Cxx",
	"level": 3
}, {
	"code": "20C15",
	"title": " Ordinary representations and characters",
	"parentcode": "20Cxx",
	"level": 3
}, {
	"code": "20C20",
	"title": " Modular representations and characters",
	"parentcode": "20Cxx",
	"level": 3
}, {
	"code": "20C25",
	"title": " Projective representations and multipliers",
	"parentcode": "20Cxx",
	"level": 3
}, {
	"code": "20C30",
	"title": " Representations of finite symmetric groups",
	"parentcode": "20Cxx",
	"level": 3
}, {
	"code": "20C32",
	"title": " Representations of infinite symmetric groups",
	"parentcode": "20Cxx",
	"level": 3
}, {
	"code": "20C33",
	"title": " Representations of finite groups of Lie type",
	"parentcode": "20Cxx",
	"level": 3
}, {
	"code": "20C34",
	"title": " Representations of sporadic groups",
	"parentcode": "20Cxx",
	"level": 3
}, {
	"code": "20C35",
	"title": " Applications of group representations to physics",
	"parentcode": "20Cxx",
	"level": 3
}, {
	"code": "20C40",
	"title": " Computational methods",
	"parentcode": "20Cxx",
	"level": 3
}, {
	"code": "20C99",
	"title": " None of the above, but in this section",
	"parentcode": "20Cxx",
	"level": 3
}, {
	"code": "20Dxx",
	"title": " Abstract finite groups",
	"parentcode": "20-XX",
	"level": 2
}, {
	"code": "20D05",
	"title": " Finite simple groups and their classification",
	"parentcode": "20Dxx",
	"level": 3
}, {
	"code": "20D06",
	"title": " Simple groups",
	"parentcode": "20Dxx",
	"level": 3
}, {
	"code": "20D08",
	"title": " Simple groups",
	"parentcode": "20Dxx",
	"level": 3
}, {
	"code": "20D10",
	"title": " Solvable groups, theory of formations, Schunck classes, Fitting classes, $\\pi$-length, ranks [See also 20F17]",
	"parentcode": "20Dxx",
	"level": 3
}, {
	"code": "20D15",
	"title": " Nilpotent groups, $p$-groups",
	"parentcode": "20Dxx",
	"level": 3
}, {
	"code": "20D20",
	"title": " Sylow subgroups, Sylow properties, $\\pi$-groups, $\\pi$-structure",
	"parentcode": "20Dxx",
	"level": 3
}, {
	"code": "20D25",
	"title": " Special subgroups (Frattini, Fitting, etc.)",
	"parentcode": "20Dxx",
	"level": 3
}, {
	"code": "20D30",
	"title": " Series and lattices of subgroups",
	"parentcode": "20Dxx",
	"level": 3
}, {
	"code": "20D35",
	"title": " Subnormal subgroups",
	"parentcode": "20Dxx",
	"level": 3
}, {
	"code": "20D40",
	"title": " Products of subgroups",
	"parentcode": "20Dxx",
	"level": 3
}, {
	"code": "20D45",
	"title": " Automorphisms",
	"parentcode": "20Dxx",
	"level": 3
}, {
	"code": "20D60",
	"title": " Arithmetic and combinatorial problems",
	"parentcode": "20Dxx",
	"level": 3
}, {
	"code": "20D99",
	"title": " None of the above, but in this section",
	"parentcode": "20Dxx",
	"level": 3
}, {
	"code": "20Exx",
	"title": " Structure and classification of infinite or finite groups",
	"parentcode": "20-XX",
	"level": 2
}, {
	"code": "20E05",
	"title": " Free nonabelian groups",
	"parentcode": "20Exx",
	"level": 3
}, {
	"code": "20E06",
	"title": " Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations",
	"parentcode": "20Exx",
	"level": 3
}, {
	"code": "20E07",
	"title": " Subgroup theorems; subgroup growth",
	"parentcode": "20Exx",
	"level": 3
}, {
	"code": "20E08",
	"title": " Groups acting on trees [See also 20F65]",
	"parentcode": "20Exx",
	"level": 3
}, {
	"code": "20E10",
	"title": " Quasivarieties and varieties of groups",
	"parentcode": "20Exx",
	"level": 3
}, {
	"code": "20E15",
	"title": " Chains and lattices of subgroups, subnormal subgroups [See also 20F22]",
	"parentcode": "20Exx",
	"level": 3
}, {
	"code": "20E18",
	"title": " Limits, profinite groups",
	"parentcode": "20Exx",
	"level": 3
}, {
	"code": "20E22",
	"title": " Extensions, wreath products, and other compositions [See also 20J05]",
	"parentcode": "20Exx",
	"level": 3
}, {
	"code": "20E25",
	"title": " Local properties",
	"parentcode": "20Exx",
	"level": 3
}, {
	"code": "20E26",
	"title": " Residual properties and generalizations; residually finite groups",
	"parentcode": "20Exx",
	"level": 3
}, {
	"code": "20E28",
	"title": " Maximal subgroups",
	"parentcode": "20Exx",
	"level": 3
}, {
	"code": "20E32",
	"title": " Simple groups [See also 20D05]",
	"parentcode": "20Exx",
	"level": 3
}, {
	"code": "20E34",
	"title": " General structure theorems",
	"parentcode": "20Exx",
	"level": 3
}, {
	"code": "20E36",
	"title": " Automorphisms of infinite groups [For automorphisms of finite groups, see 20D45]",
	"parentcode": "20Exx",
	"level": 3
}, {
	"code": "20E42",
	"title": " Groups with a $BN$-pair; buildings [See also 51E24]",
	"parentcode": "20Exx",
	"level": 3
}, {
	"code": "20E45",
	"title": " Conjugacy classes",
	"parentcode": "20Exx",
	"level": 3
}, {
	"code": "20E99",
	"title": " None of the above, but in this section",
	"parentcode": "20Exx",
	"level": 3
}, {
	"code": "20Fxx",
	"title": " Special aspects of infinite or finite groups",
	"parentcode": "20-XX",
	"level": 2
}, {
	"code": "20F05",
	"title": " Generators, relations, and presentations",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F06",
	"title": " Cancellation theory; application of van Kampen diagrams [See also 57M05]",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F10",
	"title": " Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70]",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F11",
	"title": " Groups of finite Morley rank [See also 03C45, 03C60]",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F12",
	"title": " Commutator calculus",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F14",
	"title": " Derived series, central series, and generalizations",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F16",
	"title": " Solvable groups, supersolvable groups [See also 20D10]",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F17",
	"title": " Formations of groups, Fitting classes [See also 20D10]",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F18",
	"title": " Nilpotent groups [See also 20D15]",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F19",
	"title": " Generalizations of solvable and nilpotent groups",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F22",
	"title": " Other classes of groups defined by subgroup chains",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F24",
	"title": " FC-groups and their generalizations",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F28",
	"title": " Automorphism groups of groups [See also 20E36]",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F29",
	"title": " Representations of groups as automorphism groups of algebraic systems",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F34",
	"title": " Fundamental groups and their automorphisms [See also 57M05, 57Sxx]",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F36",
	"title": " Braid groups; Artin groups",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F38",
	"title": " Other groups related to topology or analysis",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F40",
	"title": " Associated Lie structures",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F45",
	"title": " Engel conditions",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F50",
	"title": " Periodic groups; locally finite groups",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F55",
	"title": " Reflection and Coxeter groups [See also 22E40, 51F15]",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F60",
	"title": " Ordered groups [See mainly 06F15]",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F65",
	"title": " Geometric group theory [See also 05C25, 20E08, 57Mxx]",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F67",
	"title": " Hyperbolic groups and nonpositively curved groups",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F69",
	"title": " Asymptotic properties of groups",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F70",
	"title": " Algebraic geometry over groups; equations over groups",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20F99",
	"title": " None of the above, but in this section",
	"parentcode": "20Fxx",
	"level": 3
}, {
	"code": "20Gxx",
	"title": " Linear algebraic groups and related topics {For arithmetic theory, see 11E57, 11H56; for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47, 22E50, 22E55}",
	"parentcode": "20-XX",
	"level": 2
}, {
	"code": "20G05",
	"title": " Representation theory",
	"parentcode": "20Gxx",
	"level": 3
}, {
	"code": "20G07",
	"title": " Structure theory",
	"parentcode": "20Gxx",
	"level": 3
}, {
	"code": "20G10",
	"title": " Cohomology theory",
	"parentcode": "20Gxx",
	"level": 3
}, {
	"code": "20G15",
	"title": " Linear algebraic groups over arbitrary fields",
	"parentcode": "20Gxx",
	"level": 3
}, {
	"code": "20G20",
	"title": " Linear algebraic groups over the reals, the complexes, the quaternions",
	"parentcode": "20Gxx",
	"level": 3
}, {
	"code": "20G25",
	"title": " Linear algebraic groups over local fields and their integers",
	"parentcode": "20Gxx",
	"level": 3
}, {
	"code": "20G30",
	"title": " Linear algebraic groups over global fields and their integers",
	"parentcode": "20Gxx",
	"level": 3
}, {
	"code": "20G35",
	"title": " Linear algebraic groups over adèles and other rings and schemes",
	"parentcode": "20Gxx",
	"level": 3
}, {
	"code": "20G40",
	"title": " Linear algebraic groups over finite fields",
	"parentcode": "20Gxx",
	"level": 3
}, {
	"code": "20G41",
	"title": " Exceptional groups",
	"parentcode": "20Gxx",
	"level": 3
}, {
	"code": "20G42",
	"title": " Quantum groups (quantized function algebras) and their representations [See also 16T20, 17B37, 81R50]",
	"parentcode": "20Gxx",
	"level": 3
}, {
	"code": "20G43",
	"title": " Schur and $q$-Schur algebras",
	"parentcode": "20Gxx",
	"level": 3
}, {
	"code": "20G44",
	"title": " Kac-Moody groups",
	"parentcode": "20Gxx",
	"level": 3
}, {
	"code": "20G45",
	"title": " Applications to physics",
	"parentcode": "20Gxx",
	"level": 3
}, {
	"code": "20G99",
	"title": " None of the above, but in this section",
	"parentcode": "20Gxx",
	"level": 3
}, {
	"code": "20Hxx",
	"title": " Other groups of matrices [See also 15A30]",
	"parentcode": "20-XX",
	"level": 2
}, {
	"code": "20H05",
	"title": " Unimodular groups, congruence subgroups [See also 11F06, 19B37, 22E40, 51F20]",
	"parentcode": "20Hxx",
	"level": 3
}, {
	"code": "20H10",
	"title": " Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]",
	"parentcode": "20Hxx",
	"level": 3
}, {
	"code": "20H15",
	"title": " Other geometric groups, including crystallographic groups [See also 51-XX, especially 51F15, and 82D25]",
	"parentcode": "20Hxx",
	"level": 3
}, {
	"code": "20H20",
	"title": " Other matrix groups over fields",
	"parentcode": "20Hxx",
	"level": 3
}, {
	"code": "20H25",
	"title": " Other matrix groups over rings",
	"parentcode": "20Hxx",
	"level": 3
}, {
	"code": "20H30",
	"title": " Other matrix groups over finite fields",
	"parentcode": "20Hxx",
	"level": 3
}, {
	"code": "20H99",
	"title": " None of the above, but in this section",
	"parentcode": "20Hxx",
	"level": 3
}, {
	"code": "20Jxx",
	"title": " Connections with homological algebra and category theory",
	"parentcode": "20-XX",
	"level": 2
}, {
	"code": "20J05",
	"title": " Homological methods in group theory",
	"parentcode": "20Jxx",
	"level": 3
}, {
	"code": "20J06",
	"title": " Cohomology of groups",
	"parentcode": "20Jxx",
	"level": 3
}, {
	"code": "20J15",
	"title": " Category of groups",
	"parentcode": "20Jxx",
	"level": 3
}, {
	"code": "20J99",
	"title": " None of the above, but in this section",
	"parentcode": "20Jxx",
	"level": 3
}, {
	"code": "20Kxx",
	"title": " Abelian groups",
	"parentcode": "20-XX",
	"level": 2
}, {
	"code": "20K01",
	"title": " Finite abelian groups [For sumsets, see 11B13 and 11P70]",
	"parentcode": "20Kxx",
	"level": 3
}, {
	"code": "20K10",
	"title": " Torsion groups, primary groups and generalized primary groups",
	"parentcode": "20Kxx",
	"level": 3
}, {
	"code": "20K15",
	"title": " Torsion-free groups, finite rank",
	"parentcode": "20Kxx",
	"level": 3
}, {
	"code": "20K20",
	"title": " Torsion-free groups, infinite rank",
	"parentcode": "20Kxx",
	"level": 3
}, {
	"code": "20K21",
	"title": " Mixed groups",
	"parentcode": "20Kxx",
	"level": 3
}, {
	"code": "20K25",
	"title": " Direct sums, direct products, etc.",
	"parentcode": "20Kxx",
	"level": 3
}, {
	"code": "20K27",
	"title": " Subgroups",
	"parentcode": "20Kxx",
	"level": 3
}, {
	"code": "20K30",
	"title": " Automorphisms, homomorphisms, endomorphisms, etc.",
	"parentcode": "20Kxx",
	"level": 3
}, {
	"code": "20K35",
	"title": " Extensions",
	"parentcode": "20Kxx",
	"level": 3
}, {
	"code": "20K40",
	"title": " Homological and categorical methods",
	"parentcode": "20Kxx",
	"level": 3
}, {
	"code": "20K45",
	"title": " Topological methods [See also 22A05, 22B05]",
	"parentcode": "20Kxx",
	"level": 3
}, {
	"code": "20K99",
	"title": " None of the above, but in this section",
	"parentcode": "20Kxx",
	"level": 3
}, {
	"code": "20Lxx",
	"title": " Groupoids (i.e. small categories in which all morphisms are isomorphisms) {For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05}",
	"parentcode": "20-XX",
	"level": 2
}, {
	"code": "20L05",
	"title": " Groupoids (i.e. small categories in which all morphisms are isomorphisms) {For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05}",
	"parentcode": "20Lxx",
	"level": 3
}, {
	"code": "20L99",
	"title": " None of the above, but in this section",
	"parentcode": "20Lxx",
	"level": 3
}, {
	"code": "20Mxx",
	"title": " Semigroups",
	"parentcode": "20-XX",
	"level": 2
}, {
	"code": "20M05",
	"title": " Free semigroups, generators and relations, word problems [See also 03D40, 08A50, 20F10]",
	"parentcode": "20Mxx",
	"level": 3
}, {
	"code": "20M07",
	"title": " Varieties and pseudovarieties of semigroups",
	"parentcode": "20Mxx",
	"level": 3
}, {
	"code": "20M10",
	"title": " General structure theory",
	"parentcode": "20Mxx",
	"level": 3
}, {
	"code": "20M11",
	"title": " Radical theory",
	"parentcode": "20Mxx",
	"level": 3
}, {
	"code": "20M12",
	"title": " Ideal theory",
	"parentcode": "20Mxx",
	"level": 3
}, {
	"code": "20M13",
	"title": " Arithmetic theory of monoids",
	"parentcode": "20Mxx",
	"level": 3
}, {
	"code": "20M14",
	"title": " Commutative semigroups",
	"parentcode": "20Mxx",
	"level": 3
}, {
	"code": "20M15",
	"title": " Mappings of semigroups",
	"parentcode": "20Mxx",
	"level": 3
}, {
	"code": "20M17",
	"title": " Regular semigroups",
	"parentcode": "20Mxx",
	"level": 3
}, {
	"code": "20M18",
	"title": " Inverse semigroups",
	"parentcode": "20Mxx",
	"level": 3
}, {
	"code": "20M19",
	"title": " Orthodox semigroups",
	"parentcode": "20Mxx",
	"level": 3
}, {
	"code": "20M20",
	"title": " Semigroups of transformations, etc. [See also 47D03, 47H20, 54H15]",
	"parentcode": "20Mxx",
	"level": 3
}, {
	"code": "20M25",
	"title": " Semigroup rings, multiplicative semigroups of rings [See also 16S36, 16Y60]",
	"parentcode": "20Mxx",
	"level": 3
}, {
	"code": "20M30",
	"title": " Representation of semigroups; actions of semigroups on sets",
	"parentcode": "20Mxx",
	"level": 3
}, {
	"code": "20M32",
	"title": " Algebraic monoids",
	"parentcode": "20Mxx",
	"level": 3
}, {
	"code": "20M35",
	"title": " Semigroups in automata theory, linguistics, etc. [See also 03D05, 68Q70, 68T50]",
	"parentcode": "20Mxx",
	"level": 3
}, {
	"code": "20M50",
	"title": " Connections of semigroups with homological algebra and category theory",
	"parentcode": "20Mxx",
	"level": 3
}, {
	"code": "20M99",
	"title": " None of the above, but in this section",
	"parentcode": "20Mxx",
	"level": 3
}, {
	"code": "20Nxx",
	"title": " Other generalizations of groups",
	"parentcode": "20-XX",
	"level": 2
}, {
	"code": "20N02",
	"title": " Sets with a single binary operation (groupoids)",
	"parentcode": "20Nxx",
	"level": 3
}, {
	"code": "20N05",
	"title": " Loops, quasigroups [See also 05Bxx]",
	"parentcode": "20Nxx",
	"level": 3
}, {
	"code": "20N10",
	"title": " Ternary systems (heaps, semiheaps, heapoids, etc.)",
	"parentcode": "20Nxx",
	"level": 3
}, {
	"code": "20N15",
	"title": " $n$-ary systems $(n\\ge 3)$",
	"parentcode": "20Nxx",
	"level": 3
}, {
	"code": "20N20",
	"title": " Hypergroups",
	"parentcode": "20Nxx",
	"level": 3
}, {
	"code": "20N25",
	"title": " Fuzzy groups [See also 03E72]",
	"parentcode": "20Nxx",
	"level": 3
}, {
	"code": "20N99",
	"title": " None of the above, but in this section",
	"parentcode": "20Nxx",
	"level": 3
}, {
	"code": "20Pxx",
	"title": " Probabilistic methods in group theory [See also 60Bxx]",
	"parentcode": "20-XX",
	"level": 2
}, {
	"code": "20P05",
	"title": " Probabilistic methods in group theory  [See also 60Bxx]",
	"parentcode": "20Pxx",
	"level": 3
}, {
	"code": "20P99",
	"title": " None of the above, but in this section",
	"parentcode": "20Pxx",
	"level": 3
}, {
	"code": "22-XX",
	"title": " Topological groups, Lie groups {For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX}",
	"parentcode": null,
	"level": 1
}, {
	"code": "22-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "22-XX",
	"level": 2
}, {
	"code": "22-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "22-XX",
	"level": 2
}, {
	"code": "22-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "22-XX",
	"level": 2
}, {
	"code": "22-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "22-XX",
	"level": 2
}, {
	"code": "22-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "22-XX",
	"level": 2
}, {
	"code": "22-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "22-XX",
	"level": 2
}, {
	"code": "22Axx",
	"title": " Topological and differentiable algebraic systems {For topological rings and fields, see 12Jxx, 13Jxx, 16W80}",
	"parentcode": "22-XX",
	"level": 2
}, {
	"code": "22A05",
	"title": " Structure of general topological groups",
	"parentcode": "22Axx",
	"level": 3
}, {
	"code": "22A10",
	"title": " Analysis on general topological groups",
	"parentcode": "22Axx",
	"level": 3
}, {
	"code": "22A15",
	"title": " Structure of topological semigroups",
	"parentcode": "22Axx",
	"level": 3
}, {
	"code": "22A20",
	"title": " Analysis on topological semigroups",
	"parentcode": "22Axx",
	"level": 3
}, {
	"code": "22A22",
	"title": " Topological groupoids (including differentiable and Lie groupoids) [See also 58H05]",
	"parentcode": "22Axx",
	"level": 3
}, {
	"code": "22A25",
	"title": " Representations of general topological groups and semigroups",
	"parentcode": "22Axx",
	"level": 3
}, {
	"code": "22A26",
	"title": " Topological semilattices, lattices and applications [See also 06B30, 06B35, 06F30]",
	"parentcode": "22Axx",
	"level": 3
}, {
	"code": "22A30",
	"title": " Other topological algebraic systems and their representations",
	"parentcode": "22Axx",
	"level": 3
}, {
	"code": "22A99",
	"title": " None of the above, but in this section",
	"parentcode": "22Axx",
	"level": 3
}, {
	"code": "22Bxx",
	"title": " Locally compact abelian groups (LCA groups)",
	"parentcode": "22-XX",
	"level": 2
}, {
	"code": "22B05",
	"title": " General properties and structure of LCA groups",
	"parentcode": "22Bxx",
	"level": 3
}, {
	"code": "22B10",
	"title": " Structure of group algebras of LCA groups",
	"parentcode": "22Bxx",
	"level": 3
}, {
	"code": "22B99",
	"title": " None of the above, but in this section",
	"parentcode": "22Bxx",
	"level": 3
}, {
	"code": "22Cxx",
	"title": " Compact groups",
	"parentcode": "22-XX",
	"level": 2
}, {
	"code": "22C05",
	"title": " Compact groups",
	"parentcode": "22Cxx",
	"level": 3
}, {
	"code": "22C99",
	"title": " None of the above, but in this section",
	"parentcode": "22Cxx",
	"level": 3
}, {
	"code": "22Dxx",
	"title": " Locally compact groups and their algebras",
	"parentcode": "22-XX",
	"level": 2
}, {
	"code": "22D05",
	"title": " General properties and structure of locally compact groups",
	"parentcode": "22Dxx",
	"level": 3
}, {
	"code": "22D10",
	"title": " Unitary representations of locally compact groups",
	"parentcode": "22Dxx",
	"level": 3
}, {
	"code": "22D12",
	"title": " Other representations of locally compact groups",
	"parentcode": "22Dxx",
	"level": 3
}, {
	"code": "22D15",
	"title": " Group algebras of locally compact groups",
	"parentcode": "22Dxx",
	"level": 3
}, {
	"code": "22D20",
	"title": " Representations of group algebras",
	"parentcode": "22Dxx",
	"level": 3
}, {
	"code": "22D25",
	"title": " $C^*$-algebras and $W^*$-algebras in relation to group representations [See also 46Lxx]",
	"parentcode": "22Dxx",
	"level": 3
}, {
	"code": "22D30",
	"title": " Induced representations",
	"parentcode": "22Dxx",
	"level": 3
}, {
	"code": "22D35",
	"title": " Duality theorems",
	"parentcode": "22Dxx",
	"level": 3
}, {
	"code": "22D40",
	"title": " Ergodic theory on groups [See also 28Dxx]",
	"parentcode": "22Dxx",
	"level": 3
}, {
	"code": "22D45",
	"title": " Automorphism groups of locally compact groups",
	"parentcode": "22Dxx",
	"level": 3
}, {
	"code": "22D99",
	"title": " None of the above, but in this section",
	"parentcode": "22Dxx",
	"level": 3
}, {
	"code": "22Exx",
	"title": " Lie groups {For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx; for analysis thereon, see 43A80, 43A85, 43A90}",
	"parentcode": "22-XX",
	"level": 2
}, {
	"code": "22E05",
	"title": " Local Lie groups [See also 34-XX, 35-XX, 58H05]",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E10",
	"title": " General properties and structure of complex Lie groups [See also 32M05]",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E15",
	"title": " General properties and structure of real Lie groups",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E20",
	"title": " General properties and structure of other Lie groups",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E25",
	"title": " Nilpotent and solvable Lie groups",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E27",
	"title": " Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E30",
	"title": " Analysis on real and complex Lie groups [See also 33C80, 43-XX]",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E35",
	"title": " Analysis on $p$-adic Lie groups",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E40",
	"title": " Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E41",
	"title": " Continuous cohomology [See also 57R32, 57Txx, 58H10]",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E43",
	"title": " Structure and representation of the Lorentz group",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E45",
	"title": " Representations of Lie and linear algebraic groups over real fields",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E46",
	"title": " Semisimple Lie groups and their representations",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E47",
	"title": " Representations of Lie and real algebraic groups",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E50",
	"title": " Representations of Lie and linear algebraic groups over local fields [See also 20G05]",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E55",
	"title": " Representations of Lie and linear algebraic groups over global fields and adèle rings [See also 20G05]",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E57",
	"title": " Geometric Langlands program",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E60",
	"title": " Lie algebras of Lie groups {For the algebraic theory of Lie algebras, see 17Bxx}",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E65",
	"title": " Infinite-dimensional Lie groups and their Lie algebras",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E66",
	"title": " Analysis on and representations of infinite-dimensional Lie groups",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E67",
	"title": " Loop groups and related constructions, group-theoretic treatment [See also 58D05]",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E70",
	"title": " Applications of Lie groups to physics; explicit representations [See also 81R05, 81R10]",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22E99",
	"title": " None of the above, but in this section",
	"parentcode": "22Exx",
	"level": 3
}, {
	"code": "22Fxx",
	"title": " Noncompact transformation groups",
	"parentcode": "22-XX",
	"level": 2
}, {
	"code": "22F05",
	"title": " General theory of group and pseudogroup actions {For topological properties of spaces with an action, see 57S20}",
	"parentcode": "22Fxx",
	"level": 3
}, {
	"code": "22F10",
	"title": " Measurable group actions [See also 22D40, 28Dxx, 37Axx]",
	"parentcode": "22Fxx",
	"level": 3
}, {
	"code": "22F30",
	"title": " Homogeneous spaces {For general actions on manifolds or preserving geometrical structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40}",
	"parentcode": "22Fxx",
	"level": 3
}, {
	"code": "22F50",
	"title": " Groups as automorphisms of other structures",
	"parentcode": "22Fxx",
	"level": 3
}, {
	"code": "22F99",
	"title": " None of the above, but in this section",
	"parentcode": "22Fxx",
	"level": 3
}, {
	"code": "26-XX",
	"title": " Real functions [See also 54C30]",
	"parentcode": null,
	"level": 1
}, {
	"code": "26-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "26-XX",
	"level": 2
}, {
	"code": "26-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "26-XX",
	"level": 2
}, {
	"code": "26-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "26-XX",
	"level": 2
}, {
	"code": "26-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "26-XX",
	"level": 2
}, {
	"code": "26-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "26-XX",
	"level": 2
}, {
	"code": "26-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "26-XX",
	"level": 2
}, {
	"code": "26Axx",
	"title": " Functions of one variable",
	"parentcode": "26-XX",
	"level": 2
}, {
	"code": "26A03",
	"title": " Foundations",
	"parentcode": "26Axx",
	"level": 3
}, {
	"code": "26A06",
	"title": " One-variable calculus",
	"parentcode": "26Axx",
	"level": 3
}, {
	"code": "26A09",
	"title": " Elementary functions",
	"parentcode": "26Axx",
	"level": 3
}, {
	"code": "26A12",
	"title": " Rate of growth of functions, orders of infinity, slowly varying functions [See also 26A48]",
	"parentcode": "26Axx",
	"level": 3
}, {
	"code": "26A15",
	"title": " Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27}",
	"parentcode": "26Axx",
	"level": 3
}, {
	"code": "26A16",
	"title": " Lipschitz (Hölder) classes",
	"parentcode": "26Axx",
	"level": 3
}, {
	"code": "26A18",
	"title": " Iteration [See also 37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H25]",
	"parentcode": "26Axx",
	"level": 3
}, {
	"code": "26A21",
	"title": " Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05]",
	"parentcode": "26Axx",
	"level": 3
}, {
	"code": "26A24",
	"title": " Differentiation (functions of one variable)",
	"parentcode": "26Axx",
	"level": 3
}, {
	"code": "26A27",
	"title": " Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives",
	"parentcode": "26Axx",
	"level": 3
}, {
	"code": "26A30",
	"title": " Singular functions, Cantor functions, functions with other special properties",
	"parentcode": "26Axx",
	"level": 3
}, {
	"code": "26A33",
	"title": " Fractional derivatives and integrals",
	"parentcode": "26Axx",
	"level": 3
}, {
	"code": "26A36",
	"title": " Antidifferentiation",
	"parentcode": "26Axx",
	"level": 3
}, {
	"code": "26A39",
	"title": " Denjoy and Perron integrals, other special integrals",
	"parentcode": "26Axx",
	"level": 3
}, {
	"code": "26A42",
	"title": " Integrals of Riemann, Stieltjes and Lebesgue type [See also 28-XX]",
	"parentcode": "26Axx",
	"level": 3
}, {
	"code": "26A45",
	"title": " Functions of bounded variation, generalizations",
	"parentcode": "26Axx",
	"level": 3
}, {
	"code": "26A46",
	"title": " Absolutely continuous functions",
	"parentcode": "26Axx",
	"level": 3
}, {
	"code": "26A48",
	"title": " Monotonic functions, generalizations",
	"parentcode": "26Axx",
	"level": 3
}, {
	"code": "26A51",
	"title": " Convexity, generalizations",
	"parentcode": "26Axx",
	"level": 3
}, {
	"code": "26A99",
	"title": " None of the above, but in this section",
	"parentcode": "26Axx",
	"level": 3
}, {
	"code": "26Bxx",
	"title": " Functions of several variables",
	"parentcode": "26-XX",
	"level": 2
}, {
	"code": "26B05",
	"title": " Continuity and differentiation questions",
	"parentcode": "26Bxx",
	"level": 3
}, {
	"code": "26B10",
	"title": " Implicit function theorems, Jacobians, transformations with several variables",
	"parentcode": "26Bxx",
	"level": 3
}, {
	"code": "26B12",
	"title": " Calculus of vector functions",
	"parentcode": "26Bxx",
	"level": 3
}, {
	"code": "26B15",
	"title": " Integration",
	"parentcode": "26Bxx",
	"level": 3
}, {
	"code": "26B20",
	"title": " Integral formulas (Stokes, Gauss, Green, etc.)",
	"parentcode": "26Bxx",
	"level": 3
}, {
	"code": "26B25",
	"title": " Convexity, generalizations",
	"parentcode": "26Bxx",
	"level": 3
}, {
	"code": "26B30",
	"title": " Absolutely continuous functions, functions of bounded variation",
	"parentcode": "26Bxx",
	"level": 3
}, {
	"code": "26B35",
	"title": " Special properties of functions of several variables, Hölder conditions, etc.",
	"parentcode": "26Bxx",
	"level": 3
}, {
	"code": "26B40",
	"title": " Representation and superposition of functions",
	"parentcode": "26Bxx",
	"level": 3
}, {
	"code": "26B99",
	"title": " None of the above, but in this section",
	"parentcode": "26Bxx",
	"level": 3
}, {
	"code": "26Cxx",
	"title": " Polynomials, rational functions",
	"parentcode": "26-XX",
	"level": 2
}, {
	"code": "26C05",
	"title": " Polynomials",
	"parentcode": "26Cxx",
	"level": 3
}, {
	"code": "26C10",
	"title": " Polynomials",
	"parentcode": "26Cxx",
	"level": 3
}, {
	"code": "26C15",
	"title": " Rational functions [See also 14Pxx]",
	"parentcode": "26Cxx",
	"level": 3
}, {
	"code": "26C99",
	"title": " None of the above, but in this section",
	"parentcode": "26Cxx",
	"level": 3
}, {
	"code": "26Dxx",
	"title": " Inequalities {For maximal function inequalities, see 42B25; for functional inequalities, see 39B72; for probabilistic inequalities, see 60E15}",
	"parentcode": "26-XX",
	"level": 2
}, {
	"code": "26D05",
	"title": " Inequalities for trigonometric functions and polynomials",
	"parentcode": "26Dxx",
	"level": 3
}, {
	"code": "26D07",
	"title": " Inequalities involving other types of functions",
	"parentcode": "26Dxx",
	"level": 3
}, {
	"code": "26D10",
	"title": " Inequalities involving derivatives and differential and integral operators",
	"parentcode": "26Dxx",
	"level": 3
}, {
	"code": "26D15",
	"title": " Inequalities for sums, series and integrals",
	"parentcode": "26Dxx",
	"level": 3
}, {
	"code": "26D20",
	"title": " Other analytical inequalities",
	"parentcode": "26Dxx",
	"level": 3
}, {
	"code": "26D99",
	"title": " None of the above, but in this section",
	"parentcode": "26Dxx",
	"level": 3
}, {
	"code": "26Exx",
	"title": " Miscellaneous topics [See also 58Cxx]",
	"parentcode": "26-XX",
	"level": 2
}, {
	"code": "26E05",
	"title": " Real-analytic functions [See also 32B05, 32C05]",
	"parentcode": "26Exx",
	"level": 3
}, {
	"code": "26E10",
	"title": " $C^\\infty$-functions, quasi-analytic functions [See also 58C25]",
	"parentcode": "26Exx",
	"level": 3
}, {
	"code": "26E15",
	"title": " Calculus of functions on infinite-dimensional spaces [See also 46G05, 58Cxx]",
	"parentcode": "26Exx",
	"level": 3
}, {
	"code": "26E20",
	"title": " Calculus of functions taking values in infinite-dimensional spaces [See also 46E40, 46G10, 58Cxx]",
	"parentcode": "26Exx",
	"level": 3
}, {
	"code": "26E25",
	"title": " Set-valued functions [See also 28B20, 49J53, 54C60] {For nonsmooth analysis, see 49J52, 58Cxx, 90Cxx}",
	"parentcode": "26Exx",
	"level": 3
}, {
	"code": "26E30",
	"title": " Non-Archimedean analysis [See also 12J25]",
	"parentcode": "26Exx",
	"level": 3
}, {
	"code": "26E35",
	"title": " Nonstandard analysis [See also 03H05, 28E05, 54J05]",
	"parentcode": "26Exx",
	"level": 3
}, {
	"code": "26E40",
	"title": " Constructive real analysis [See also 03F60]",
	"parentcode": "26Exx",
	"level": 3
}, {
	"code": "26E50",
	"title": " Fuzzy real analysis [See also 03E72, 28E10]",
	"parentcode": "26Exx",
	"level": 3
}, {
	"code": "26E60",
	"title": " Means [See also 47A64]",
	"parentcode": "26Exx",
	"level": 3
}, {
	"code": "26E70",
	"title": " Real analysis on time scales or measure chains {For dynamic equations on time scales or measure chains see 34N05}",
	"parentcode": "26Exx",
	"level": 3
}, {
	"code": "26E99",
	"title": " None of the above, but in this section",
	"parentcode": "26Exx",
	"level": 3
}, {
	"code": "28-XX",
	"title": " Measure and integration {For analysis on manifolds, see 58-XX}",
	"parentcode": null,
	"level": 1
}, {
	"code": "28-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "28-XX",
	"level": 2
}, {
	"code": "28-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "28-XX",
	"level": 2
}, {
	"code": "28-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "28-XX",
	"level": 2
}, {
	"code": "28-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "28-XX",
	"level": 2
}, {
	"code": "28-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "28-XX",
	"level": 2
}, {
	"code": "28-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "28-XX",
	"level": 2
}, {
	"code": "28Axx",
	"title": " Classical measure theory",
	"parentcode": "28-XX",
	"level": 2
}, {
	"code": "28A05",
	"title": " Classes of sets (Borel fields, $\\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]",
	"parentcode": "28Axx",
	"level": 3
}, {
	"code": "28A10",
	"title": " Real- or complex-valued set functions",
	"parentcode": "28Axx",
	"level": 3
}, {
	"code": "28A12",
	"title": " Contents, measures, outer measures, capacities",
	"parentcode": "28Axx",
	"level": 3
}, {
	"code": "28A15",
	"title": " Abstract differentiation theory, differentiation of set functions [See also 26A24]",
	"parentcode": "28Axx",
	"level": 3
}, {
	"code": "28A20",
	"title": " Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence",
	"parentcode": "28Axx",
	"level": 3
}, {
	"code": "28A25",
	"title": " Integration with respect to measures and other set functions",
	"parentcode": "28Axx",
	"level": 3
}, {
	"code": "28A33",
	"title": " Spaces of measures, convergence of measures [See also 46E27, 60Bxx]",
	"parentcode": "28Axx",
	"level": 3
}, {
	"code": "28A35",
	"title": " Measures and integrals in product spaces",
	"parentcode": "28Axx",
	"level": 3
}, {
	"code": "28A50",
	"title": " Integration and disintegration of measures",
	"parentcode": "28Axx",
	"level": 3
}, {
	"code": "28A51",
	"title": " Lifting theory [See also 46G15]",
	"parentcode": "28Axx",
	"level": 3
}, {
	"code": "28A60",
	"title": " Measures on Boolean rings, measure algebras [See also 54H10]",
	"parentcode": "28Axx",
	"level": 3
}, {
	"code": "28A75",
	"title": " Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]",
	"parentcode": "28Axx",
	"level": 3
}, {
	"code": "28A78",
	"title": " Hausdorff and packing measures",
	"parentcode": "28Axx",
	"level": 3
}, {
	"code": "28A80",
	"title": " Fractals [See also 37Fxx]",
	"parentcode": "28Axx",
	"level": 3
}, {
	"code": "28A99",
	"title": " None of the above, but in this section",
	"parentcode": "28Axx",
	"level": 3
}, {
	"code": "28Bxx",
	"title": " Set functions, measures and integrals with values in abstract spaces",
	"parentcode": "28-XX",
	"level": 2
}, {
	"code": "28B05",
	"title": " Vector-valued set functions, measures and integrals [See also 46G10]",
	"parentcode": "28Bxx",
	"level": 3
}, {
	"code": "28B10",
	"title": " Group- or semigroup-valued set functions, measures and integrals",
	"parentcode": "28Bxx",
	"level": 3
}, {
	"code": "28B15",
	"title": " Set functions, measures and integrals with values in ordered spaces",
	"parentcode": "28Bxx",
	"level": 3
}, {
	"code": "28B20",
	"title": " Set-valued set functions and measures; integration of set-valued functions; measurable selections [See also 26E25, 54C60, 54C65, 91B14]",
	"parentcode": "28Bxx",
	"level": 3
}, {
	"code": "28B99",
	"title": " None of the above, but in this section",
	"parentcode": "28Bxx",
	"level": 3
}, {
	"code": "28Cxx",
	"title": " Set functions and measures on spaces with additional structure [See also 46G12, 58C35, 58D20]",
	"parentcode": "28-XX",
	"level": 2
}, {
	"code": "28C05",
	"title": " Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures",
	"parentcode": "28Cxx",
	"level": 3
}, {
	"code": "28C10",
	"title": " Set functions and measures on topological groups or semigroups, Haar measures, invariant measures [See also 22Axx, 43A05]",
	"parentcode": "28Cxx",
	"level": 3
}, {
	"code": "28C15",
	"title": " Set functions and measures on topological spaces (regularity of measures, etc.)",
	"parentcode": "28Cxx",
	"level": 3
}, {
	"code": "28C20",
	"title": " Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11]",
	"parentcode": "28Cxx",
	"level": 3
}, {
	"code": "28C99",
	"title": " None of the above, but in this section",
	"parentcode": "28Cxx",
	"level": 3
}, {
	"code": "28Dxx",
	"title": " Measure-theoretic ergodic theory [See also 11K50, 11K55, 22D40, 37Axx, 47A35, 54H20, 60Fxx, 60G10]",
	"parentcode": "28-XX",
	"level": 2
}, {
	"code": "28D05",
	"title": " Measure-preserving transformations",
	"parentcode": "28Dxx",
	"level": 3
}, {
	"code": "28D10",
	"title": " One-parameter continuous families of measure-preserving transformations",
	"parentcode": "28Dxx",
	"level": 3
}, {
	"code": "28D15",
	"title": " General groups of measure-preserving transformations",
	"parentcode": "28Dxx",
	"level": 3
}, {
	"code": "28D20",
	"title": " Entropy and other invariants",
	"parentcode": "28Dxx",
	"level": 3
}, {
	"code": "28D99",
	"title": " None of the above, but in this section",
	"parentcode": "28Dxx",
	"level": 3
}, {
	"code": "28Exx",
	"title": " Miscellaneous topics in measure theory",
	"parentcode": "28-XX",
	"level": 2
}, {
	"code": "28E05",
	"title": " Nonstandard measure theory [See also 03H05, 26E35]",
	"parentcode": "28Exx",
	"level": 3
}, {
	"code": "28E10",
	"title": " Fuzzy measure theory [See also 03E72, 26E50, 94D05]",
	"parentcode": "28Exx",
	"level": 3
}, {
	"code": "28E15",
	"title": " Other connections with logic and set theory",
	"parentcode": "28Exx",
	"level": 3
}, {
	"code": "28E99",
	"title": " None of the above, but in this section",
	"parentcode": "28Exx",
	"level": 3
}, {
	"code": "30-XX",
	"title": " Functions of a complex variable {For analysis on manifolds, see 58-XX}",
	"parentcode": null,
	"level": 1
}, {
	"code": "30-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "30-XX",
	"level": 2
}, {
	"code": "30-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "30-XX",
	"level": 2
}, {
	"code": "30-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "30-XX",
	"level": 2
}, {
	"code": "30-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "30-XX",
	"level": 2
}, {
	"code": "30-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "30-XX",
	"level": 2
}, {
	"code": "30-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "30-XX",
	"level": 2
}, {
	"code": "30Axx",
	"title": " General properties",
	"parentcode": "30-XX",
	"level": 2
}, {
	"code": "30A05",
	"title": " Monogenic properties of complex functions (including polygenic and areolar monogenic functions)",
	"parentcode": "30Axx",
	"level": 3
}, {
	"code": "30A10",
	"title": " Inequalities in the complex domain",
	"parentcode": "30Axx",
	"level": 3
}, {
	"code": "30A99",
	"title": " None of the above, but in this section",
	"parentcode": "30Axx",
	"level": 3
}, {
	"code": "30Bxx",
	"title": " Series expansions",
	"parentcode": "30-XX",
	"level": 2
}, {
	"code": "30B10",
	"title": " Power series (including lacunary series)",
	"parentcode": "30Bxx",
	"level": 3
}, {
	"code": "30B20",
	"title": " Random power series",
	"parentcode": "30Bxx",
	"level": 3
}, {
	"code": "30B30",
	"title": " Boundary behavior of power series, over-convergence",
	"parentcode": "30Bxx",
	"level": 3
}, {
	"code": "30B40",
	"title": " Analytic continuation",
	"parentcode": "30Bxx",
	"level": 3
}, {
	"code": "30B50",
	"title": " Dirichlet series and other series expansions, exponential series [See also 11M41, 42-XX]",
	"parentcode": "30Bxx",
	"level": 3
}, {
	"code": "30B60",
	"title": " Completeness problems, closure of a system of functions",
	"parentcode": "30Bxx",
	"level": 3
}, {
	"code": "30B70",
	"title": " Continued fractions [See also 11A55, 40A15]",
	"parentcode": "30Bxx",
	"level": 3
}, {
	"code": "30B99",
	"title": " None of the above, but in this section",
	"parentcode": "30Bxx",
	"level": 3
}, {
	"code": "30Cxx",
	"title": " Geometric function theory",
	"parentcode": "30-XX",
	"level": 2
}, {
	"code": "30C10",
	"title": " Polynomials",
	"parentcode": "30Cxx",
	"level": 3
}, {
	"code": "30C15",
	"title": " Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) {For algebraic theory, see 12D10; for real methods, see 26C10}",
	"parentcode": "30Cxx",
	"level": 3
}, {
	"code": "30C20",
	"title": " Conformal mappings of special domains",
	"parentcode": "30Cxx",
	"level": 3
}, {
	"code": "30C25",
	"title": " Covering theorems in conformal mapping theory",
	"parentcode": "30Cxx",
	"level": 3
}, {
	"code": "30C30",
	"title": " Numerical methods in conformal mapping theory [See also 65E05]",
	"parentcode": "30Cxx",
	"level": 3
}, {
	"code": "30C35",
	"title": " General theory of conformal mappings",
	"parentcode": "30Cxx",
	"level": 3
}, {
	"code": "30C40",
	"title": " Kernel functions and applications",
	"parentcode": "30Cxx",
	"level": 3
}, {
	"code": "30C45",
	"title": " Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)",
	"parentcode": "30Cxx",
	"level": 3
}, {
	"code": "30C50",
	"title": " Coefficient problems for univalent and multivalent functions",
	"parentcode": "30Cxx",
	"level": 3
}, {
	"code": "30C55",
	"title": " General theory of univalent and multivalent functions",
	"parentcode": "30Cxx",
	"level": 3
}, {
	"code": "30C62",
	"title": " Quasiconformal mappings in the plane",
	"parentcode": "30Cxx",
	"level": 3
}, {
	"code": "30C65",
	"title": " Quasiconformal mappings in ${\\bf R}^n$, other generalizations",
	"parentcode": "30Cxx",
	"level": 3
}, {
	"code": "30C70",
	"title": " Extremal problems for conformal and quasiconformal mappings, variational methods",
	"parentcode": "30Cxx",
	"level": 3
}, {
	"code": "30C75",
	"title": " Extremal problems for conformal and quasiconformal mappings, other methods",
	"parentcode": "30Cxx",
	"level": 3
}, {
	"code": "30C80",
	"title": " Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination",
	"parentcode": "30Cxx",
	"level": 3
}, {
	"code": "30C85",
	"title": " Capacity and harmonic measure in the complex plane [See also 31A15]",
	"parentcode": "30Cxx",
	"level": 3
}, {
	"code": "30C99",
	"title": " None of the above, but in this section",
	"parentcode": "30Cxx",
	"level": 3
}, {
	"code": "30Dxx",
	"title": " Entire and meromorphic functions, and related topics",
	"parentcode": "30-XX",
	"level": 2
}, {
	"code": "30D05",
	"title": " Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX]",
	"parentcode": "30Dxx",
	"level": 3
}, {
	"code": "30D10",
	"title": " Representations of entire functions by series and integrals",
	"parentcode": "30Dxx",
	"level": 3
}, {
	"code": "30D15",
	"title": " Special classes of entire functions and growth estimates",
	"parentcode": "30Dxx",
	"level": 3
}, {
	"code": "30D20",
	"title": " Entire functions, general theory",
	"parentcode": "30Dxx",
	"level": 3
}, {
	"code": "30D30",
	"title": " Meromorphic functions, general theory",
	"parentcode": "30Dxx",
	"level": 3
}, {
	"code": "30D35",
	"title": " Distribution of values, Nevanlinna theory",
	"parentcode": "30Dxx",
	"level": 3
}, {
	"code": "30D40",
	"title": " Cluster sets, prime ends, boundary behavior",
	"parentcode": "30Dxx",
	"level": 3
}, {
	"code": "30D45",
	"title": " Bloch functions, normal functions, normal families",
	"parentcode": "30Dxx",
	"level": 3
}, {
	"code": "30D60",
	"title": " Quasi-analytic and other classes of functions",
	"parentcode": "30Dxx",
	"level": 3
}, {
	"code": "30D99",
	"title": " None of the above, but in this section",
	"parentcode": "30Dxx",
	"level": 3
}, {
	"code": "30Exx",
	"title": " Miscellaneous topics of analysis in the complex domain",
	"parentcode": "30-XX",
	"level": 2
}, {
	"code": "30E05",
	"title": " Moment problems, interpolation problems",
	"parentcode": "30Exx",
	"level": 3
}, {
	"code": "30E10",
	"title": " Approximation in the complex domain",
	"parentcode": "30Exx",
	"level": 3
}, {
	"code": "30E15",
	"title": " Asymptotic representations in the complex domain",
	"parentcode": "30Exx",
	"level": 3
}, {
	"code": "30E20",
	"title": " Integration, integrals of Cauchy type, integral representations of analytic functions [See also 45Exx]",
	"parentcode": "30Exx",
	"level": 3
}, {
	"code": "30E25",
	"title": " Boundary value problems [See also 45Exx]",
	"parentcode": "30Exx",
	"level": 3
}, {
	"code": "30E99",
	"title": " None of the above, but in this section",
	"parentcode": "30Exx",
	"level": 3
}, {
	"code": "30Fxx",
	"title": " Riemann surfaces",
	"parentcode": "30-XX",
	"level": 2
}, {
	"code": "30F10",
	"title": " Compact Riemann surfaces and uniformization [See also 14H15, 32G15]",
	"parentcode": "30Fxx",
	"level": 3
}, {
	"code": "30F15",
	"title": " Harmonic functions on Riemann surfaces",
	"parentcode": "30Fxx",
	"level": 3
}, {
	"code": "30F20",
	"title": " Classification theory of Riemann surfaces",
	"parentcode": "30Fxx",
	"level": 3
}, {
	"code": "30F25",
	"title": " Ideal boundary theory",
	"parentcode": "30Fxx",
	"level": 3
}, {
	"code": "30F30",
	"title": " Differentials on Riemann surfaces",
	"parentcode": "30Fxx",
	"level": 3
}, {
	"code": "30F35",
	"title": " Fuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx]",
	"parentcode": "30Fxx",
	"level": 3
}, {
	"code": "30F40",
	"title": " Kleinian groups [See also 20H10]",
	"parentcode": "30Fxx",
	"level": 3
}, {
	"code": "30F45",
	"title": " Conformal metrics (hyperbolic, Poincaré, distance functions)",
	"parentcode": "30Fxx",
	"level": 3
}, {
	"code": "30F50",
	"title": " Klein surfaces",
	"parentcode": "30Fxx",
	"level": 3
}, {
	"code": "30F60",
	"title": " Teichmüller theory [See also 32G15]",
	"parentcode": "30Fxx",
	"level": 3
}, {
	"code": "30F99",
	"title": " None of the above, but in this section",
	"parentcode": "30Fxx",
	"level": 3
}, {
	"code": "30Gxx",
	"title": " Generalized function theory",
	"parentcode": "30-XX",
	"level": 2
}, {
	"code": "30G06",
	"title": " Non-Archimedean function theory [See also 12J25]; nonstandard function theory [See also 03H05]",
	"parentcode": "30Gxx",
	"level": 3
}, {
	"code": "30G12",
	"title": " Finely holomorphic functions and topological function theory",
	"parentcode": "30Gxx",
	"level": 3
}, {
	"code": "30G20",
	"title": " Generalizations of Bers or Vekua type (pseudoanalytic, $p$-analytic, etc.)",
	"parentcode": "30Gxx",
	"level": 3
}, {
	"code": "30G25",
	"title": " Discrete analytic functions",
	"parentcode": "30Gxx",
	"level": 3
}, {
	"code": "30G30",
	"title": " Other generalizations of analytic functions (including abstract-valued functions)",
	"parentcode": "30Gxx",
	"level": 3
}, {
	"code": "30G35",
	"title": " Functions of hypercomplex variables and generalized variables",
	"parentcode": "30Gxx",
	"level": 3
}, {
	"code": "30G99",
	"title": " None of the above, but in this section",
	"parentcode": "30Gxx",
	"level": 3
}, {
	"code": "30Hxx",
	"title": " Spaces and algebras of analytic functions",
	"parentcode": "30-XX",
	"level": 2
}, {
	"code": "30H05",
	"title": " Bounded analytic functions",
	"parentcode": "30Hxx",
	"level": 3
}, {
	"code": "30H10",
	"title": " Hardy spaces",
	"parentcode": "30Hxx",
	"level": 3
}, {
	"code": "30H15",
	"title": " Nevanlinna class and Smirnov class",
	"parentcode": "30Hxx",
	"level": 3
}, {
	"code": "30H20",
	"title": " Bergman spaces, Fock spaces",
	"parentcode": "30Hxx",
	"level": 3
}, {
	"code": "30H25",
	"title": " Besov spaces and $Q_p$-spaces",
	"parentcode": "30Hxx",
	"level": 3
}, {
	"code": "30H30",
	"title": " Bloch spaces",
	"parentcode": "30Hxx",
	"level": 3
}, {
	"code": "30H35",
	"title": " BMO-spaces",
	"parentcode": "30Hxx",
	"level": 3
}, {
	"code": "30H50",
	"title": " Algebras of analytic functions",
	"parentcode": "30Hxx",
	"level": 3
}, {
	"code": "30H80",
	"title": " Corona theorems",
	"parentcode": "30Hxx",
	"level": 3
}, {
	"code": "30H99",
	"title": " None of the above, but in this section",
	"parentcode": "30Hxx",
	"level": 3
}, {
	"code": "30Jxx",
	"title": " Function theory on the disc",
	"parentcode": "30-XX",
	"level": 2
}, {
	"code": "30J05",
	"title": " Inner functions",
	"parentcode": "30Jxx",
	"level": 3
}, {
	"code": "30J10",
	"title": " Blaschke products",
	"parentcode": "30Jxx",
	"level": 3
}, {
	"code": "30J15",
	"title": " Singular inner functions",
	"parentcode": "30Jxx",
	"level": 3
}, {
	"code": "30J99",
	"title": " None of the above, but in this section",
	"parentcode": "30Jxx",
	"level": 3
}, {
	"code": "30Kxx",
	"title": " Universal holomorphic functions",
	"parentcode": "30-XX",
	"level": 2
}, {
	"code": "30K05",
	"title": " Universal Taylor series",
	"parentcode": "30Kxx",
	"level": 3
}, {
	"code": "30K10",
	"title": " Universal Dirichlet series",
	"parentcode": "30Kxx",
	"level": 3
}, {
	"code": "30K15",
	"title": " Bounded universal functions",
	"parentcode": "30Kxx",
	"level": 3
}, {
	"code": "30K20",
	"title": " Compositional universality",
	"parentcode": "30Kxx",
	"level": 3
}, {
	"code": "30K99",
	"title": " None of the above, but in this section",
	"parentcode": "30Kxx",
	"level": 3
}, {
	"code": "30Lxx",
	"title": " Analysis on metric spaces",
	"parentcode": "30-XX",
	"level": 2
}, {
	"code": "30L05",
	"title": " Geometric embeddings of metric spaces",
	"parentcode": "30Lxx",
	"level": 3
}, {
	"code": "30L10",
	"title": " Quasiconformal mappings  in metric spaces",
	"parentcode": "30Lxx",
	"level": 3
}, {
	"code": "30L99",
	"title": " None of the above, but in this section",
	"parentcode": "30Lxx",
	"level": 3
}, {
	"code": "31-XX",
	"title": " Potential theory {For probabilistic potential theory, see 60J45}",
	"parentcode": null,
	"level": 1
}, {
	"code": "31-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "31-XX",
	"level": 2
}, {
	"code": "31-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "31-XX",
	"level": 2
}, {
	"code": "31-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "31-XX",
	"level": 2
}, {
	"code": "31-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "31-XX",
	"level": 2
}, {
	"code": "31-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "31-XX",
	"level": 2
}, {
	"code": "31-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "31-XX",
	"level": 2
}, {
	"code": "31Axx",
	"title": " Two-dimensional theory",
	"parentcode": "31-XX",
	"level": 2
}, {
	"code": "31A05",
	"title": " Harmonic, subharmonic, superharmonic functions",
	"parentcode": "31Axx",
	"level": 3
}, {
	"code": "31A10",
	"title": " Integral representations, integral operators, integral equations methods",
	"parentcode": "31Axx",
	"level": 3
}, {
	"code": "31A15",
	"title": " Potentials and capacity, harmonic measure, extremal length [See also 30C85]",
	"parentcode": "31Axx",
	"level": 3
}, {
	"code": "31A20",
	"title": " Boundary behavior (theorems of Fatou type, etc.)",
	"parentcode": "31Axx",
	"level": 3
}, {
	"code": "31A25",
	"title": " Boundary value and inverse problems",
	"parentcode": "31Axx",
	"level": 3
}, {
	"code": "31A30",
	"title": " Biharmonic, polyharmonic functions and equations, Poisson's equation",
	"parentcode": "31Axx",
	"level": 3
}, {
	"code": "31A35",
	"title": " Connections with differential equations",
	"parentcode": "31Axx",
	"level": 3
}, {
	"code": "31A99",
	"title": " None of the above, but in this section",
	"parentcode": "31Axx",
	"level": 3
}, {
	"code": "31Bxx",
	"title": " Higher-dimensional theory",
	"parentcode": "31-XX",
	"level": 2
}, {
	"code": "31B05",
	"title": " Harmonic, subharmonic, superharmonic functions",
	"parentcode": "31Bxx",
	"level": 3
}, {
	"code": "31B10",
	"title": " Integral representations, integral operators, integral equations methods",
	"parentcode": "31Bxx",
	"level": 3
}, {
	"code": "31B15",
	"title": " Potentials and capacities, extremal length",
	"parentcode": "31Bxx",
	"level": 3
}, {
	"code": "31B20",
	"title": " Boundary value and inverse problems",
	"parentcode": "31Bxx",
	"level": 3
}, {
	"code": "31B25",
	"title": " Boundary behavior",
	"parentcode": "31Bxx",
	"level": 3
}, {
	"code": "31B30",
	"title": " Biharmonic and polyharmonic equations and functions",
	"parentcode": "31Bxx",
	"level": 3
}, {
	"code": "31B35",
	"title": " Connections with differential equations",
	"parentcode": "31Bxx",
	"level": 3
}, {
	"code": "31B99",
	"title": " None of the above, but in this section",
	"parentcode": "31Bxx",
	"level": 3
}, {
	"code": "31Cxx",
	"title": " Other generalizations",
	"parentcode": "31-XX",
	"level": 2
}, {
	"code": "31C05",
	"title": " Harmonic, subharmonic, superharmonic functions",
	"parentcode": "31Cxx",
	"level": 3
}, {
	"code": "31C10",
	"title": " Pluriharmonic and plurisubharmonic functions [See also 32U05]",
	"parentcode": "31Cxx",
	"level": 3
}, {
	"code": "31C12",
	"title": " Potential theory on Riemannian manifolds [See also 53C20; for Hodge theory, see 58A14]",
	"parentcode": "31Cxx",
	"level": 3
}, {
	"code": "31C15",
	"title": " Potentials and capacities",
	"parentcode": "31Cxx",
	"level": 3
}, {
	"code": "31C20",
	"title": " Discrete potential theory and numerical methods",
	"parentcode": "31Cxx",
	"level": 3
}, {
	"code": "31C25",
	"title": " Dirichlet spaces",
	"parentcode": "31Cxx",
	"level": 3
}, {
	"code": "31C35",
	"title": " Martin boundary theory [See also 60J50]",
	"parentcode": "31Cxx",
	"level": 3
}, {
	"code": "31C40",
	"title": " Fine potential theory",
	"parentcode": "31Cxx",
	"level": 3
}, {
	"code": "31C45",
	"title": " Other generalizations (nonlinear potential theory, etc.)",
	"parentcode": "31Cxx",
	"level": 3
}, {
	"code": "31C99",
	"title": " None of the above, but in this section",
	"parentcode": "31Cxx",
	"level": 3
}, {
	"code": "31Dxx",
	"title": "  Axiomatic potential theory",
	"parentcode": "31-XX",
	"level": 2
}, {
	"code": "31D05",
	"title": "  Axiomatic potential theory",
	"parentcode": "31Dxx",
	"level": 3
}, {
	"code": "31D99",
	"title": "  None of the above, but in this section",
	"parentcode": "31Dxx",
	"level": 3
}, {
	"code": "31Exx",
	"title": "  Potential theory on metric spaces",
	"parentcode": "31-XX",
	"level": 2
}, {
	"code": "31E05",
	"title": "  Potential theory on metric spaces",
	"parentcode": "31Exx",
	"level": 3
}, {
	"code": "31E99",
	"title": "  None of the above, but in this section",
	"parentcode": "31Exx",
	"level": 3
}, {
	"code": "32-XX",
	"title": " Several complex variables and analytic spaces {For infinite-dimensional holomorphy, see 46G20, 58B12}",
	"parentcode": null,
	"level": 1
}, {
	"code": "32-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32Axx",
	"title": " Holomorphic functions of several complex variables",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32A05",
	"title": " Power series, series of functions",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A07",
	"title": " Special domains (Reinhardt, Hartogs, circular, tube)",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A10",
	"title": " Holomorphic functions",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A12",
	"title": " Multifunctions",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A15",
	"title": " Entire functions",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A17",
	"title": " Special families of functions",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A18",
	"title": " Bloch functions, normal functions",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A19",
	"title": " Normal families of functions, mappings",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A20",
	"title": " Meromorphic functions",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A22",
	"title": " Nevanlinna theory (local); growth estimates; other inequalities {For geometric theory, see 32H25, 32H30}",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A25",
	"title": " Integral representations; canonical kernels (Szegő, Bergman, etc.)",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A26",
	"title": " Integral representations, constructed kernels (e.g. Cauchy, Fantappiè-type kernels)",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A27",
	"title": " Local theory of residues [See also 32C30]",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A30",
	"title": " Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30) {For functions of several hypercomplex variables, see 30G35}",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A35",
	"title": " $H^p$-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15]",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A36",
	"title": " Bergman spaces",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A37",
	"title": " Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx]",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A38",
	"title": " Algebras of holomorphic functions [See also 30H05, 46J10, 46J15]",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A40",
	"title": " Boundary behavior of holomorphic functions",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A45",
	"title": " Hyperfunctions [See also 46F15]",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A50",
	"title": " Harmonic analysis of several complex variables [See mainly 43-XX]",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A55",
	"title": " Singular integrals",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A60",
	"title": " Zero sets of holomorphic functions",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A65",
	"title": " Banach algebra techniques [See mainly 46Jxx]",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A70",
	"title": " Functional analysis techniques [See mainly 46Exx]",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32A99",
	"title": " None of the above, but in this section",
	"parentcode": "32Axx",
	"level": 3
}, {
	"code": "32Bxx",
	"title": " Local analytic geometry [See also 13-XX and 14-XX]",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32B05",
	"title": " Analytic algebras and generalizations, preparation theorems",
	"parentcode": "32Bxx",
	"level": 3
}, {
	"code": "32B10",
	"title": " Germs of analytic sets, local parametrization",
	"parentcode": "32Bxx",
	"level": 3
}, {
	"code": "32B15",
	"title": " Analytic subsets of affine space",
	"parentcode": "32Bxx",
	"level": 3
}, {
	"code": "32B20",
	"title": " Semi-analytic sets and subanalytic sets [See also 14P15]",
	"parentcode": "32Bxx",
	"level": 3
}, {
	"code": "32B25",
	"title": " Triangulation and related questions",
	"parentcode": "32Bxx",
	"level": 3
}, {
	"code": "32B99",
	"title": " None of the above, but in this section",
	"parentcode": "32Bxx",
	"level": 3
}, {
	"code": "32Cxx",
	"title": " Analytic spaces",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32C05",
	"title": " Real-analytic manifolds, real-analytic spaces [See also 14Pxx, 58A07]",
	"parentcode": "32Cxx",
	"level": 3
}, {
	"code": "32C07",
	"title": " Real-analytic sets, complex Nash functions [See also 14P15, 14P20]",
	"parentcode": "32Cxx",
	"level": 3
}, {
	"code": "32C09",
	"title": " Embedding of real analytic manifolds",
	"parentcode": "32Cxx",
	"level": 3
}, {
	"code": "32C11",
	"title": " Complex supergeometry [See also 14A22, 14M30, 58A50]",
	"parentcode": "32Cxx",
	"level": 3
}, {
	"code": "32C15",
	"title": " Complex spaces",
	"parentcode": "32Cxx",
	"level": 3
}, {
	"code": "32C18",
	"title": " Topology of analytic spaces",
	"parentcode": "32Cxx",
	"level": 3
}, {
	"code": "32C20",
	"title": " Normal analytic spaces",
	"parentcode": "32Cxx",
	"level": 3
}, {
	"code": "32C22",
	"title": " Embedding of analytic spaces",
	"parentcode": "32Cxx",
	"level": 3
}, {
	"code": "32C25",
	"title": " Analytic subsets and submanifolds",
	"parentcode": "32Cxx",
	"level": 3
}, {
	"code": "32C30",
	"title": " Integration on analytic sets and spaces, currents {For local theory, see 32A25 or 32A27}",
	"parentcode": "32Cxx",
	"level": 3
}, {
	"code": "32C35",
	"title": " Analytic sheaves and cohomology groups [See also 14Fxx, 18F20, 55N30]",
	"parentcode": "32Cxx",
	"level": 3
}, {
	"code": "32C36",
	"title": " Local cohomology of analytic spaces",
	"parentcode": "32Cxx",
	"level": 3
}, {
	"code": "32C37",
	"title": " Duality theorems",
	"parentcode": "32Cxx",
	"level": 3
}, {
	"code": "32C38",
	"title": " Sheaves of differential operators and their modules, $D$-modules [See also 14F10, 16S32, 35A27, 58J15]",
	"parentcode": "32Cxx",
	"level": 3
}, {
	"code": "32C55",
	"title": " The Levi problem in complex spaces; generalizations",
	"parentcode": "32Cxx",
	"level": 3
}, {
	"code": "32C81",
	"title": " Applications to physics",
	"parentcode": "32Cxx",
	"level": 3
}, {
	"code": "32C99",
	"title": " None of the above, but in this section",
	"parentcode": "32Cxx",
	"level": 3
}, {
	"code": "32Dxx",
	"title": " Analytic continuation",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32D05",
	"title": " Domains of holomorphy",
	"parentcode": "32Dxx",
	"level": 3
}, {
	"code": "32D10",
	"title": " Envelopes of holomorphy",
	"parentcode": "32Dxx",
	"level": 3
}, {
	"code": "32D15",
	"title": " Continuation of analytic objects",
	"parentcode": "32Dxx",
	"level": 3
}, {
	"code": "32D20",
	"title": " Removable singularities",
	"parentcode": "32Dxx",
	"level": 3
}, {
	"code": "32D26",
	"title": " Riemann domains",
	"parentcode": "32Dxx",
	"level": 3
}, {
	"code": "32D99",
	"title": " None of the above, but in this section",
	"parentcode": "32Dxx",
	"level": 3
}, {
	"code": "32Exx",
	"title": " Holomorphic convexity",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32E05",
	"title": " Holomorphically convex complex spaces, reduction theory",
	"parentcode": "32Exx",
	"level": 3
}, {
	"code": "32E10",
	"title": " Stein spaces, Stein manifolds",
	"parentcode": "32Exx",
	"level": 3
}, {
	"code": "32E20",
	"title": " Polynomial convexity",
	"parentcode": "32Exx",
	"level": 3
}, {
	"code": "32E30",
	"title": " Holomorphic and polynomial approximation, Runge pairs, interpolation",
	"parentcode": "32Exx",
	"level": 3
}, {
	"code": "32E35",
	"title": " Global boundary behavior of holomorphic functions",
	"parentcode": "32Exx",
	"level": 3
}, {
	"code": "32E40",
	"title": " The Levi problem",
	"parentcode": "32Exx",
	"level": 3
}, {
	"code": "32E99",
	"title": " None of the above, but in this section",
	"parentcode": "32Exx",
	"level": 3
}, {
	"code": "32Fxx",
	"title": " Geometric convexity",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32F10",
	"title": " $q$-convexity, $q$-concavity",
	"parentcode": "32Fxx",
	"level": 3
}, {
	"code": "32F17",
	"title": " Other notions of convexity",
	"parentcode": "32Fxx",
	"level": 3
}, {
	"code": "32F18",
	"title": " Finite-type conditions",
	"parentcode": "32Fxx",
	"level": 3
}, {
	"code": "32F27",
	"title": " Topological consequences of geometric convexity",
	"parentcode": "32Fxx",
	"level": 3
}, {
	"code": "32F32",
	"title": " Analytical consequences of geometric convexity (vanishing theorems, etc.)",
	"parentcode": "32Fxx",
	"level": 3
}, {
	"code": "32F45",
	"title": " Invariant metrics and pseudodistances",
	"parentcode": "32Fxx",
	"level": 3
}, {
	"code": "32F99",
	"title": " None of the above, but in this section",
	"parentcode": "32Fxx",
	"level": 3
}, {
	"code": "32Gxx",
	"title": " Deformations of analytic structures",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32G05",
	"title": " Deformations of complex structures [See also 13D10, 16S80, 58H10, 58H15]",
	"parentcode": "32Gxx",
	"level": 3
}, {
	"code": "32G07",
	"title": " Deformations of special (e.g. CR) structures",
	"parentcode": "32Gxx",
	"level": 3
}, {
	"code": "32G08",
	"title": " Deformations of fiber bundles",
	"parentcode": "32Gxx",
	"level": 3
}, {
	"code": "32G10",
	"title": " Deformations of submanifolds and subspaces",
	"parentcode": "32Gxx",
	"level": 3
}, {
	"code": "32G13",
	"title": " Analytic moduli problems {For algebraic moduli problems, see 14D20, 14D22, 14H10, 14J10} [See also 14H15, 14J15]",
	"parentcode": "32Gxx",
	"level": 3
}, {
	"code": "32G15",
	"title": " Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]",
	"parentcode": "32Gxx",
	"level": 3
}, {
	"code": "32G20",
	"title": " Period matrices, variation of Hodge structure; degenerations [See also 14D05, 14D07, 14K30]",
	"parentcode": "32Gxx",
	"level": 3
}, {
	"code": "32G34",
	"title": " Moduli and deformations for ordinary differential equations (e.g. Knizhnik-Zamolodchikov equation) [See also 34Mxx]",
	"parentcode": "32Gxx",
	"level": 3
}, {
	"code": "32G81",
	"title": " Applications to physics",
	"parentcode": "32Gxx",
	"level": 3
}, {
	"code": "32G99",
	"title": " None of the above, but in this section",
	"parentcode": "32Gxx",
	"level": 3
}, {
	"code": "32Hxx",
	"title": " Holomorphic mappings and correspondences",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32H02",
	"title": " Holomorphic mappings, (holomorphic) embeddings and related questions",
	"parentcode": "32Hxx",
	"level": 3
}, {
	"code": "32H04",
	"title": " Meromorphic mappings",
	"parentcode": "32Hxx",
	"level": 3
}, {
	"code": "32H12",
	"title": " Boundary uniqueness of mappings",
	"parentcode": "32Hxx",
	"level": 3
}, {
	"code": "32H25",
	"title": " Picard-type theorems and generalizations {For function-theoretic properties, see 32A22}",
	"parentcode": "32Hxx",
	"level": 3
}, {
	"code": "32H30",
	"title": " Value distribution theory in higher dimensions {For function-theoretic properties, see 32A22}",
	"parentcode": "32Hxx",
	"level": 3
}, {
	"code": "32H35",
	"title": " Proper mappings, finiteness theorems",
	"parentcode": "32Hxx",
	"level": 3
}, {
	"code": "32H40",
	"title": " Boundary regularity of mappings",
	"parentcode": "32Hxx",
	"level": 3
}, {
	"code": "32H50",
	"title": " Iteration problems",
	"parentcode": "32Hxx",
	"level": 3
}, {
	"code": "32H99",
	"title": " None of the above, but in this section",
	"parentcode": "32Hxx",
	"level": 3
}, {
	"code": "32Jxx",
	"title": " Compact analytic spaces {For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic theory, see 14Jxx}",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32J05",
	"title": " Compactification of analytic spaces",
	"parentcode": "32Jxx",
	"level": 3
}, {
	"code": "32J10",
	"title": " Algebraic dependence theorems",
	"parentcode": "32Jxx",
	"level": 3
}, {
	"code": "32J15",
	"title": " Compact surfaces",
	"parentcode": "32Jxx",
	"level": 3
}, {
	"code": "32J17",
	"title": " Compact $3$-folds",
	"parentcode": "32Jxx",
	"level": 3
}, {
	"code": "32J18",
	"title": " Compact $n$-folds",
	"parentcode": "32Jxx",
	"level": 3
}, {
	"code": "32J25",
	"title": " Transcendental methods of algebraic geometry [See also 14C30]",
	"parentcode": "32Jxx",
	"level": 3
}, {
	"code": "32J27",
	"title": " Compact Kähler manifolds",
	"parentcode": "32Jxx",
	"level": 3
}, {
	"code": "32J81",
	"title": " Applications to physics",
	"parentcode": "32Jxx",
	"level": 3
}, {
	"code": "32J99",
	"title": " None of the above, but in this section",
	"parentcode": "32Jxx",
	"level": 3
}, {
	"code": "32Kxx",
	"title": " Generalizations of analytic spaces (should also be assigned at least one other classification number from Section 32 describing the type of problem)",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32K05",
	"title": " Banach analytic spaces [See also 58Bxx]",
	"parentcode": "32Kxx",
	"level": 3
}, {
	"code": "32K07",
	"title": " Formal and graded complex spaces [See also 58C50]",
	"parentcode": "32Kxx",
	"level": 3
}, {
	"code": "32K15",
	"title": " Differentiable functions on analytic spaces, differentiable spaces [See also 58C25]",
	"parentcode": "32Kxx",
	"level": 3
}, {
	"code": "32K99",
	"title": " None of the above, but in this section",
	"parentcode": "32Kxx",
	"level": 3
}, {
	"code": "32Lxx",
	"title": " Holomorphic fiber spaces [See also 55Rxx]",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32L05",
	"title": " Holomorphic bundles and generalizations",
	"parentcode": "32Lxx",
	"level": 3
}, {
	"code": "32L10",
	"title": " Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F05, 18F20, 55N30]",
	"parentcode": "32Lxx",
	"level": 3
}, {
	"code": "32L15",
	"title": " Bundle convexity [See also 32F10]",
	"parentcode": "32Lxx",
	"level": 3
}, {
	"code": "32L20",
	"title": " Vanishing theorems",
	"parentcode": "32Lxx",
	"level": 3
}, {
	"code": "32L25",
	"title": " Twistor theory, double fibrations [See also 53C28]",
	"parentcode": "32Lxx",
	"level": 3
}, {
	"code": "32L81",
	"title": " Applications to physics",
	"parentcode": "32Lxx",
	"level": 3
}, {
	"code": "32L99",
	"title": " None of the above, but in this section",
	"parentcode": "32Lxx",
	"level": 3
}, {
	"code": "32Mxx",
	"title": " Complex spaces with a group of automorphisms",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32M05",
	"title": " Complex Lie groups, automorphism groups acting on complex spaces [See also 22E10]",
	"parentcode": "32Mxx",
	"level": 3
}, {
	"code": "32M10",
	"title": " Homogeneous complex manifolds [See also 14M17, 57T15]",
	"parentcode": "32Mxx",
	"level": 3
}, {
	"code": "32M12",
	"title": " Almost homogeneous manifolds and spaces [See also 14M17]",
	"parentcode": "32Mxx",
	"level": 3
}, {
	"code": "32M15",
	"title": " Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15]",
	"parentcode": "32Mxx",
	"level": 3
}, {
	"code": "32M17",
	"title": " Automorphism groups of ${\\bf C}^n$ and affine manifolds",
	"parentcode": "32Mxx",
	"level": 3
}, {
	"code": "32M25",
	"title": " Complex vector fields",
	"parentcode": "32Mxx",
	"level": 3
}, {
	"code": "32M99",
	"title": " None of the above, but in this section",
	"parentcode": "32Mxx",
	"level": 3
}, {
	"code": "32Nxx",
	"title": " Automorphic functions [See also 11Fxx, 20H10, 22E40, 30F35]",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32N05",
	"title": " General theory of automorphic functions of several complex variables",
	"parentcode": "32Nxx",
	"level": 3
}, {
	"code": "32N10",
	"title": " Automorphic forms",
	"parentcode": "32Nxx",
	"level": 3
}, {
	"code": "32N15",
	"title": " Automorphic functions in symmetric domains",
	"parentcode": "32Nxx",
	"level": 3
}, {
	"code": "32N99",
	"title": " None of the above, but in this section",
	"parentcode": "32Nxx",
	"level": 3
}, {
	"code": "32Pxx",
	"title": " Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32P05",
	"title": " Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)",
	"parentcode": "32Pxx",
	"level": 3
}, {
	"code": "32P99",
	"title": " None of the above, but in this section",
	"parentcode": "32Pxx",
	"level": 3
}, {
	"code": "32Qxx",
	"title": " Complex manifolds",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32Q05",
	"title": " Negative curvature manifolds",
	"parentcode": "32Qxx",
	"level": 3
}, {
	"code": "32Q10",
	"title": " Positive curvature manifolds",
	"parentcode": "32Qxx",
	"level": 3
}, {
	"code": "32Q15",
	"title": " Kähler manifolds",
	"parentcode": "32Qxx",
	"level": 3
}, {
	"code": "32Q20",
	"title": " Kähler-Einstein manifolds [See also 53Cxx]",
	"parentcode": "32Qxx",
	"level": 3
}, {
	"code": "32Q25",
	"title": " Calabi-Yau theory [See also 14J30]",
	"parentcode": "32Qxx",
	"level": 3
}, {
	"code": "32Q26",
	"title": " Notions of stability",
	"parentcode": "32Qxx",
	"level": 3
}, {
	"code": "32Q28",
	"title": " Stein manifolds",
	"parentcode": "32Qxx",
	"level": 3
}, {
	"code": "32Q30",
	"title": " Uniformization",
	"parentcode": "32Qxx",
	"level": 3
}, {
	"code": "32Q35",
	"title": " Complex manifolds as subdomains of Euclidean space",
	"parentcode": "32Qxx",
	"level": 3
}, {
	"code": "32Q40",
	"title": " Embedding theorems",
	"parentcode": "32Qxx",
	"level": 3
}, {
	"code": "32Q45",
	"title": " Hyperbolic and Kobayashi hyperbolic manifolds",
	"parentcode": "32Qxx",
	"level": 3
}, {
	"code": "32Q55",
	"title": " Topological aspects of complex manifolds",
	"parentcode": "32Qxx",
	"level": 3
}, {
	"code": "32Q57",
	"title": " Classification theorems",
	"parentcode": "32Qxx",
	"level": 3
}, {
	"code": "32Q60",
	"title": " Almost complex manifolds",
	"parentcode": "32Qxx",
	"level": 3
}, {
	"code": "32Q65",
	"title": " Pseudoholomorphic curves",
	"parentcode": "32Qxx",
	"level": 3
}, {
	"code": "32Q99",
	"title": " None of the above, but in this section",
	"parentcode": "32Qxx",
	"level": 3
}, {
	"code": "32Sxx",
	"title": " Singularities [See also 58Kxx]",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32S05",
	"title": " Local singularities [See also 14J17]",
	"parentcode": "32Sxx",
	"level": 3
}, {
	"code": "32S10",
	"title": " Invariants of analytic local rings",
	"parentcode": "32Sxx",
	"level": 3
}, {
	"code": "32S15",
	"title": " Equisingularity (topological and analytic) [See also 14E15]",
	"parentcode": "32Sxx",
	"level": 3
}, {
	"code": "32S20",
	"title": " Global theory of singularities; cohomological properties [See also 14E15]",
	"parentcode": "32Sxx",
	"level": 3
}, {
	"code": "32S22",
	"title": " Relations with arrangements of hyperplanes [See also 52C35]",
	"parentcode": "32Sxx",
	"level": 3
}, {
	"code": "32S25",
	"title": " Surface and hypersurface singularities [See also 14J17]",
	"parentcode": "32Sxx",
	"level": 3
}, {
	"code": "32S30",
	"title": " Deformations of singularities; vanishing cycles [See also 14B07]",
	"parentcode": "32Sxx",
	"level": 3
}, {
	"code": "32S35",
	"title": " Mixed Hodge theory of singular varieties [See also 14C30, 14D07]",
	"parentcode": "32Sxx",
	"level": 3
}, {
	"code": "32S40",
	"title": " Monodromy; relations with differential equations and $D$-modules",
	"parentcode": "32Sxx",
	"level": 3
}, {
	"code": "32S45",
	"title": " Modifications; resolution of singularities [See also 14E15]",
	"parentcode": "32Sxx",
	"level": 3
}, {
	"code": "32S50",
	"title": " Topological aspects",
	"parentcode": "32Sxx",
	"level": 3
}, {
	"code": "32S55",
	"title": " Milnor fibration; relations with knot theory [See also 57M25, 57Q45]",
	"parentcode": "32Sxx",
	"level": 3
}, {
	"code": "32S60",
	"title": " Stratifications; constructible sheaves; intersection cohomology [See also 58Kxx]",
	"parentcode": "32Sxx",
	"level": 3
}, {
	"code": "32S65",
	"title": " Singularities of holomorphic vector fields and foliations",
	"parentcode": "32Sxx",
	"level": 3
}, {
	"code": "32S70",
	"title": " Other operations on singularities",
	"parentcode": "32Sxx",
	"level": 3
}, {
	"code": "32S99",
	"title": " None of the above, but in this section",
	"parentcode": "32Sxx",
	"level": 3
}, {
	"code": "32Txx",
	"title": " Pseudoconvex domains",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32T05",
	"title": " Domains of holomorphy",
	"parentcode": "32Txx",
	"level": 3
}, {
	"code": "32T15",
	"title": " Strongly pseudoconvex domains",
	"parentcode": "32Txx",
	"level": 3
}, {
	"code": "32T20",
	"title": " Worm domains",
	"parentcode": "32Txx",
	"level": 3
}, {
	"code": "32T25",
	"title": " Finite type domains",
	"parentcode": "32Txx",
	"level": 3
}, {
	"code": "32T27",
	"title": " Geometric and analytic invariants on weakly pseudoconvex boundaries",
	"parentcode": "32Txx",
	"level": 3
}, {
	"code": "32T35",
	"title": " Exhaustion functions",
	"parentcode": "32Txx",
	"level": 3
}, {
	"code": "32T40",
	"title": " Peak functions",
	"parentcode": "32Txx",
	"level": 3
}, {
	"code": "32T99",
	"title": " None of the above, but in this section",
	"parentcode": "32Txx",
	"level": 3
}, {
	"code": "32Uxx",
	"title": " Pluripotential theory",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32U05",
	"title": " Plurisubharmonic functions and generalizations [See also 31C10]",
	"parentcode": "32Uxx",
	"level": 3
}, {
	"code": "32U10",
	"title": " Plurisubharmonic exhaustion functions",
	"parentcode": "32Uxx",
	"level": 3
}, {
	"code": "32U15",
	"title": " General pluripotential theory",
	"parentcode": "32Uxx",
	"level": 3
}, {
	"code": "32U20",
	"title": " Capacity theory and generalizations",
	"parentcode": "32Uxx",
	"level": 3
}, {
	"code": "32U25",
	"title": " Lelong numbers",
	"parentcode": "32Uxx",
	"level": 3
}, {
	"code": "32U30",
	"title": " Removable sets",
	"parentcode": "32Uxx",
	"level": 3
}, {
	"code": "32U35",
	"title": " Pluricomplex Green functions",
	"parentcode": "32Uxx",
	"level": 3
}, {
	"code": "32U40",
	"title": " Currents",
	"parentcode": "32Uxx",
	"level": 3
}, {
	"code": "32U99",
	"title": " None of the above, but in this section",
	"parentcode": "32Uxx",
	"level": 3
}, {
	"code": "32Vxx",
	"title": " CR manifolds",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32V05",
	"title": " CR structures, CR operators, and generalizations",
	"parentcode": "32Vxx",
	"level": 3
}, {
	"code": "32V10",
	"title": " CR functions",
	"parentcode": "32Vxx",
	"level": 3
}, {
	"code": "32V15",
	"title": " CR manifolds as boundaries of domains",
	"parentcode": "32Vxx",
	"level": 3
}, {
	"code": "32V20",
	"title": " Analysis on CR manifolds",
	"parentcode": "32Vxx",
	"level": 3
}, {
	"code": "32V25",
	"title": " Extension of functions and other analytic objects from CR manifolds",
	"parentcode": "32Vxx",
	"level": 3
}, {
	"code": "32V30",
	"title": " Embeddings of CR manifolds",
	"parentcode": "32Vxx",
	"level": 3
}, {
	"code": "32V35",
	"title": " Finite type conditions on CR manifolds",
	"parentcode": "32Vxx",
	"level": 3
}, {
	"code": "32V40",
	"title": " Real submanifolds in complex manifolds",
	"parentcode": "32Vxx",
	"level": 3
}, {
	"code": "32V99",
	"title": " None of the above, but in this section",
	"parentcode": "32Vxx",
	"level": 3
}, {
	"code": "32Wxx",
	"title": " Differential operators in several variables",
	"parentcode": "32-XX",
	"level": 2
}, {
	"code": "32W05",
	"title": " $\\overline\\partial$ and $\\overline\\partial$-Neumann operators",
	"parentcode": "32Wxx",
	"level": 3
}, {
	"code": "32W10",
	"title": " $\\overline\\partial_b$ and $\\overline\\partial_b$-Neumann operators",
	"parentcode": "32Wxx",
	"level": 3
}, {
	"code": "32W20",
	"title": " Complex Monge-Ampère operators",
	"parentcode": "32Wxx",
	"level": 3
}, {
	"code": "32W25",
	"title": " Pseudodifferential operators in several complex variables",
	"parentcode": "32Wxx",
	"level": 3
}, {
	"code": "32W30",
	"title": " Heat kernels in several complex variables",
	"parentcode": "32Wxx",
	"level": 3
}, {
	"code": "32W50",
	"title": " Other partial differential equations of complex analysis",
	"parentcode": "32Wxx",
	"level": 3
}, {
	"code": "32W99",
	"title": " None of the above, but in this section",
	"parentcode": "32Wxx",
	"level": 3
}, {
	"code": "33-XX",
	"title": " Special functions (33-XX deals with the properties of functions as functions) {For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for representation theory see 22Exx}",
	"parentcode": null,
	"level": 1
}, {
	"code": "33-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "33-XX",
	"level": 2
}, {
	"code": "33-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "33-XX",
	"level": 2
}, {
	"code": "33-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "33-XX",
	"level": 2
}, {
	"code": "33-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "33-XX",
	"level": 2
}, {
	"code": "33-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "33-XX",
	"level": 2
}, {
	"code": "33-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "33-XX",
	"level": 2
}, {
	"code": "33Bxx",
	"title": " Elementary classical functions",
	"parentcode": "33-XX",
	"level": 2
}, {
	"code": "33B10",
	"title": " Exponential and trigonometric functions",
	"parentcode": "33Bxx",
	"level": 3
}, {
	"code": "33B15",
	"title": " Gamma, beta and polygamma functions",
	"parentcode": "33Bxx",
	"level": 3
}, {
	"code": "33B20",
	"title": " Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)",
	"parentcode": "33Bxx",
	"level": 3
}, {
	"code": "33B30",
	"title": " Higher logarithm functions",
	"parentcode": "33Bxx",
	"level": 3
}, {
	"code": "33B99",
	"title": " None of the above, but in this section",
	"parentcode": "33Bxx",
	"level": 3
}, {
	"code": "33Cxx",
	"title": " Hypergeometric functions",
	"parentcode": "33-XX",
	"level": 2
}, {
	"code": "33C05",
	"title": " Classical hypergeometric functions, ${}_2F_1$",
	"parentcode": "33Cxx",
	"level": 3
}, {
	"code": "33C10",
	"title": " Bessel and Airy functions, cylinder functions, ${}_0F_1$",
	"parentcode": "33Cxx",
	"level": 3
}, {
	"code": "33C15",
	"title": " Confluent hypergeometric functions, Whittaker functions, ${}_1F_1$",
	"parentcode": "33Cxx",
	"level": 3
}, {
	"code": "33C20",
	"title": " Generalized hypergeometric series, ${}_pF_q$",
	"parentcode": "33Cxx",
	"level": 3
}, {
	"code": "33C45",
	"title": " Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions]",
	"parentcode": "33Cxx",
	"level": 3
}, {
	"code": "33C47",
	"title": " Other special orthogonal polynomials and functions",
	"parentcode": "33Cxx",
	"level": 3
}, {
	"code": "33C50",
	"title": " Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable",
	"parentcode": "33Cxx",
	"level": 3
}, {
	"code": "33C52",
	"title": " Orthogonal polynomials and functions associated with root systems",
	"parentcode": "33Cxx",
	"level": 3
}, {
	"code": "33C55",
	"title": " Spherical harmonics",
	"parentcode": "33Cxx",
	"level": 3
}, {
	"code": "33C60",
	"title": " Hypergeometric integrals and functions defined by them ($E$, $G$, $H$  and $I$ functions)",
	"parentcode": "33Cxx",
	"level": 3
}, {
	"code": "33C65",
	"title": " Appell, Horn and Lauricella functions",
	"parentcode": "33Cxx",
	"level": 3
}, {
	"code": "33C67",
	"title": " Hypergeometric functions associated with root systems",
	"parentcode": "33Cxx",
	"level": 3
}, {
	"code": "33C70",
	"title": " Other hypergeometric functions and integrals in several variables",
	"parentcode": "33Cxx",
	"level": 3
}, {
	"code": "33C75",
	"title": " Elliptic integrals as hypergeometric functions",
	"parentcode": "33Cxx",
	"level": 3
}, {
	"code": "33C80",
	"title": " Connections with groups and algebras, and related topics",
	"parentcode": "33Cxx",
	"level": 3
}, {
	"code": "33C90",
	"title": " Applications",
	"parentcode": "33Cxx",
	"level": 3
}, {
	"code": "33C99",
	"title": " None of the above, but in this section",
	"parentcode": "33Cxx",
	"level": 3
}, {
	"code": "33Dxx",
	"title": " Basic hypergeometric functions",
	"parentcode": "33-XX",
	"level": 2
}, {
	"code": "33D05",
	"title": " $q$-gamma functions, $q$-beta functions and integrals",
	"parentcode": "33Dxx",
	"level": 3
}, {
	"code": "33D15",
	"title": " Basic hypergeometric functions in one variable, ${}_r\\phi_s$",
	"parentcode": "33Dxx",
	"level": 3
}, {
	"code": "33D45",
	"title": " Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)",
	"parentcode": "33Dxx",
	"level": 3
}, {
	"code": "33D50",
	"title": " Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable",
	"parentcode": "33Dxx",
	"level": 3
}, {
	"code": "33D52",
	"title": " Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)",
	"parentcode": "33Dxx",
	"level": 3
}, {
	"code": "33D60",
	"title": " Basic hypergeometric integrals and functions defined by them",
	"parentcode": "33Dxx",
	"level": 3
}, {
	"code": "33D65",
	"title": " Bibasic functions and multiple bases",
	"parentcode": "33Dxx",
	"level": 3
}, {
	"code": "33D67",
	"title": " Basic hypergeometric functions associated with root systems",
	"parentcode": "33Dxx",
	"level": 3
}, {
	"code": "33D70",
	"title": " Other basic hypergeometric functions and integrals in several variables",
	"parentcode": "33Dxx",
	"level": 3
}, {
	"code": "33D80",
	"title": " Connections with quantum groups, Chevalley groups, $p$-adic groups, Hecke algebras, and related topics",
	"parentcode": "33Dxx",
	"level": 3
}, {
	"code": "33D90",
	"title": " Applications",
	"parentcode": "33Dxx",
	"level": 3
}, {
	"code": "33D99",
	"title": " None of the above, but in this section",
	"parentcode": "33Dxx",
	"level": 3
}, {
	"code": "33Exx",
	"title": " Other special functions",
	"parentcode": "33-XX",
	"level": 2
}, {
	"code": "33E05",
	"title": " Elliptic functions and integrals",
	"parentcode": "33Exx",
	"level": 3
}, {
	"code": "33E10",
	"title": " Lamé, Mathieu, and spheroidal wave functions",
	"parentcode": "33Exx",
	"level": 3
}, {
	"code": "33E12",
	"title": " Mittag-Leffler functions and generalizations",
	"parentcode": "33Exx",
	"level": 3
}, {
	"code": "33E15",
	"title": " Other wave functions",
	"parentcode": "33Exx",
	"level": 3
}, {
	"code": "33E17",
	"title": " Painlevé-type functions",
	"parentcode": "33Exx",
	"level": 3
}, {
	"code": "33E20",
	"title": " Other functions defined by series and integrals",
	"parentcode": "33Exx",
	"level": 3
}, {
	"code": "33E30",
	"title": " Other functions coming from differential, difference and integral equations",
	"parentcode": "33Exx",
	"level": 3
}, {
	"code": "33E50",
	"title": " Special functions in characteristic $p$ (gamma functions, etc.)",
	"parentcode": "33Exx",
	"level": 3
}, {
	"code": "33E99",
	"title": " None of the above, but in this section",
	"parentcode": "33Exx",
	"level": 3
}, {
	"code": "33Fxx",
	"title": " Computational aspects",
	"parentcode": "33-XX",
	"level": 2
}, {
	"code": "33F05",
	"title": " Numerical approximation and evaluation [See also 65D20]",
	"parentcode": "33Fxx",
	"level": 3
}, {
	"code": "33F10",
	"title": " Symbolic computation (Gosper and Zeilberger algorithms, etc.) [See also 68W30]",
	"parentcode": "33Fxx",
	"level": 3
}, {
	"code": "33F99",
	"title": " None of the above, but in this section",
	"parentcode": "33Fxx",
	"level": 3
}, {
	"code": "34-XX",
	"title": " Ordinary differential equations",
	"parentcode": null,
	"level": 1
}, {
	"code": "34-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "34-XX",
	"level": 2
}, {
	"code": "34-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "34-XX",
	"level": 2
}, {
	"code": "34-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "34-XX",
	"level": 2
}, {
	"code": "34-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "34-XX",
	"level": 2
}, {
	"code": "34-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "34-XX",
	"level": 2
}, {
	"code": "34-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "34-XX",
	"level": 2
}, {
	"code": "34Axx",
	"title": " General theory",
	"parentcode": "34-XX",
	"level": 2
}, {
	"code": "34A05",
	"title": " Explicit solutions and reductions",
	"parentcode": "34Axx",
	"level": 3
}, {
	"code": "34A07",
	"title": " Fuzzy differential equations",
	"parentcode": "34Axx",
	"level": 3
}, {
	"code": "34A08",
	"title": " Fractional differential equations",
	"parentcode": "34Axx",
	"level": 3
}, {
	"code": "34A09",
	"title": " Implicit equations, differential-algebraic equations [See also 65L80]",
	"parentcode": "34Axx",
	"level": 3
}, {
	"code": "34A12",
	"title": " Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions",
	"parentcode": "34Axx",
	"level": 3
}, {
	"code": "34A25",
	"title": " Analytical theory",
	"parentcode": "34Axx",
	"level": 3
}, {
	"code": "34A26",
	"title": " Geometric methods in differential equations",
	"parentcode": "34Axx",
	"level": 3
}, {
	"code": "34A30",
	"title": " Linear equations and systems, general",
	"parentcode": "34Axx",
	"level": 3
}, {
	"code": "34A33",
	"title": " Lattice differential equations",
	"parentcode": "34Axx",
	"level": 3
}, {
	"code": "34A34",
	"title": " Nonlinear equations and systems, general",
	"parentcode": "34Axx",
	"level": 3
}, {
	"code": "34A35",
	"title": " Differential equations of infinite order",
	"parentcode": "34Axx",
	"level": 3
}, {
	"code": "34A36",
	"title": " Discontinuous equations",
	"parentcode": "34Axx",
	"level": 3
}, {
	"code": "34A37",
	"title": " Differential equations with impulses",
	"parentcode": "34Axx",
	"level": 3
}, {
	"code": "34A38",
	"title": " Hybrid systems",
	"parentcode": "34Axx",
	"level": 3
}, {
	"code": "34A40",
	"title": " Differential inequalities [See also 26D20]",
	"parentcode": "34Axx",
	"level": 3
}, {
	"code": "34A45",
	"title": " Theoretical approximation of solutions {For numerical analysis, see 65Lxx}",
	"parentcode": "34Axx",
	"level": 3
}, {
	"code": "34A55",
	"title": " Inverse problems",
	"parentcode": "34Axx",
	"level": 3
}, {
	"code": "34A60",
	"title": " Differential inclusions [See also 49J21, 49K21]",
	"parentcode": "34Axx",
	"level": 3
}, {
	"code": "34A99",
	"title": " None of the above, but in this section",
	"parentcode": "34Axx",
	"level": 3
}, {
	"code": "34Bxx",
	"title": " Boundary value problems {For ordinary differential operators, see 34Lxx}",
	"parentcode": "34-XX",
	"level": 2
}, {
	"code": "34B05",
	"title": " Linear boundary value problems",
	"parentcode": "34Bxx",
	"level": 3
}, {
	"code": "34B07",
	"title": " Linear boundary value problems with nonlinear dependence on the spectral parameter",
	"parentcode": "34Bxx",
	"level": 3
}, {
	"code": "34B08",
	"title": " Parameter dependent boundary value problems",
	"parentcode": "34Bxx",
	"level": 3
}, {
	"code": "34B09",
	"title": " Boundary eigenvalue problems",
	"parentcode": "34Bxx",
	"level": 3
}, {
	"code": "34B10",
	"title": " Nonlocal and multipoint boundary value problems",
	"parentcode": "34Bxx",
	"level": 3
}, {
	"code": "34B15",
	"title": " Nonlinear boundary value problems",
	"parentcode": "34Bxx",
	"level": 3
}, {
	"code": "34B16",
	"title": " Singular nonlinear boundary value problems",
	"parentcode": "34Bxx",
	"level": 3
}, {
	"code": "34B18",
	"title": " Positive solutions of nonlinear boundary value problems",
	"parentcode": "34Bxx",
	"level": 3
}, {
	"code": "34B20",
	"title": " Weyl theory and its generalizations",
	"parentcode": "34Bxx",
	"level": 3
}, {
	"code": "34B24",
	"title": " Sturm-Liouville theory [See also 34Lxx]",
	"parentcode": "34Bxx",
	"level": 3
}, {
	"code": "34B27",
	"title": " Green functions",
	"parentcode": "34Bxx",
	"level": 3
}, {
	"code": "34B30",
	"title": " Special equations (Mathieu, Hill, Bessel, etc.)",
	"parentcode": "34Bxx",
	"level": 3
}, {
	"code": "34B37",
	"title": " Boundary value problems with impulses",
	"parentcode": "34Bxx",
	"level": 3
}, {
	"code": "34B40",
	"title": " Boundary value problems on infinite intervals",
	"parentcode": "34Bxx",
	"level": 3
}, {
	"code": "34B45",
	"title": " Boundary value problems on graphs and networks",
	"parentcode": "34Bxx",
	"level": 3
}, {
	"code": "34B60",
	"title": " Applications",
	"parentcode": "34Bxx",
	"level": 3
}, {
	"code": "34B99",
	"title": " None of the above, but in this section",
	"parentcode": "34Bxx",
	"level": 3
}, {
	"code": "34Cxx",
	"title": " Qualitative theory [See also 37-XX]",
	"parentcode": "34-XX",
	"level": 2
}, {
	"code": "34C05",
	"title": " Location of integral curves, singular points, limit cycles",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C07",
	"title": " Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications)",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C08",
	"title": " Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.)",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C10",
	"title": " Oscillation theory, zeros, disconjugacy and comparison theory",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C11",
	"title": " Growth, boundedness",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C12",
	"title": " Monotone systems",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C14",
	"title": " Symmetries, invariants",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C15",
	"title": " Nonlinear oscillations, coupled oscillators",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C20",
	"title": " Transformation and reduction of equations and systems, normal forms",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C23",
	"title": " Bifurcation [See also 37Gxx]",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C25",
	"title": " Periodic solutions",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C26",
	"title": " Relaxation oscillations",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C27",
	"title": " Almost and pseudo-almost periodic solutions",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C28",
	"title": " Complex behavior, chaotic systems [See also 37Dxx]",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C29",
	"title": " Averaging method",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C37",
	"title": " Homoclinic and heteroclinic solutions",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C40",
	"title": " Equations and systems on manifolds",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C41",
	"title": " Equivalence, asymptotic equivalence",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C45",
	"title": " Invariant manifolds",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C46",
	"title": " Multifrequency systems",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C55",
	"title": " Hysteresis",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C60",
	"title": " Qualitative investigation and simulation of models",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34C99",
	"title": " None of the above, but in this section",
	"parentcode": "34Cxx",
	"level": 3
}, {
	"code": "34Dxx",
	"title": " Stability theory [See also 37C75, 93Dxx]",
	"parentcode": "34-XX",
	"level": 2
}, {
	"code": "34D05",
	"title": " Asymptotic properties",
	"parentcode": "34Dxx",
	"level": 3
}, {
	"code": "34D06",
	"title": " Synchronization",
	"parentcode": "34Dxx",
	"level": 3
}, {
	"code": "34D08",
	"title": " Characteristic and Lyapunov exponents",
	"parentcode": "34Dxx",
	"level": 3
}, {
	"code": "34D09",
	"title": " Dichotomy, trichotomy",
	"parentcode": "34Dxx",
	"level": 3
}, {
	"code": "34D10",
	"title": " Perturbations",
	"parentcode": "34Dxx",
	"level": 3
}, {
	"code": "34D15",
	"title": " Singular perturbations",
	"parentcode": "34Dxx",
	"level": 3
}, {
	"code": "34D20",
	"title": " Stability",
	"parentcode": "34Dxx",
	"level": 3
}, {
	"code": "34D23",
	"title": " Global stability",
	"parentcode": "34Dxx",
	"level": 3
}, {
	"code": "34D30",
	"title": " Structural stability and analogous concepts [See also 37C20]",
	"parentcode": "34Dxx",
	"level": 3
}, {
	"code": "34D35",
	"title": " Stability of manifolds of solutions",
	"parentcode": "34Dxx",
	"level": 3
}, {
	"code": "34D45",
	"title": " Attractors [See also 37C70, 37D45]",
	"parentcode": "34Dxx",
	"level": 3
}, {
	"code": "34D99",
	"title": " None of the above, but in this section",
	"parentcode": "34Dxx",
	"level": 3
}, {
	"code": "34Exx",
	"title": " Asymptotic theory",
	"parentcode": "34-XX",
	"level": 2
}, {
	"code": "34E05",
	"title": " Asymptotic expansions",
	"parentcode": "34Exx",
	"level": 3
}, {
	"code": "34E10",
	"title": " Perturbations, asymptotics",
	"parentcode": "34Exx",
	"level": 3
}, {
	"code": "34E13",
	"title": " Multiple scale methods",
	"parentcode": "34Exx",
	"level": 3
}, {
	"code": "34E15",
	"title": " Singular perturbations, general theory",
	"parentcode": "34Exx",
	"level": 3
}, {
	"code": "34E17",
	"title": " Canard solutions",
	"parentcode": "34Exx",
	"level": 3
}, {
	"code": "34E18",
	"title": " Methods of nonstandard analysis",
	"parentcode": "34Exx",
	"level": 3
}, {
	"code": "34E20",
	"title": " Singular perturbations, turning point theory, WKB methods",
	"parentcode": "34Exx",
	"level": 3
}, {
	"code": "34E99",
	"title": " None of the above, but in this section",
	"parentcode": "34Exx",
	"level": 3
}, {
	"code": "34Fxx",
	"title": " Equations and systems with randomness [See also 34K50, 60H10, 93E03]",
	"parentcode": "34-XX",
	"level": 2
}, {
	"code": "34F05",
	"title": " Equations and systems with randomness [See also 34K50, 60H10, 93E03]",
	"parentcode": "34Fxx",
	"level": 3
}, {
	"code": "34F10",
	"title": " Bifurcation",
	"parentcode": "34Fxx",
	"level": 3
}, {
	"code": "34F15",
	"title": " Resonance phenomena",
	"parentcode": "34Fxx",
	"level": 3
}, {
	"code": "34F99",
	"title": " None of the above, but in this section",
	"parentcode": "34Fxx",
	"level": 3
}, {
	"code": "34Gxx",
	"title": " Differential equations in abstract spaces [See also 34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx, 58D25]",
	"parentcode": "34-XX",
	"level": 2
}, {
	"code": "34G10",
	"title": " Linear equations [See also 47D06, 47D09]",
	"parentcode": "34Gxx",
	"level": 3
}, {
	"code": "34G20",
	"title": " Nonlinear equations [See also 47Hxx, 47Jxx]",
	"parentcode": "34Gxx",
	"level": 3
}, {
	"code": "34G25",
	"title": " Evolution inclusions",
	"parentcode": "34Gxx",
	"level": 3
}, {
	"code": "34G99",
	"title": " None of the above, but in this section",
	"parentcode": "34Gxx",
	"level": 3
}, {
	"code": "34Hxx",
	"title": "  Control problems [See also 49J15, 49K15, 93C15]",
	"parentcode": "34-XX",
	"level": 2
}, {
	"code": "34H05",
	"title": " Control problems [See also 49J15, 49K15, 93C15]",
	"parentcode": "34Hxx",
	"level": 3
}, {
	"code": "34H10",
	"title": " Chaos control",
	"parentcode": "34Hxx",
	"level": 3
}, {
	"code": "34H15",
	"title": " Stabilization",
	"parentcode": "34Hxx",
	"level": 3
}, {
	"code": "34H20",
	"title": " Bifurcation control",
	"parentcode": "34Hxx",
	"level": 3
}, {
	"code": "34H99",
	"title": " None of the above, but in this section",
	"parentcode": "34Hxx",
	"level": 3
}, {
	"code": "34Kxx",
	"title": " Functional-differential and differential-difference equations [See also 37-XX]",
	"parentcode": "34-XX",
	"level": 2
}, {
	"code": "34K05",
	"title": " General theory",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K06",
	"title": " Linear functional-differential equations",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K07",
	"title": " Theoretical approximation of solutions",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K08",
	"title": " Spectral theory of functional-differential operators",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K09",
	"title": " Functional-differential inclusions",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K10",
	"title": " Boundary value problems",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K11",
	"title": " Oscillation theory",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K12",
	"title": " Growth, boundedness, comparison of solutions",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K13",
	"title": " Periodic solutions",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K14",
	"title": " Almost and pseudo-periodic solutions",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K17",
	"title": " Transformation and reduction of equations and systems, normal forms",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K18",
	"title": " Bifurcation theory",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K19",
	"title": " Invariant manifolds",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K20",
	"title": " Stability theory",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K21",
	"title": " Stationary solutions",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K23",
	"title": " Complex (chaotic) behavior of solutions",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K25",
	"title": " Asymptotic theory",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K26",
	"title": " Singular perturbations",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K27",
	"title": " Perturbations",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K28",
	"title": " Numerical approximation of solutions",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K29",
	"title": " Inverse problems",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K30",
	"title": " Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx]",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K31",
	"title": " Lattice functional-differential equations",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K32",
	"title": " Implicit equations",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K33",
	"title": " Averaging",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K34",
	"title": " Hybrid systems",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K35",
	"title": " Control problems [See also 49J21, 49K21, 93C23]",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K36",
	"title": " Fuzzy functional-differential equations",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K37",
	"title": " Functional-differential equations with fractional derivatives",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K38",
	"title": " Functional-differential inequalities",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K40",
	"title": " Neutral equations",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K45",
	"title": " Equations with impulses",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K50",
	"title": " Stochastic functional-differential equations  [See also  60Hxx]",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K60",
	"title": " Qualitative investigation and simulation of models",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34K99",
	"title": " None of the above, but in this section",
	"parentcode": "34Kxx",
	"level": 3
}, {
	"code": "34Lxx",
	"title": " Ordinary differential operators [See also 47E05]",
	"parentcode": "34-XX",
	"level": 2
}, {
	"code": "34L05",
	"title": " General spectral theory",
	"parentcode": "34Lxx",
	"level": 3
}, {
	"code": "34L10",
	"title": " Eigenfunctions, eigenfunction  expansions, completeness of eigenfunctions",
	"parentcode": "34Lxx",
	"level": 3
}, {
	"code": "34L15",
	"title": " Eigenvalues, estimation of eigenvalues, upper and lower bounds",
	"parentcode": "34Lxx",
	"level": 3
}, {
	"code": "34L16",
	"title": " Numerical approximation of eigenvalues and of other parts of the spectrum",
	"parentcode": "34Lxx",
	"level": 3
}, {
	"code": "34L20",
	"title": " Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions",
	"parentcode": "34Lxx",
	"level": 3
}, {
	"code": "34L25",
	"title": " Scattering theory, inverse scattering",
	"parentcode": "34Lxx",
	"level": 3
}, {
	"code": "34L30",
	"title": " Nonlinear ordinary differential operators",
	"parentcode": "34Lxx",
	"level": 3
}, {
	"code": "34L40",
	"title": " Particular operators (Dirac, one-dimensional Schrödinger, etc.)",
	"parentcode": "34Lxx",
	"level": 3
}, {
	"code": "34L99",
	"title": " None of the above, but in this section",
	"parentcode": "34Lxx",
	"level": 3
}, {
	"code": "34Mxx",
	"title": " Differential equations in the complex domain [See also 30Dxx, 32G34]",
	"parentcode": "34-XX",
	"level": 2
}, {
	"code": "34M03",
	"title": " Linear equations and systems",
	"parentcode": "34Mxx",
	"level": 3
}, {
	"code": "34M05",
	"title": " Entire and meromorphic solutions",
	"parentcode": "34Mxx",
	"level": 3
}, {
	"code": "34M10",
	"title": " Oscillation, growth of solutions",
	"parentcode": "34Mxx",
	"level": 3
}, {
	"code": "34M15",
	"title": " Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical)",
	"parentcode": "34Mxx",
	"level": 3
}, {
	"code": "34M25",
	"title": " Formal solutions, transform techniques",
	"parentcode": "34Mxx",
	"level": 3
}, {
	"code": "34M30",
	"title": " Asymptotics, summation methods",
	"parentcode": "34Mxx",
	"level": 3
}, {
	"code": "34M35",
	"title": " Singularities, monodromy, local behavior of solutions, normal forms",
	"parentcode": "34Mxx",
	"level": 3
}, {
	"code": "34M40",
	"title": " Stokes phenomena and connection problems (linear and nonlinear)",
	"parentcode": "34Mxx",
	"level": 3
}, {
	"code": "34M45",
	"title": " Differential equations on complex manifolds",
	"parentcode": "34Mxx",
	"level": 3
}, {
	"code": "34M50",
	"title": " Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.)",
	"parentcode": "34Mxx",
	"level": 3
}, {
	"code": "34M55",
	"title": " Painlevé and other special equations; classification, hierarchies;",
	"parentcode": "34Mxx",
	"level": 3
}, {
	"code": "34M56",
	"title": " Isomonodromic deformations",
	"parentcode": "34Mxx",
	"level": 3
}, {
	"code": "34M60",
	"title": " Singular perturbation problems in the complex domain (complex WKB, turning points, steepest descent) [See also 34E20]",
	"parentcode": "34Mxx",
	"level": 3
}, {
	"code": "34M99",
	"title": " None of the above, but in this section",
	"parentcode": "34Mxx",
	"level": 3
}, {
	"code": "34Nxx",
	"title": " Dynamic equations on time scales or measure chains {For real analysis on time scales see  26E70}",
	"parentcode": "34-XX",
	"level": 2
}, {
	"code": "34N05",
	"title": " Dynamic equations on time scales or measure chains {For real analysis on time scales or measure chains, see  26E70}",
	"parentcode": "34Nxx",
	"level": 3
}, {
	"code": "34N99",
	"title": " None of the above, but in this section",
	"parentcode": "34Nxx",
	"level": 3
}, {
	"code": "35-XX",
	"title": " Partial differential equations",
	"parentcode": null,
	"level": 1
}, {
	"code": "35-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35Axx",
	"title": " General topics",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35A01",
	"title": " Existence problems",
	"parentcode": "35Axx",
	"level": 3
}, {
	"code": "35A02",
	"title": " Uniqueness problems",
	"parentcode": "35Axx",
	"level": 3
}, {
	"code": "35A08",
	"title": " Fundamental solutions",
	"parentcode": "35Axx",
	"level": 3
}, {
	"code": "35A09",
	"title": " Classical solutions",
	"parentcode": "35Axx",
	"level": 3
}, {
	"code": "35A10",
	"title": " Cauchy-Kovalevskaya theorems",
	"parentcode": "35Axx",
	"level": 3
}, {
	"code": "35A15",
	"title": " Variational methods",
	"parentcode": "35Axx",
	"level": 3
}, {
	"code": "35A16",
	"title": " Topological and monotonicity methods",
	"parentcode": "35Axx",
	"level": 3
}, {
	"code": "35A17",
	"title": " Parametrices",
	"parentcode": "35Axx",
	"level": 3
}, {
	"code": "35A18",
	"title": " Wave front sets",
	"parentcode": "35Axx",
	"level": 3
}, {
	"code": "35A20",
	"title": " Analytic methods, singularities",
	"parentcode": "35Axx",
	"level": 3
}, {
	"code": "35A21",
	"title": " Propagation of singularities",
	"parentcode": "35Axx",
	"level": 3
}, {
	"code": "35A22",
	"title": " Transform methods (e.g. integral transforms)",
	"parentcode": "35Axx",
	"level": 3
}, {
	"code": "35A23",
	"title": " Inequalities  involving derivatives and differential and integral operators, inequalities for integrals",
	"parentcode": "35Axx",
	"level": 3
}, {
	"code": "35A24",
	"title": " Methods of ordinary differential equations",
	"parentcode": "35Axx",
	"level": 3
}, {
	"code": "35A25",
	"title": " Other special methods",
	"parentcode": "35Axx",
	"level": 3
}, {
	"code": "35A27",
	"title": " Microlocal methods; methods of sheaf theory and homological algebra in PDE [See also 32C38, 58J15]",
	"parentcode": "35Axx",
	"level": 3
}, {
	"code": "35A30",
	"title": " Geometric theory, characteristics, transformations [See also 58J70, 58J72]",
	"parentcode": "35Axx",
	"level": 3
}, {
	"code": "35A35",
	"title": " Theoretical approximation to solutions {For numerical analysis, see 65Mxx, 65Nxx}",
	"parentcode": "35Axx",
	"level": 3
}, {
	"code": "35A99",
	"title": " None of the above, but in this section",
	"parentcode": "35Axx",
	"level": 3
}, {
	"code": "35Bxx",
	"title": " Qualitative properties of solutions",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35B05",
	"title": " Oscillation, zeros of solutions, mean value theorems, etc.",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B06",
	"title": " Symmetries, invariants,  etc.",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B07",
	"title": " Axially symmetric solutions",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B08",
	"title": " Entire solutions",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B09",
	"title": " Positive solutions",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B10",
	"title": " Periodic solutions",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B15",
	"title": " Almost and pseudo-almost periodic solutions",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B20",
	"title": " Perturbations",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B25",
	"title": " Singular perturbations",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B27",
	"title": " Homogenization;  equations in media with periodic structure [See also 74Qxx, 76M50]",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B30",
	"title": " Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B32",
	"title": " Bifurcation [See also 37Gxx, 37K50]",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B33",
	"title": " Critical exponents",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B34",
	"title": " Resonances",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B35",
	"title": " Stability",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B36",
	"title": " Pattern formation",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B38",
	"title": " Critical points",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B40",
	"title": " Asymptotic behavior of solutions",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B41",
	"title": " Attractors",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B42",
	"title": " Inertial manifolds",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B44",
	"title": " Blow-up",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B45",
	"title": " A priori estimates",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B50",
	"title": " Maximum principles",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B51",
	"title": " Comparison principles",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B53",
	"title": " Liouville theorems, Phragmén-Lindelöf theorems",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B60",
	"title": " Continuation and prolongation of solutions  [See also 58A15, 58A17, 58Hxx]",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B65",
	"title": " Smoothness and regularity of solutions",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35B99",
	"title": " None of the above, but in this section",
	"parentcode": "35Bxx",
	"level": 3
}, {
	"code": "35Cxx",
	"title": " Representations of solutions",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35C05",
	"title": " Solutions in closed form",
	"parentcode": "35Cxx",
	"level": 3
}, {
	"code": "35C06",
	"title": " Self-similar  solutions",
	"parentcode": "35Cxx",
	"level": 3
}, {
	"code": "35C07",
	"title": " Traveling wave  solutions",
	"parentcode": "35Cxx",
	"level": 3
}, {
	"code": "35C08",
	"title": " Soliton   solutions",
	"parentcode": "35Cxx",
	"level": 3
}, {
	"code": "35C09",
	"title": " Trigonometric   solutions",
	"parentcode": "35Cxx",
	"level": 3
}, {
	"code": "35C10",
	"title": " Series solutions",
	"parentcode": "35Cxx",
	"level": 3
}, {
	"code": "35C11",
	"title": " Polynomial  solutions",
	"parentcode": "35Cxx",
	"level": 3
}, {
	"code": "35C15",
	"title": " Integral representations of solutions",
	"parentcode": "35Cxx",
	"level": 3
}, {
	"code": "35C20",
	"title": " Asymptotic expansions",
	"parentcode": "35Cxx",
	"level": 3
}, {
	"code": "35C99",
	"title": " None of the above, but in this section",
	"parentcode": "35Cxx",
	"level": 3
}, {
	"code": "35Dxx",
	"title": " Generalized solutions",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35D30",
	"title": " Weak solutions",
	"parentcode": "35Dxx",
	"level": 3
}, {
	"code": "35D35",
	"title": " Strong solutions",
	"parentcode": "35Dxx",
	"level": 3
}, {
	"code": "35D40",
	"title": " Viscosity solutions",
	"parentcode": "35Dxx",
	"level": 3
}, {
	"code": "35D99",
	"title": " None of the above, but in this section",
	"parentcode": "35Dxx",
	"level": 3
}, {
	"code": "35Exx",
	"title": " Equations and systems with constant coefficients [See also 35N05]",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35E05",
	"title": " Fundamental solutions",
	"parentcode": "35Exx",
	"level": 3
}, {
	"code": "35E10",
	"title": " Convexity properties",
	"parentcode": "35Exx",
	"level": 3
}, {
	"code": "35E15",
	"title": " Initial value problems",
	"parentcode": "35Exx",
	"level": 3
}, {
	"code": "35E20",
	"title": " General theory",
	"parentcode": "35Exx",
	"level": 3
}, {
	"code": "35E99",
	"title": " None of the above, but in this section",
	"parentcode": "35Exx",
	"level": 3
}, {
	"code": "35Fxx",
	"title": " General first-order equations and systems",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35F05",
	"title": " Linear first-order equations",
	"parentcode": "35Fxx",
	"level": 3
}, {
	"code": "35F10",
	"title": " Initial value problems for linear first-order equations",
	"parentcode": "35Fxx",
	"level": 3
}, {
	"code": "35F15",
	"title": " Boundary value problems for linear first-order equations",
	"parentcode": "35Fxx",
	"level": 3
}, {
	"code": "35F16",
	"title": " Initial-boundary value problems for linear first-order equations",
	"parentcode": "35Fxx",
	"level": 3
}, {
	"code": "35F20",
	"title": " Nonlinear first-order equations",
	"parentcode": "35Fxx",
	"level": 3
}, {
	"code": "35F21",
	"title": " Hamilton-Jacobi equations",
	"parentcode": "35Fxx",
	"level": 3
}, {
	"code": "35F25",
	"title": " Initial value problems for nonlinear first-order equations",
	"parentcode": "35Fxx",
	"level": 3
}, {
	"code": "35F30",
	"title": " Boundary value problems for nonlinear first-order equations",
	"parentcode": "35Fxx",
	"level": 3
}, {
	"code": "35F31",
	"title": " Initial-boundary value problems for nonlinear first-order  equations",
	"parentcode": "35Fxx",
	"level": 3
}, {
	"code": "35F35",
	"title": " Linear first-order systems",
	"parentcode": "35Fxx",
	"level": 3
}, {
	"code": "35F40",
	"title": " Initial value problems for linear first-order systems",
	"parentcode": "35Fxx",
	"level": 3
}, {
	"code": "35F45",
	"title": " Boundary value problems for linear first-order systems",
	"parentcode": "35Fxx",
	"level": 3
}, {
	"code": "35F46",
	"title": " Initial-boundary value problems for linear first-order systems",
	"parentcode": "35Fxx",
	"level": 3
}, {
	"code": "35F50",
	"title": " Nonlinear first-order systems",
	"parentcode": "35Fxx",
	"level": 3
}, {
	"code": "35F55",
	"title": " Initial value problems for nonlinear first-order systems",
	"parentcode": "35Fxx",
	"level": 3
}, {
	"code": "35F60",
	"title": " Boundary value problems for nonlinear first-order systems",
	"parentcode": "35Fxx",
	"level": 3
}, {
	"code": "35F61",
	"title": " Initial-boundary value problems for nonlinear first-order systems",
	"parentcode": "35Fxx",
	"level": 3
}, {
	"code": "35F99",
	"title": " None of the above, but in this section",
	"parentcode": "35Fxx",
	"level": 3
}, {
	"code": "35Gxx",
	"title": " General higher-order equations and systems",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35G05",
	"title": " Linear higher-order equations",
	"parentcode": "35Gxx",
	"level": 3
}, {
	"code": "35G10",
	"title": "  Initial value problems for linear higher-order equations",
	"parentcode": "35Gxx",
	"level": 3
}, {
	"code": "35G15",
	"title": " Boundary value problems for linear higher-order equations",
	"parentcode": "35Gxx",
	"level": 3
}, {
	"code": "35G16",
	"title": " Initial-boundary value problems for linear higher-order equations",
	"parentcode": "35Gxx",
	"level": 3
}, {
	"code": "35G20",
	"title": " Nonlinear higher-order equations",
	"parentcode": "35Gxx",
	"level": 3
}, {
	"code": "35G25",
	"title": " Initial value problems for nonlinear higher-order equations",
	"parentcode": "35Gxx",
	"level": 3
}, {
	"code": "35G30",
	"title": " Boundary value problems for nonlinear higher-order equations",
	"parentcode": "35Gxx",
	"level": 3
}, {
	"code": "35G31",
	"title": " Initial-boundary value problems for nonlinear higher-order equations",
	"parentcode": "35Gxx",
	"level": 3
}, {
	"code": "35G35",
	"title": " Linear higher-order systems",
	"parentcode": "35Gxx",
	"level": 3
}, {
	"code": "35G40",
	"title": " Initial value problems for linear higher-order systems",
	"parentcode": "35Gxx",
	"level": 3
}, {
	"code": "35G45",
	"title": " Boundary value problems for linear higher-order systems",
	"parentcode": "35Gxx",
	"level": 3
}, {
	"code": "35G46",
	"title": " Initial-boundary value problems for linear higher-order systems",
	"parentcode": "35Gxx",
	"level": 3
}, {
	"code": "35G50",
	"title": " Nonlinear higher-order systems",
	"parentcode": "35Gxx",
	"level": 3
}, {
	"code": "35G55",
	"title": " Initial value problems for nonlinear higher-order systems",
	"parentcode": "35Gxx",
	"level": 3
}, {
	"code": "35G60",
	"title": " Boundary value problems for nonlinear higher-order systems",
	"parentcode": "35Gxx",
	"level": 3
}, {
	"code": "35G61",
	"title": " Initial-boundary value problems for nonlinear higher-order systems",
	"parentcode": "35Gxx",
	"level": 3
}, {
	"code": "35G99",
	"title": " None of the above, but in this section",
	"parentcode": "35Gxx",
	"level": 3
}, {
	"code": "35Hxx",
	"title": " Close-to-elliptic equations and systems",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35H10",
	"title": " Hypoelliptic equations",
	"parentcode": "35Hxx",
	"level": 3
}, {
	"code": "35H20",
	"title": " Subelliptic equations",
	"parentcode": "35Hxx",
	"level": 3
}, {
	"code": "35H30",
	"title": " Quasi-elliptic equations",
	"parentcode": "35Hxx",
	"level": 3
}, {
	"code": "35H99",
	"title": " None of the above, but in this section",
	"parentcode": "35Hxx",
	"level": 3
}, {
	"code": "35Jxx",
	"title": " Elliptic equations and systems [See also 58J10, 58J20]",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35J05",
	"title": " Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx]",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J08",
	"title": " Green's functions",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J10",
	"title": " Schrödinger operator [See also 35Pxx]",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J15",
	"title": " Second-order elliptic equations",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J20",
	"title": " Variational methods for second-order elliptic equations",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J25",
	"title": " Boundary value problems for second-order elliptic equations",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J30",
	"title": " Higher-order elliptic equations [See also 31A30, 31B30]",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J35",
	"title": " Variational methods for higher-order elliptic equations",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J40",
	"title": " Boundary value problems for higher-order elliptic equations",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J46",
	"title": " First-order elliptic systems",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J47",
	"title": " Second-order elliptic systems",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J48",
	"title": " Higher-order elliptic systems",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J50",
	"title": " Variational methods for elliptic systems",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J56",
	"title": " Boundary value problems for first-order elliptic systems",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J57",
	"title": " Boundary value problems for second-order elliptic systems",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J58",
	"title": " Boundary value problems for higher-order elliptic systems",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J60",
	"title": " Nonlinear elliptic equations",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J61",
	"title": " Semilinear elliptic equations",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J62",
	"title": " Quasilinear elliptic equations",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J65",
	"title": " Nonlinear boundary value problems for linear elliptic equations",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J66",
	"title": " Nonlinear boundary value problems for nonlinear elliptic equations",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J67",
	"title": " Boundary values of solutions to elliptic equations",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J70",
	"title": " Degenerate elliptic equations",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J75",
	"title": " Singular elliptic equations",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J86",
	"title": " Linear elliptic unilateral problems and linear elliptic variational inequalities [See also 35R35, 49J40]",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J87",
	"title": " Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities [See also 35R35, 49J40]",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J88",
	"title": "  Systems of elliptic variational inequalities  [See also 35R35, 49J40]",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J91",
	"title": " Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J92",
	"title": " Quasilinear elliptic equations with $p$-Laplacian",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J93",
	"title": " Quasilinear elliptic equations with mean curvature operator",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J96",
	"title": " Elliptic Monge-Ampère equations",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35J99",
	"title": " None of the above, but in this section",
	"parentcode": "35Jxx",
	"level": 3
}, {
	"code": "35Kxx",
	"title": " Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35]",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35K05",
	"title": " Heat equation",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K08",
	"title": " Heat kernel",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K10",
	"title": " Second-order parabolic equations",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K15",
	"title": " Initial value problems for second-order parabolic equations",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K20",
	"title": " Initial-boundary value problems for second-order parabolic equations",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K25",
	"title": " Higher-order parabolic equations",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K30",
	"title": " Initial value problems for higher-order parabolic equations",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K35",
	"title": " Initial-boundary value problems for higher-order parabolic equations",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K40",
	"title": " Second-order parabolic systems",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K41",
	"title": " Higher-order parabolic systems",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K45",
	"title": " Initial value problems for second-order parabolic systems",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K46",
	"title": " Initial value problems for higher-order parabolic systems",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K51",
	"title": " Initial-boundary value problems for  second-order parabolic systems",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K52",
	"title": " Initial-boundary value problems for higher-order parabolic systems",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K55",
	"title": " Nonlinear parabolic equations",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K57",
	"title": " Reaction-diffusion equations",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K58",
	"title": " Semilinear parabolic equations",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K59",
	"title": " Quasilinear parabolic equations",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K60",
	"title": " Nonlinear initial value problems for linear parabolic equations",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K61",
	"title": " Nonlinear initial-boundary value problems for nonlinear parabolic equations",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K65",
	"title": " Degenerate parabolic equations",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K67",
	"title": " Singular parabolic equations",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K70",
	"title": " Ultraparabolic equations, pseudoparabolic equations, etc.",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K85",
	"title": " Linear parabolic unilateral problems and linear parabolic variational inequalities [See also 35R35, 49J40]",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K86",
	"title": " Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities [See also 35R35, 49J40]",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K87",
	"title": " Systems of parabolic variational inequalities  [See also 35R35, 49J40]",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K90",
	"title": " Abstract parabolic equations",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K91",
	"title": " Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K92",
	"title": " Quasilinear parabolic equations with $p$-Laplacian",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K93",
	"title": " Quasilinear parabolic equations with mean curvature operator",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K96",
	"title": " Parabolic Monge-Ampère equations",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35K99",
	"title": " None of the above, but in this section",
	"parentcode": "35Kxx",
	"level": 3
}, {
	"code": "35Lxx",
	"title": " Hyperbolic equations and systems [See also 58J45]",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35L02",
	"title": " First-order hyperbolic equations",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L03",
	"title": " Initial value problems for first-order hyperbolic equations",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L04",
	"title": " Initial-boundary value problems for first-order hyperbolic equations",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L05",
	"title": " Wave equation",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L10",
	"title": " Second-order hyperbolic equations",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L15",
	"title": " Initial value problems for second-order hyperbolic equations",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L20",
	"title": " Initial-boundary value problems for second-order hyperbolic equations",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L25",
	"title": " Higher-order hyperbolic equations",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L30",
	"title": " Initial value problems for higher-order hyperbolic equations",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L35",
	"title": " Initial-boundary value problems for higher-order hyperbolic equations",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L40",
	"title": " First-order hyperbolic systems",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L45",
	"title": " Initial value problems for first-order hyperbolic systems",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L50",
	"title": " Initial-boundary value problems for first-order hyperbolic systems",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L51",
	"title": " Second-order hyperbolic systems",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L52",
	"title": " Initial value problems for second-order hyperbolic systems",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L53",
	"title": " Initial-boundary value problems for second-order hyperbolic systems",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L55",
	"title": "  Higher-order hyperbolic systems",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L56",
	"title": " Initial value problems for higher-order hyperbolic systems",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L57",
	"title": " Initial-boundary value problems for higher-order hyperbolic systems",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L60",
	"title": " Nonlinear first-order hyperbolic equations",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L65",
	"title": " Conservation laws",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L67",
	"title": " Shocks and singularities [See also 58Kxx, 76L05]",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L70",
	"title": " Nonlinear second-order hyperbolic equations",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L71",
	"title": " Semilinear second-order hyperbolic equations",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L72",
	"title": " Quasilinear second-order hyperbolic equations",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L75",
	"title": " Nonlinear higher-order hyperbolic equations",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L76",
	"title": " Semilinear higher-order hyperbolic equations",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L77",
	"title": " Quasilinear higher-order hyperbolic equations",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L80",
	"title": "  Degenerate hyperbolic equations",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L81",
	"title": " Singular hyperbolic equations",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L82",
	"title": " Pseudohyperbolic equations",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L85",
	"title": " Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities [See also 35R35, 49J40]",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L86",
	"title": " Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variational inequalities [See also 35R35, 49J40]",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L87",
	"title": " Unilateral problems and variational inequalities for hyperbolic systems  [See also 35R35, 49J40]",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L90",
	"title": " Abstract hyperbolic equations",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35L99",
	"title": " None of the above, but in this section",
	"parentcode": "35Lxx",
	"level": 3
}, {
	"code": "35Mxx",
	"title": " Equations and systems of special type (mixed, composite, etc.)",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35M10",
	"title": " Equations of  mixed type",
	"parentcode": "35Mxx",
	"level": 3
}, {
	"code": "35M11",
	"title": " Initial value problems for equations of mixed type",
	"parentcode": "35Mxx",
	"level": 3
}, {
	"code": "35M12",
	"title": " Boundary value problems for equations of mixed type",
	"parentcode": "35Mxx",
	"level": 3
}, {
	"code": "35M13",
	"title": " Initial-boundary value problems for equations of mixed type",
	"parentcode": "35Mxx",
	"level": 3
}, {
	"code": "35M30",
	"title": " Systems of mixed type",
	"parentcode": "35Mxx",
	"level": 3
}, {
	"code": "35M31",
	"title": " Initial value problems for systems of mixed type",
	"parentcode": "35Mxx",
	"level": 3
}, {
	"code": "35M32",
	"title": " Boundary value problems for systems of mixed type",
	"parentcode": "35Mxx",
	"level": 3
}, {
	"code": "35M33",
	"title": " Initial-boundary value problems for systems of mixed type",
	"parentcode": "35Mxx",
	"level": 3
}, {
	"code": "35M85",
	"title": " Linear unilateral problems and variational inequalities of mixed type [See also 35R35, 49J40]",
	"parentcode": "35Mxx",
	"level": 3
}, {
	"code": "35M86",
	"title": " Nonlinear unilateral problems and nonlinear variational inequalities of mixed type [See also 35R35, 49J40]",
	"parentcode": "35Mxx",
	"level": 3
}, {
	"code": "35M87",
	"title": " Systems of variational inequalities of mixed type [See also 35R35, 49J40]",
	"parentcode": "35Mxx",
	"level": 3
}, {
	"code": "35M99",
	"title": " None of the above, but in this section",
	"parentcode": "35Mxx",
	"level": 3
}, {
	"code": "35Nxx",
	"title": " Overdetermined systems [See also 58Hxx, 58J10, 58J15]",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35N05",
	"title": " Overdetermined systems with constant coefficients",
	"parentcode": "35Nxx",
	"level": 3
}, {
	"code": "35N10",
	"title": " Overdetermined systems with variable coefficients",
	"parentcode": "35Nxx",
	"level": 3
}, {
	"code": "35N15",
	"title": " $\\overline\\partial$-Neumann problem and generalizations; formal complexes [See also 32W05, 32W10, 58J10]",
	"parentcode": "35Nxx",
	"level": 3
}, {
	"code": "35N20",
	"title": " Overdetermined initial value problems",
	"parentcode": "35Nxx",
	"level": 3
}, {
	"code": "35N25",
	"title": " Overdetermined boundary value problems",
	"parentcode": "35Nxx",
	"level": 3
}, {
	"code": "35N30",
	"title": " Overdetermined initial-boundary value problems",
	"parentcode": "35Nxx",
	"level": 3
}, {
	"code": "35N99",
	"title": " None of the above, but in this section",
	"parentcode": "35Nxx",
	"level": 3
}, {
	"code": "35Pxx",
	"title": " Spectral theory and eigenvalue problems [See also 47Axx, 47Bxx, 47F05]",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35P05",
	"title": " General topics in linear spectral theory",
	"parentcode": "35Pxx",
	"level": 3
}, {
	"code": "35P10",
	"title": " Completeness of eigenfunctions, eigenfunction expansions",
	"parentcode": "35Pxx",
	"level": 3
}, {
	"code": "35P15",
	"title": " Estimation of eigenvalues, upper and lower bounds",
	"parentcode": "35Pxx",
	"level": 3
}, {
	"code": "35P20",
	"title": " Asymptotic distribution of eigenvalues and eigenfunctions",
	"parentcode": "35Pxx",
	"level": 3
}, {
	"code": "35P25",
	"title": " Scattering theory [See also 47A40]",
	"parentcode": "35Pxx",
	"level": 3
}, {
	"code": "35P30",
	"title": " Nonlinear eigenvalue problems, nonlinear spectral theory",
	"parentcode": "35Pxx",
	"level": 3
}, {
	"code": "35P99",
	"title": " None of the above, but in this section",
	"parentcode": "35Pxx",
	"level": 3
}, {
	"code": "35Qxx",
	"title": " Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05]",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35Q05",
	"title": " Euler-Poisson-Darboux equations",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q15",
	"title": " Riemann-Hilbert problems [See also 30E25, 31A25, 31B20]",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q20",
	"title": " Boltzmann equations",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q30",
	"title": " Navier-Stokes equations [See also 76D05, 76D07, 76N10]",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q31",
	"title": " Euler equations [See also 76D05, 76D07, 76N10]",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q35",
	"title": " PDEs in connection with fluid mechanics",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q40",
	"title": " PDEs in connection with quantum mechanics",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q41",
	"title": "  Time-dependent Schrödinger equations, Dirac equations",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q51",
	"title": " Soliton-like equations [See also 37K40]",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q53",
	"title": " KdV-like equations (Korteweg-de Vries) [See also 37K10]",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q55",
	"title": " NLS-like  equations (nonlinear Schrödinger) [See also 37K10]",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q56",
	"title": "  Ginzburg-Landau equations",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q60",
	"title": " PDEs in connection with optics and electromagnetic theory",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q61",
	"title": " Maxwell equations",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q62",
	"title": " PDEs in connection with statistics",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q68",
	"title": " PDEs in connection with computer science",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q70",
	"title": " PDEs in connection with mechanics of particles and systems",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q74",
	"title": " PDEs in connection with mechanics of deformable solids",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q75",
	"title": " PDEs in connection with relativity and gravitational theory",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q76",
	"title": " Einstein equations",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q79",
	"title": " PDEs in connection with classical thermodynamics and heat transfer",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q82",
	"title": " PDEs in connection with statistical mechanics",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q83",
	"title": " Vlasov-like equations",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q84",
	"title": " Fokker-Planck equations",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q85",
	"title": " PDEs in connection with astronomy and astrophysics",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q86",
	"title": " PDEs in connection with geophysics",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q90",
	"title": " PDEs in connection with mathematical programming",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q91",
	"title": " PDEs in connection with game theory, economics, social and behavioral sciences",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q92",
	"title": " PDEs in connection with biology and other natural sciences",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q93",
	"title": " PDEs in connection with control and optimization",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q94",
	"title": " PDEs in connection with information and communication",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Q99",
	"title": " None of the above, but in this section",
	"parentcode": "35Qxx",
	"level": 3
}, {
	"code": "35Rxx",
	"title": " Miscellaneous topics {For equations on manifolds, see 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDE, see also 60H15}",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35R01",
	"title": " Partial differential equations on manifolds [See also 32Wxx, 53Cxx, 58Jxx]",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35R02",
	"title": " Partial differential equations on graphs and networks  (ramified or polygonal spaces)",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35R03",
	"title": " Partial differential equations on  Heisenberg groups, Lie groups, Carnot groups, etc.",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35R05",
	"title": " Partial differential equations with discontinuous coefficients or data",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35R06",
	"title": " Partial differential equations with measure",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35R09",
	"title": " Integro-partial differential equations [See also 45Kxx]",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35R10",
	"title": " Partial functional-differential  equations",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35R11",
	"title": " Fractional partial differential equations",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35R12",
	"title": " Impulsive partial differential equations",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35R13",
	"title": " Fuzzy partial differential equations",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35R15",
	"title": " Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables) [See also 46Gxx, 58D25]",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35R20",
	"title": " Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for abstract space valued functions) [See also 34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx]",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35R25",
	"title": " Improperly posed problems",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35R30",
	"title": " Inverse problems",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35R35",
	"title": " Free boundary problems",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35R37",
	"title": " Moving boundary problems",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35R45",
	"title": " Partial differential inequalities",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35R50",
	"title": " Partial differential equations of infinite order",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35R60",
	"title": " Partial differential equations with randomness, stochastic partial differential equations  [See also 60H15]",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35R70",
	"title": " Partial differential equations with multivalued right-hand sides",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35R99",
	"title": " None of the above, but in this section",
	"parentcode": "35Rxx",
	"level": 3
}, {
	"code": "35Sxx",
	"title": " Pseudodifferential operators and other generalizations of partial differential operators [See also 47G30, 58J40]",
	"parentcode": "35-XX",
	"level": 2
}, {
	"code": "35S05",
	"title": " Pseudodifferential operators",
	"parentcode": "35Sxx",
	"level": 3
}, {
	"code": "35S10",
	"title": " Initial value problems for pseudodifferential operators",
	"parentcode": "35Sxx",
	"level": 3
}, {
	"code": "35S11",
	"title": " Initial-boundary value problems for pseudodifferential operators",
	"parentcode": "35Sxx",
	"level": 3
}, {
	"code": "35S15",
	"title": " Boundary value problems for pseudodifferential operators",
	"parentcode": "35Sxx",
	"level": 3
}, {
	"code": "35S30",
	"title": " Fourier integral operators",
	"parentcode": "35Sxx",
	"level": 3
}, {
	"code": "35S35",
	"title": " Topological aspects",
	"parentcode": "35Sxx",
	"level": 3
}, {
	"code": "35S50",
	"title": " Paradifferential operators",
	"parentcode": "35Sxx",
	"level": 3
}, {
	"code": "35S99",
	"title": " None of the above, but in this section",
	"parentcode": "35Sxx",
	"level": 3
}, {
	"code": "37-XX",
	"title": " Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]",
	"parentcode": null,
	"level": 1
}, {
	"code": "37-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "37-XX",
	"level": 2
}, {
	"code": "37-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "37-XX",
	"level": 2
}, {
	"code": "37-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "37-XX",
	"level": 2
}, {
	"code": "37-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "37-XX",
	"level": 2
}, {
	"code": "37-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "37-XX",
	"level": 2
}, {
	"code": "37-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "37-XX",
	"level": 2
}, {
	"code": "37Axx",
	"title": " Ergodic theory [See also 28Dxx]",
	"parentcode": "37-XX",
	"level": 2
}, {
	"code": "37A05",
	"title": " Measure-preserving transformations",
	"parentcode": "37Axx",
	"level": 3
}, {
	"code": "37A10",
	"title": " One-parameter continuous families of measure-preserving transformations",
	"parentcode": "37Axx",
	"level": 3
}, {
	"code": "37A15",
	"title": " General groups of measure-preserving transformations [See mainly 22Fxx]",
	"parentcode": "37Axx",
	"level": 3
}, {
	"code": "37A17",
	"title": " Homogeneous flows [See also 22Fxx]",
	"parentcode": "37Axx",
	"level": 3
}, {
	"code": "37A20",
	"title": " Orbit equivalence, cocycles, ergodic equivalence relations",
	"parentcode": "37Axx",
	"level": 3
}, {
	"code": "37A25",
	"title": " Ergodicity, mixing, rates of mixing",
	"parentcode": "37Axx",
	"level": 3
}, {
	"code": "37A30",
	"title": " Ergodic theorems, spectral theory, Markov operators {For operator ergodic theory, see mainly 47A35}",
	"parentcode": "37Axx",
	"level": 3
}, {
	"code": "37A35",
	"title": " Entropy and other invariants, isomorphism, classification",
	"parentcode": "37Axx",
	"level": 3
}, {
	"code": "37A40",
	"title": " Nonsingular (and infinite-measure preserving) transformations",
	"parentcode": "37Axx",
	"level": 3
}, {
	"code": "37A45",
	"title": " Relations with number theory and harmonic analysis [See also 11Kxx]",
	"parentcode": "37Axx",
	"level": 3
}, {
	"code": "37A50",
	"title": " Relations with probability theory and stochastic processes [See also 60Fxx and 60G10]",
	"parentcode": "37Axx",
	"level": 3
}, {
	"code": "37A55",
	"title": " Relations with the theory of $C^*$-algebras [See mainly 46L55]",
	"parentcode": "37Axx",
	"level": 3
}, {
	"code": "37A60",
	"title": " Dynamical systems in statistical mechanics [See also 82Cxx]",
	"parentcode": "37Axx",
	"level": 3
}, {
	"code": "37A99",
	"title": " None of the above, but in this section",
	"parentcode": "37Axx",
	"level": 3
}, {
	"code": "37Bxx",
	"title": " Topological dynamics [See also 54H20]",
	"parentcode": "37-XX",
	"level": 2
}, {
	"code": "37B05",
	"title": " Transformations and group actions with special properties (minimality, distality, proximality, etc.)",
	"parentcode": "37Bxx",
	"level": 3
}, {
	"code": "37B10",
	"title": " Symbolic dynamics [See also 37Cxx, 37Dxx]",
	"parentcode": "37Bxx",
	"level": 3
}, {
	"code": "37B15",
	"title": " Cellular automata [See also 68Q80]",
	"parentcode": "37Bxx",
	"level": 3
}, {
	"code": "37B20",
	"title": " Notions of recurrence",
	"parentcode": "37Bxx",
	"level": 3
}, {
	"code": "37B25",
	"title": " Lyapunov functions and stability; attractors, repellers",
	"parentcode": "37Bxx",
	"level": 3
}, {
	"code": "37B30",
	"title": " Index theory, Morse-Conley indices",
	"parentcode": "37Bxx",
	"level": 3
}, {
	"code": "37B35",
	"title": " Gradient-like and recurrent behavior; isolated (locally maximal) invariant sets",
	"parentcode": "37Bxx",
	"level": 3
}, {
	"code": "37B40",
	"title": " Topological entropy",
	"parentcode": "37Bxx",
	"level": 3
}, {
	"code": "37B45",
	"title": " Continua theory in dynamics",
	"parentcode": "37Bxx",
	"level": 3
}, {
	"code": "37B50",
	"title": " Multi-dimensional shifts of finite type, tiling dynamics",
	"parentcode": "37Bxx",
	"level": 3
}, {
	"code": "37B55",
	"title": " Nonautonomous dynamical systems",
	"parentcode": "37Bxx",
	"level": 3
}, {
	"code": "37B99",
	"title": " None of the above, but in this section",
	"parentcode": "37Bxx",
	"level": 3
}, {
	"code": "37Cxx",
	"title": " Smooth dynamical systems",
	"parentcode": "37-XX",
	"level": 2
}, {
	"code": "37C05",
	"title": " Smooth mappings and diffeomorphisms",
	"parentcode": "37Cxx",
	"level": 3
}, {
	"code": "37C10",
	"title": " Vector fields, flows, ordinary differential equations",
	"parentcode": "37Cxx",
	"level": 3
}, {
	"code": "37C15",
	"title": " Topological and differentiable equivalence, conjugacy, invariants, moduli, classification",
	"parentcode": "37Cxx",
	"level": 3
}, {
	"code": "37C20",
	"title": " Generic properties, structural stability",
	"parentcode": "37Cxx",
	"level": 3
}, {
	"code": "37C25",
	"title": " Fixed points, periodic points, fixed-point index theory",
	"parentcode": "37Cxx",
	"level": 3
}, {
	"code": "37C27",
	"title": " Periodic orbits of vector fields and flows",
	"parentcode": "37Cxx",
	"level": 3
}, {
	"code": "37C29",
	"title": " Homoclinic and heteroclinic orbits",
	"parentcode": "37Cxx",
	"level": 3
}, {
	"code": "37C30",
	"title": " Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems",
	"parentcode": "37Cxx",
	"level": 3
}, {
	"code": "37C35",
	"title": " Orbit growth",
	"parentcode": "37Cxx",
	"level": 3
}, {
	"code": "37C40",
	"title": " Smooth ergodic theory, invariant measures [See also 37Dxx]",
	"parentcode": "37Cxx",
	"level": 3
}, {
	"code": "37C45",
	"title": " Dimension theory of dynamical systems",
	"parentcode": "37Cxx",
	"level": 3
}, {
	"code": "37C50",
	"title": " Approximate trajectories (pseudotrajectories, shadowing, etc.)",
	"parentcode": "37Cxx",
	"level": 3
}, {
	"code": "37C55",
	"title": " Periodic and quasiperiodic flows and diffeomorphisms",
	"parentcode": "37Cxx",
	"level": 3
}, {
	"code": "37C60",
	"title": " Nonautonomous smooth dynamical systems [See also 37B55]",
	"parentcode": "37Cxx",
	"level": 3
}, {
	"code": "37C65",
	"title": " Monotone flows",
	"parentcode": "37Cxx",
	"level": 3
}, {
	"code": "37C70",
	"title": " Attractors and repellers, topological structure",
	"parentcode": "37Cxx",
	"level": 3
}, {
	"code": "37C75",
	"title": " Stability theory",
	"parentcode": "37Cxx",
	"level": 3
}, {
	"code": "37C80",
	"title": " Symmetries, equivariant dynamical systems",
	"parentcode": "37Cxx",
	"level": 3
}, {
	"code": "37C85",
	"title": " Dynamics of group actions other than ${\\bf Z}$ and ${\\bf R}$, and foliations [See mainly 22Fxx, and also 57R30, 57Sxx]",
	"parentcode": "37Cxx",
	"level": 3
}, {
	"code": "37C99",
	"title": " None of the above, but in this section",
	"parentcode": "37Cxx",
	"level": 3
}, {
	"code": "37Dxx",
	"title": " Dynamical systems with hyperbolic behavior",
	"parentcode": "37-XX",
	"level": 2
}, {
	"code": "37D05",
	"title": " Hyperbolic orbits and sets",
	"parentcode": "37Dxx",
	"level": 3
}, {
	"code": "37D10",
	"title": " Invariant manifold theory",
	"parentcode": "37Dxx",
	"level": 3
}, {
	"code": "37D15",
	"title": " Morse-Smale systems",
	"parentcode": "37Dxx",
	"level": 3
}, {
	"code": "37D20",
	"title": " Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)",
	"parentcode": "37Dxx",
	"level": 3
}, {
	"code": "37D25",
	"title": " Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)",
	"parentcode": "37Dxx",
	"level": 3
}, {
	"code": "37D30",
	"title": " Partially hyperbolic systems and dominated splittings",
	"parentcode": "37Dxx",
	"level": 3
}, {
	"code": "37D35",
	"title": " Thermodynamic formalism, variational principles, equilibrium states",
	"parentcode": "37Dxx",
	"level": 3
}, {
	"code": "37D40",
	"title": " Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)",
	"parentcode": "37Dxx",
	"level": 3
}, {
	"code": "37D45",
	"title": " Strange attractors, chaotic dynamics",
	"parentcode": "37Dxx",
	"level": 3
}, {
	"code": "37D50",
	"title": " Hyperbolic systems with singularities (billiards, etc.)",
	"parentcode": "37Dxx",
	"level": 3
}, {
	"code": "37D99",
	"title": " None of the above, but in this section",
	"parentcode": "37Dxx",
	"level": 3
}, {
	"code": "37Exx",
	"title": " Low-dimensional dynamical systems",
	"parentcode": "37-XX",
	"level": 2
}, {
	"code": "37E05",
	"title": " Maps of the interval (piecewise continuous, continuous, smooth)",
	"parentcode": "37Exx",
	"level": 3
}, {
	"code": "37E10",
	"title": " Maps of the circle",
	"parentcode": "37Exx",
	"level": 3
}, {
	"code": "37E15",
	"title": " Combinatorial dynamics (types of periodic orbits)",
	"parentcode": "37Exx",
	"level": 3
}, {
	"code": "37E20",
	"title": " Universality, renormalization [See also 37F25]",
	"parentcode": "37Exx",
	"level": 3
}, {
	"code": "37E25",
	"title": " Maps of trees and graphs",
	"parentcode": "37Exx",
	"level": 3
}, {
	"code": "37E30",
	"title": " Homeomorphisms and diffeomorphisms of planes and surfaces",
	"parentcode": "37Exx",
	"level": 3
}, {
	"code": "37E35",
	"title": " Flows on surfaces",
	"parentcode": "37Exx",
	"level": 3
}, {
	"code": "37E40",
	"title": " Twist maps",
	"parentcode": "37Exx",
	"level": 3
}, {
	"code": "37E45",
	"title": " Rotation numbers and vectors",
	"parentcode": "37Exx",
	"level": 3
}, {
	"code": "37E99",
	"title": " None of the above, but in this section",
	"parentcode": "37Exx",
	"level": 3
}, {
	"code": "37Fxx",
	"title": " Complex dynamical systems [See also 30D05, 32H50]",
	"parentcode": "37-XX",
	"level": 2
}, {
	"code": "37F05",
	"title": " Relations and correspondences",
	"parentcode": "37Fxx",
	"level": 3
}, {
	"code": "37F10",
	"title": " Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04]",
	"parentcode": "37Fxx",
	"level": 3
}, {
	"code": "37F15",
	"title": " Expanding maps; hyperbolicity; structural stability",
	"parentcode": "37Fxx",
	"level": 3
}, {
	"code": "37F20",
	"title": " Combinatorics and topology",
	"parentcode": "37Fxx",
	"level": 3
}, {
	"code": "37F25",
	"title": " Renormalization",
	"parentcode": "37Fxx",
	"level": 3
}, {
	"code": "37F30",
	"title": " Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems",
	"parentcode": "37Fxx",
	"level": 3
}, {
	"code": "37F35",
	"title": " Conformal densities and Hausdorff dimension",
	"parentcode": "37Fxx",
	"level": 3
}, {
	"code": "37F40",
	"title": " Geometric limits",
	"parentcode": "37Fxx",
	"level": 3
}, {
	"code": "37F45",
	"title": " Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations",
	"parentcode": "37Fxx",
	"level": 3
}, {
	"code": "37F50",
	"title": " Small divisors, rotation domains and linearization; Fatou and Julia sets",
	"parentcode": "37Fxx",
	"level": 3
}, {
	"code": "37F75",
	"title": " Holomorphic foliations and vector fields [See also 32M25, 32S65, 34Mxx]",
	"parentcode": "37Fxx",
	"level": 3
}, {
	"code": "37F99",
	"title": " None of the above, but in this section",
	"parentcode": "37Fxx",
	"level": 3
}, {
	"code": "37Gxx",
	"title": " Local and nonlocal bifurcation theory [See also 34C23, 34K18]",
	"parentcode": "37-XX",
	"level": 2
}, {
	"code": "37G05",
	"title": " Normal forms",
	"parentcode": "37Gxx",
	"level": 3
}, {
	"code": "37G10",
	"title": " Bifurcations of singular points",
	"parentcode": "37Gxx",
	"level": 3
}, {
	"code": "37G15",
	"title": " Bifurcations of limit cycles and periodic orbits",
	"parentcode": "37Gxx",
	"level": 3
}, {
	"code": "37G20",
	"title": " Hyperbolic singular points with homoclinic trajectories",
	"parentcode": "37Gxx",
	"level": 3
}, {
	"code": "37G25",
	"title": " Bifurcations connected with nontransversal intersection",
	"parentcode": "37Gxx",
	"level": 3
}, {
	"code": "37G30",
	"title": " Infinite nonwandering sets arising in bifurcations",
	"parentcode": "37Gxx",
	"level": 3
}, {
	"code": "37G35",
	"title": " Attractors and their bifurcations",
	"parentcode": "37Gxx",
	"level": 3
}, {
	"code": "37G40",
	"title": " Symmetries, equivariant bifurcation theory",
	"parentcode": "37Gxx",
	"level": 3
}, {
	"code": "37G99",
	"title": " None of the above, but in this section",
	"parentcode": "37Gxx",
	"level": 3
}, {
	"code": "37Hxx",
	"title": " Random dynamical systems [See also 15B52, 34D08, 34F05, 47B80, 70L05, 82C05, 93Exx]",
	"parentcode": "37-XX",
	"level": 2
}, {
	"code": "37H05",
	"title": " Foundations, general theory of cocycles, algebraic ergodic theory [See also 37Axx]",
	"parentcode": "37Hxx",
	"level": 3
}, {
	"code": "37H10",
	"title": " Generation, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15]",
	"parentcode": "37Hxx",
	"level": 3
}, {
	"code": "37H15",
	"title": " Multiplicative ergodic theory, Lyapunov exponents [See also 34D08, 37Axx, 37Cxx, 37Dxx]",
	"parentcode": "37Hxx",
	"level": 3
}, {
	"code": "37H20",
	"title": " Bifurcation theory [See also 37Gxx]",
	"parentcode": "37Hxx",
	"level": 3
}, {
	"code": "37H99",
	"title": " None of the above, but in this section",
	"parentcode": "37Hxx",
	"level": 3
}, {
	"code": "37Jxx",
	"title": " Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [See also 53Dxx, 70Fxx, 70Hxx]",
	"parentcode": "37-XX",
	"level": 2
}, {
	"code": "37J05",
	"title": " General theory, relations with symplectic geometry and topology",
	"parentcode": "37Jxx",
	"level": 3
}, {
	"code": "37J10",
	"title": " Symplectic mappings, fixed points",
	"parentcode": "37Jxx",
	"level": 3
}, {
	"code": "37J15",
	"title": " Symmetries, invariants, invariant manifolds, momentum maps, reduction [See also 53D20]",
	"parentcode": "37Jxx",
	"level": 3
}, {
	"code": "37J20",
	"title": " Bifurcation problems",
	"parentcode": "37Jxx",
	"level": 3
}, {
	"code": "37J25",
	"title": " Stability problems",
	"parentcode": "37Jxx",
	"level": 3
}, {
	"code": "37J30",
	"title": " Obstructions to integrability (nonintegrability criteria)",
	"parentcode": "37Jxx",
	"level": 3
}, {
	"code": "37J35",
	"title": " Completely integrable systems, topological structure of phase space, integration methods",
	"parentcode": "37Jxx",
	"level": 3
}, {
	"code": "37J40",
	"title": " Perturbations, normal forms, small divisors, KAM theory, Arnol'd diffusion",
	"parentcode": "37Jxx",
	"level": 3
}, {
	"code": "37J45",
	"title": " Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods",
	"parentcode": "37Jxx",
	"level": 3
}, {
	"code": "37J50",
	"title": " Action-minimizing orbits and measures",
	"parentcode": "37Jxx",
	"level": 3
}, {
	"code": "37J55",
	"title": " Contact systems [See also 53D10]",
	"parentcode": "37Jxx",
	"level": 3
}, {
	"code": "37J60",
	"title": " Nonholonomic dynamical systems [See also 70F25]",
	"parentcode": "37Jxx",
	"level": 3
}, {
	"code": "37J99",
	"title": " None of the above, but in this section",
	"parentcode": "37Jxx",
	"level": 3
}, {
	"code": "37Kxx",
	"title": " Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx]",
	"parentcode": "37-XX",
	"level": 2
}, {
	"code": "37K05",
	"title": " Hamiltonian structures, symmetries, variational principles, conservation laws",
	"parentcode": "37Kxx",
	"level": 3
}, {
	"code": "37K10",
	"title": " Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)",
	"parentcode": "37Kxx",
	"level": 3
}, {
	"code": "37K15",
	"title": " Integration of completely integrable systems by inverse spectral and scattering methods",
	"parentcode": "37Kxx",
	"level": 3
}, {
	"code": "37K20",
	"title": " Relations with algebraic geometry, complex analysis, special functions [See also 14H70]",
	"parentcode": "37Kxx",
	"level": 3
}, {
	"code": "37K25",
	"title": " Relations with differential geometry",
	"parentcode": "37Kxx",
	"level": 3
}, {
	"code": "37K30",
	"title": " Relations with infinite-dimensional Lie algebras and other algebraic structures",
	"parentcode": "37Kxx",
	"level": 3
}, {
	"code": "37K35",
	"title": " Lie-Bäcklund and other transformations",
	"parentcode": "37Kxx",
	"level": 3
}, {
	"code": "37K40",
	"title": " Soliton theory, asymptotic behavior of solutions",
	"parentcode": "37Kxx",
	"level": 3
}, {
	"code": "37K45",
	"title": " Stability problems",
	"parentcode": "37Kxx",
	"level": 3
}, {
	"code": "37K50",
	"title": " Bifurcation problems",
	"parentcode": "37Kxx",
	"level": 3
}, {
	"code": "37K55",
	"title": " Perturbations, KAM for infinite-dimensional systems",
	"parentcode": "37Kxx",
	"level": 3
}, {
	"code": "37K60",
	"title": " Lattice dynamics [See also 37L60]",
	"parentcode": "37Kxx",
	"level": 3
}, {
	"code": "37K65",
	"title": " Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics",
	"parentcode": "37Kxx",
	"level": 3
}, {
	"code": "37K99",
	"title": " None of the above, but in this section",
	"parentcode": "37Kxx",
	"level": 3
}, {
	"code": "37Lxx",
	"title": " Infinite-dimensional dissipative dynamical systems [See also 35Bxx, 35Qxx]",
	"parentcode": "37-XX",
	"level": 2
}, {
	"code": "37L05",
	"title": " General theory, nonlinear semigroups, evolution equations",
	"parentcode": "37Lxx",
	"level": 3
}, {
	"code": "37L10",
	"title": " Normal forms, center manifold theory, bifurcation theory",
	"parentcode": "37Lxx",
	"level": 3
}, {
	"code": "37L15",
	"title": " Stability problems",
	"parentcode": "37Lxx",
	"level": 3
}, {
	"code": "37L20",
	"title": " Symmetries",
	"parentcode": "37Lxx",
	"level": 3
}, {
	"code": "37L25",
	"title": " Inertial manifolds and other invariant attracting sets",
	"parentcode": "37Lxx",
	"level": 3
}, {
	"code": "37L30",
	"title": " Attractors and their dimensions, Lyapunov exponents",
	"parentcode": "37Lxx",
	"level": 3
}, {
	"code": "37L40",
	"title": " Invariant measures",
	"parentcode": "37Lxx",
	"level": 3
}, {
	"code": "37L45",
	"title": " Hyperbolicity; Lyapunov functions",
	"parentcode": "37Lxx",
	"level": 3
}, {
	"code": "37L50",
	"title": " Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systems",
	"parentcode": "37Lxx",
	"level": 3
}, {
	"code": "37L55",
	"title": " Infinite-dimensional random dynamical systems; stochastic equations [See also 35R60, 60H10, 60H15]",
	"parentcode": "37Lxx",
	"level": 3
}, {
	"code": "37L60",
	"title": " Lattice dynamics [See also 37K60]",
	"parentcode": "37Lxx",
	"level": 3
}, {
	"code": "37L65",
	"title": " Special approximation methods (nonlinear Galerkin, etc.)",
	"parentcode": "37Lxx",
	"level": 3
}, {
	"code": "37L99",
	"title": " None of the above, but in this section",
	"parentcode": "37Lxx",
	"level": 3
}, {
	"code": "37Mxx",
	"title": " Approximation methods and numerical treatment of dynamical systems [See also 65Pxx]",
	"parentcode": "37-XX",
	"level": 2
}, {
	"code": "37M05",
	"title": " Simulation",
	"parentcode": "37Mxx",
	"level": 3
}, {
	"code": "37M10",
	"title": " Time series analysis",
	"parentcode": "37Mxx",
	"level": 3
}, {
	"code": "37M15",
	"title": " Symplectic integrators",
	"parentcode": "37Mxx",
	"level": 3
}, {
	"code": "37M20",
	"title": " Computational methods for bifurcation problems",
	"parentcode": "37Mxx",
	"level": 3
}, {
	"code": "37M25",
	"title": " Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy)",
	"parentcode": "37Mxx",
	"level": 3
}, {
	"code": "37M99",
	"title": " None of the above, but in this section",
	"parentcode": "37Mxx",
	"level": 3
}, {
	"code": "37Nxx",
	"title": " Applications",
	"parentcode": "37-XX",
	"level": 2
}, {
	"code": "37N05",
	"title": " Dynamical systems in classical and celestial mechanics [See mainly 70Fxx, 70Hxx, 70Kxx]",
	"parentcode": "37Nxx",
	"level": 3
}, {
	"code": "37N10",
	"title": " Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly 76-XX, especially 76D05, 76F20, 86A05, 86A10]",
	"parentcode": "37Nxx",
	"level": 3
}, {
	"code": "37N15",
	"title": " Dynamical systems in solid mechanics [See mainly 74Hxx]",
	"parentcode": "37Nxx",
	"level": 3
}, {
	"code": "37N20",
	"title": " Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)",
	"parentcode": "37Nxx",
	"level": 3
}, {
	"code": "37N25",
	"title": " Dynamical systems in biology [See mainly 92-XX, but also 91-XX]",
	"parentcode": "37Nxx",
	"level": 3
}, {
	"code": "37N30",
	"title": " Dynamical systems in numerical analysis",
	"parentcode": "37Nxx",
	"level": 3
}, {
	"code": "37N35",
	"title": " Dynamical systems in control",
	"parentcode": "37Nxx",
	"level": 3
}, {
	"code": "37N40",
	"title": " Dynamical systems in optimization and economics",
	"parentcode": "37Nxx",
	"level": 3
}, {
	"code": "37N99",
	"title": " None of the above, but in this section",
	"parentcode": "37Nxx",
	"level": 3
}, {
	"code": "37Pxx",
	"title": " Arithmetic and non-Archimedean dynamical systems [See also 11S82, 37A45]",
	"parentcode": "37-XX",
	"level": 2
}, {
	"code": "37P05",
	"title": " Polynomial and rational maps",
	"parentcode": "37Pxx",
	"level": 3
}, {
	"code": "37P10",
	"title": " Analytic and meromorphic maps",
	"parentcode": "37Pxx",
	"level": 3
}, {
	"code": "37P15",
	"title": " Global ground fields",
	"parentcode": "37Pxx",
	"level": 3
}, {
	"code": "37P20",
	"title": " Non-Archimedean local ground fields",
	"parentcode": "37Pxx",
	"level": 3
}, {
	"code": "37P25",
	"title": " Finite ground fields",
	"parentcode": "37Pxx",
	"level": 3
}, {
	"code": "37P30",
	"title": " Height functions; Green functions; invariant measures [See also 11G50, 14G40]",
	"parentcode": "37Pxx",
	"level": 3
}, {
	"code": "37P35",
	"title": " Arithmetic properties of periodic points",
	"parentcode": "37Pxx",
	"level": 3
}, {
	"code": "37P40",
	"title": " Non-Archimedean Fatou and Julia sets",
	"parentcode": "37Pxx",
	"level": 3
}, {
	"code": "37P45",
	"title": " Families and moduli spaces",
	"parentcode": "37Pxx",
	"level": 3
}, {
	"code": "37P50",
	"title": " Dynamical systems on Berkovich spaces",
	"parentcode": "37Pxx",
	"level": 3
}, {
	"code": "37P55",
	"title": " Arithmetic dynamics on general algebraic varieties",
	"parentcode": "37Pxx",
	"level": 3
}, {
	"code": "37P99",
	"title": " None of the above, but in this section",
	"parentcode": "37Pxx",
	"level": 3
}, {
	"code": "39-XX",
	"title": " Difference and functional equations",
	"parentcode": null,
	"level": 1
}, {
	"code": "39-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "39-XX",
	"level": 2
}, {
	"code": "39-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "39-XX",
	"level": 2
}, {
	"code": "39-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "39-XX",
	"level": 2
}, {
	"code": "39-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "39-XX",
	"level": 2
}, {
	"code": "39-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "39-XX",
	"level": 2
}, {
	"code": "39-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "39-XX",
	"level": 2
}, {
	"code": "39Axx",
	"title": " Difference equations {For dynamical systems, see 37-XX; for dynamic equations on time scales, see 34N05}",
	"parentcode": "39-XX",
	"level": 2
}, {
	"code": "39A05",
	"title": " General theory",
	"parentcode": "39Axx",
	"level": 3
}, {
	"code": "39A06",
	"title": " Linear equations",
	"parentcode": "39Axx",
	"level": 3
}, {
	"code": "39A10",
	"title": " Difference equations, additive",
	"parentcode": "39Axx",
	"level": 3
}, {
	"code": "39A12",
	"title": " Discrete version of topics in analysis",
	"parentcode": "39Axx",
	"level": 3
}, {
	"code": "39A13",
	"title": " Difference equations, scaling ($q$-differences) [See also 33Dxx]",
	"parentcode": "39Axx",
	"level": 3
}, {
	"code": "39A14",
	"title": " Partial difference equations",
	"parentcode": "39Axx",
	"level": 3
}, {
	"code": "39A20",
	"title": " Multiplicative and other generalized difference equations, e.g. of Lyness type",
	"parentcode": "39Axx",
	"level": 3
}, {
	"code": "39A21",
	"title": " Oscillation theory",
	"parentcode": "39Axx",
	"level": 3
}, {
	"code": "39A22",
	"title": " Growth, boundedness, comparison of solutions",
	"parentcode": "39Axx",
	"level": 3
}, {
	"code": "39A23",
	"title": " Periodic solutions",
	"parentcode": "39Axx",
	"level": 3
}, {
	"code": "39A24",
	"title": " Almost periodic solutions",
	"parentcode": "39Axx",
	"level": 3
}, {
	"code": "39A28",
	"title": " Bifurcation theory",
	"parentcode": "39Axx",
	"level": 3
}, {
	"code": "39A30",
	"title": " Stability theory",
	"parentcode": "39Axx",
	"level": 3
}, {
	"code": "39A33",
	"title": " Complex (chaotic) behavior of solutions",
	"parentcode": "39Axx",
	"level": 3
}, {
	"code": "39A45",
	"title": " Equations in the complex domain",
	"parentcode": "39Axx",
	"level": 3
}, {
	"code": "39A50",
	"title": " Stochastic difference equations",
	"parentcode": "39Axx",
	"level": 3
}, {
	"code": "39A60",
	"title": " Applications",
	"parentcode": "39Axx",
	"level": 3
}, {
	"code": "39A70",
	"title": " Difference operators [See also 47B39]",
	"parentcode": "39Axx",
	"level": 3
}, {
	"code": "39A99",
	"title": " None of the above, but in this section",
	"parentcode": "39Axx",
	"level": 3
}, {
	"code": "39Bxx",
	"title": " Functional equations and inequalities [See also 30D05]",
	"parentcode": "39-XX",
	"level": 2
}, {
	"code": "39B05",
	"title": " General",
	"parentcode": "39Bxx",
	"level": 3
}, {
	"code": "39B12",
	"title": " Iteration theory, iterative and composite equations [See also 26A18, 30D05, 37-XX]",
	"parentcode": "39Bxx",
	"level": 3
}, {
	"code": "39B22",
	"title": " Equations for real functions [See also 26A51, 26B25]",
	"parentcode": "39Bxx",
	"level": 3
}, {
	"code": "39B32",
	"title": " Equations for complex functions [See also 30D05]",
	"parentcode": "39Bxx",
	"level": 3
}, {
	"code": "39B42",
	"title": " Matrix and operator equations [See also 47Jxx]",
	"parentcode": "39Bxx",
	"level": 3
}, {
	"code": "39B52",
	"title": " Equations for functions with more general domains and/or ranges",
	"parentcode": "39Bxx",
	"level": 3
}, {
	"code": "39B55",
	"title": " Orthogonal additivity and other conditional equations",
	"parentcode": "39Bxx",
	"level": 3
}, {
	"code": "39B62",
	"title": " Functional inequalities, including subadditivity, convexity, etc. [See also 26A51, 26B25, 26Dxx]",
	"parentcode": "39Bxx",
	"level": 3
}, {
	"code": "39B72",
	"title": " Systems of functional equations and inequalities",
	"parentcode": "39Bxx",
	"level": 3
}, {
	"code": "39B82",
	"title": " Stability, separation, extension, and related topics [See also 46A22]",
	"parentcode": "39Bxx",
	"level": 3
}, {
	"code": "39B99",
	"title": " None of the above, but in this section",
	"parentcode": "39Bxx",
	"level": 3
}, {
	"code": "40-XX",
	"title": " Sequences, series, summability",
	"parentcode": null,
	"level": 1
}, {
	"code": "40-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "40-XX",
	"level": 2
}, {
	"code": "40-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "40-XX",
	"level": 2
}, {
	"code": "40-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "40-XX",
	"level": 2
}, {
	"code": "40-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "40-XX",
	"level": 2
}, {
	"code": "40-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "40-XX",
	"level": 2
}, {
	"code": "40-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "40-XX",
	"level": 2
}, {
	"code": "40Axx",
	"title": " Convergence and divergence of infinite limiting processes",
	"parentcode": "40-XX",
	"level": 2
}, {
	"code": "40A05",
	"title": " Convergence and divergence of series and sequences",
	"parentcode": "40Axx",
	"level": 3
}, {
	"code": "40A10",
	"title": " Convergence and divergence of integrals",
	"parentcode": "40Axx",
	"level": 3
}, {
	"code": "40A15",
	"title": " Convergence and divergence of continued fractions [See also 30B70]",
	"parentcode": "40Axx",
	"level": 3
}, {
	"code": "40A20",
	"title": " Convergence and divergence of infinite products",
	"parentcode": "40Axx",
	"level": 3
}, {
	"code": "40A25",
	"title": " Approximation to limiting values (summation of series, etc.) {For the Euler-Maclaurin summation formula, see 65B15}",
	"parentcode": "40Axx",
	"level": 3
}, {
	"code": "40A30",
	"title": " Convergence and divergence of series and sequences of functions",
	"parentcode": "40Axx",
	"level": 3
}, {
	"code": "40A35",
	"title": " Ideal and statistical convergence [See also 40G15]",
	"parentcode": "40Axx",
	"level": 3
}, {
	"code": "40A99",
	"title": " None of the above, but in this section",
	"parentcode": "40Axx",
	"level": 3
}, {
	"code": "40Bxx",
	"title": " Multiple sequences and series",
	"parentcode": "40-XX",
	"level": 2
}, {
	"code": "40B05",
	"title": " Multiple sequences and series (should also be assigned at least one other classification number in this section)",
	"parentcode": "40Bxx",
	"level": 3
}, {
	"code": "40B99",
	"title": " None of the above, but in this section",
	"parentcode": "40Bxx",
	"level": 3
}, {
	"code": "40Cxx",
	"title": " General summability methods",
	"parentcode": "40-XX",
	"level": 2
}, {
	"code": "40C05",
	"title": " Matrix methods",
	"parentcode": "40Cxx",
	"level": 3
}, {
	"code": "40C10",
	"title": " Integral methods",
	"parentcode": "40Cxx",
	"level": 3
}, {
	"code": "40C15",
	"title": " Function-theoretic methods (including power series methods and semicontinuous methods)",
	"parentcode": "40Cxx",
	"level": 3
}, {
	"code": "40C99",
	"title": " None of the above, but in this section",
	"parentcode": "40Cxx",
	"level": 3
}, {
	"code": "40Dxx",
	"title": " Direct theorems on summability",
	"parentcode": "40-XX",
	"level": 2
}, {
	"code": "40D05",
	"title": " General theorems",
	"parentcode": "40Dxx",
	"level": 3
}, {
	"code": "40D09",
	"title": " Structure of summability fields",
	"parentcode": "40Dxx",
	"level": 3
}, {
	"code": "40D10",
	"title": " Tauberian constants and oscillation limits",
	"parentcode": "40Dxx",
	"level": 3
}, {
	"code": "40D15",
	"title": " Convergence factors and summability factors",
	"parentcode": "40Dxx",
	"level": 3
}, {
	"code": "40D20",
	"title": " Summability and bounded fields of methods",
	"parentcode": "40Dxx",
	"level": 3
}, {
	"code": "40D25",
	"title": " Inclusion and equivalence theorems",
	"parentcode": "40Dxx",
	"level": 3
}, {
	"code": "40D99",
	"title": " None of the above, but in this section",
	"parentcode": "40Dxx",
	"level": 3
}, {
	"code": "40Exx",
	"title": " Inversion theorems",
	"parentcode": "40-XX",
	"level": 2
}, {
	"code": "40E05",
	"title": " Tauberian theorems, general",
	"parentcode": "40Exx",
	"level": 3
}, {
	"code": "40E10",
	"title": " Growth estimates",
	"parentcode": "40Exx",
	"level": 3
}, {
	"code": "40E15",
	"title": " Lacunary inversion theorems",
	"parentcode": "40Exx",
	"level": 3
}, {
	"code": "40E20",
	"title": " Tauberian constants",
	"parentcode": "40Exx",
	"level": 3
}, {
	"code": "40E99",
	"title": " None of the above, but in this section",
	"parentcode": "40Exx",
	"level": 3
}, {
	"code": "40Fxx",
	"title": " Absolute and strong summability (should also be assigned at least one other classification number in Section 40)",
	"parentcode": "40-XX",
	"level": 2
}, {
	"code": "40F05",
	"title": " Absolute and strong summability (should also be assigned at least one other classification number in Section 40)",
	"parentcode": "40Fxx",
	"level": 3
}, {
	"code": "40F99",
	"title": " None of the above, but in this section",
	"parentcode": "40Fxx",
	"level": 3
}, {
	"code": "40Gxx",
	"title": " Special methods of summability",
	"parentcode": "40-XX",
	"level": 2
}, {
	"code": "40G05",
	"title": " Cesàro, Euler, Nörlund and Hausdorff methods",
	"parentcode": "40Gxx",
	"level": 3
}, {
	"code": "40G10",
	"title": " Abel, Borel and power series methods",
	"parentcode": "40Gxx",
	"level": 3
}, {
	"code": "40G15",
	"title": " Summability methods using statistical convergence [See also 40A35]",
	"parentcode": "40Gxx",
	"level": 3
}, {
	"code": "40G99",
	"title": " None of the above, but in this section",
	"parentcode": "40Gxx",
	"level": 3
}, {
	"code": "40Hxx",
	"title": " Functional analytic methods in summability",
	"parentcode": "40-XX",
	"level": 2
}, {
	"code": "40H05",
	"title": " Functional analytic methods in summability",
	"parentcode": "40Hxx",
	"level": 3
}, {
	"code": "40H99",
	"title": " None of the above, but in this section",
	"parentcode": "40Hxx",
	"level": 3
}, {
	"code": "40Jxx",
	"title": " Summability in abstract structures [See also 43A55, 46A35, 46B15]",
	"parentcode": "40-XX",
	"level": 2
}, {
	"code": "40J05",
	"title": " Summability in abstract structures [See also 43A55, 46A35, 46B15] (should also be assigned at least one other classification number in this section)",
	"parentcode": "40Jxx",
	"level": 3
}, {
	"code": "40J99",
	"title": " None of the above, but in this section",
	"parentcode": "40Jxx",
	"level": 3
}, {
	"code": "41-XX",
	"title": " Approximations and expansions {For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx}",
	"parentcode": null,
	"level": 1
}, {
	"code": "41-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "41-XX",
	"level": 2
}, {
	"code": "41-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "41-XX",
	"level": 2
}, {
	"code": "41-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "41-XX",
	"level": 2
}, {
	"code": "41-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "41-XX",
	"level": 2
}, {
	"code": "41-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "41-XX",
	"level": 2
}, {
	"code": "41-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "41-XX",
	"level": 2
}, {
	"code": "41Axx",
	"title": " Approximations and expansions {For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx}",
	"parentcode": "41-XX",
	"level": 2
}, {
	"code": "41A05",
	"title": " Interpolation [See also 42A15 and 65D05]",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A10",
	"title": " Approximation by polynomials {For approximation by trigonometric polynomials, see 42A10}",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A15",
	"title": " Spline approximation",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A17",
	"title": " Inequalities in approximation (Bernstein, Jackson, Nikol'skiĭ-type inequalities)",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A20",
	"title": " Approximation by rational functions",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A21",
	"title": " Padé approximation",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A25",
	"title": " Rate of convergence, degree of approximation",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A27",
	"title": " Inverse theorems",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A28",
	"title": " Simultaneous approximation",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A29",
	"title": " Approximation with constraints",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A30",
	"title": " Approximation by other special function classes",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A35",
	"title": " Approximation by operators (in particular, by integral operators)",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A36",
	"title": " Approximation by positive operators",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A40",
	"title": " Saturation",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A44",
	"title": " Best constants",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A45",
	"title": " Approximation by arbitrary linear expressions",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A46",
	"title": " Approximation by arbitrary nonlinear expressions; widths and entropy",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A50",
	"title": " Best approximation, Chebyshev systems",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A52",
	"title": " Uniqueness of best approximation",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A55",
	"title": " Approximate quadratures",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A58",
	"title": " Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A60",
	"title": " Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A63",
	"title": " Multidimensional problems (should also be assigned at least one other classification number in this section)",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A65",
	"title": " Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A80",
	"title": " Remainders in approximation formulas",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "41A99",
	"title": " None of the above, but in this section",
	"parentcode": "41Axx",
	"level": 3
}, {
	"code": "42-XX",
	"title": " Harmonic analysis on Euclidean spaces",
	"parentcode": null,
	"level": 1
}, {
	"code": "42-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "42-XX",
	"level": 2
}, {
	"code": "42-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "42-XX",
	"level": 2
}, {
	"code": "42-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "42-XX",
	"level": 2
}, {
	"code": "42-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "42-XX",
	"level": 2
}, {
	"code": "42-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "42-XX",
	"level": 2
}, {
	"code": "42-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "42-XX",
	"level": 2
}, {
	"code": "42Axx",
	"title": " Harmonic analysis in one variable",
	"parentcode": "42-XX",
	"level": 2
}, {
	"code": "42A05",
	"title": " Trigonometric polynomials, inequalities, extremal problems",
	"parentcode": "42Axx",
	"level": 3
}, {
	"code": "42A10",
	"title": " Trigonometric approximation",
	"parentcode": "42Axx",
	"level": 3
}, {
	"code": "42A15",
	"title": " Trigonometric interpolation",
	"parentcode": "42Axx",
	"level": 3
}, {
	"code": "42A16",
	"title": " Fourier coefficients, Fourier series of functions with special properties, special Fourier series {For automorphic theory, see mainly 11F30}",
	"parentcode": "42Axx",
	"level": 3
}, {
	"code": "42A20",
	"title": " Convergence and absolute convergence of Fourier and trigonometric series",
	"parentcode": "42Axx",
	"level": 3
}, {
	"code": "42A24",
	"title": " Summability and absolute summability of Fourier and trigonometric series",
	"parentcode": "42Axx",
	"level": 3
}, {
	"code": "42A32",
	"title": " Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)",
	"parentcode": "42Axx",
	"level": 3
}, {
	"code": "42A38",
	"title": " Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type",
	"parentcode": "42Axx",
	"level": 3
}, {
	"code": "42A45",
	"title": " Multipliers",
	"parentcode": "42Axx",
	"level": 3
}, {
	"code": "42A50",
	"title": " Conjugate functions, conjugate series, singular integrals",
	"parentcode": "42Axx",
	"level": 3
}, {
	"code": "42A55",
	"title": " Lacunary series of trigonometric and other functions; Riesz products",
	"parentcode": "42Axx",
	"level": 3
}, {
	"code": "42A61",
	"title": " Probabilistic methods",
	"parentcode": "42Axx",
	"level": 3
}, {
	"code": "42A63",
	"title": " Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization",
	"parentcode": "42Axx",
	"level": 3
}, {
	"code": "42A65",
	"title": " Completeness of sets of functions",
	"parentcode": "42Axx",
	"level": 3
}, {
	"code": "42A70",
	"title": " Trigonometric moment problems",
	"parentcode": "42Axx",
	"level": 3
}, {
	"code": "42A75",
	"title": " Classical almost periodic functions, mean periodic functions [See also 43A60]",
	"parentcode": "42Axx",
	"level": 3
}, {
	"code": "42A82",
	"title": " Positive definite functions",
	"parentcode": "42Axx",
	"level": 3
}, {
	"code": "42A85",
	"title": " Convolution, factorization",
	"parentcode": "42Axx",
	"level": 3
}, {
	"code": "42A99",
	"title": " None of the above, but in this section",
	"parentcode": "42Axx",
	"level": 3
}, {
	"code": "42Bxx",
	"title": " Harmonic analysis in several variables {For automorphic theory, see mainly 11F30}",
	"parentcode": "42-XX",
	"level": 2
}, {
	"code": "42B05",
	"title": " Fourier series and coefficients",
	"parentcode": "42Bxx",
	"level": 3
}, {
	"code": "42B08",
	"title": " Summability",
	"parentcode": "42Bxx",
	"level": 3
}, {
	"code": "42B10",
	"title": " Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type",
	"parentcode": "42Bxx",
	"level": 3
}, {
	"code": "42B15",
	"title": " Multipliers",
	"parentcode": "42Bxx",
	"level": 3
}, {
	"code": "42B20",
	"title": " Singular and oscillatory integrals (Calderón-Zygmund, etc.)",
	"parentcode": "42Bxx",
	"level": 3
}, {
	"code": "42B25",
	"title": " Maximal functions, Littlewood-Paley theory",
	"parentcode": "42Bxx",
	"level": 3
}, {
	"code": "42B30",
	"title": " $H^p$-spaces",
	"parentcode": "42Bxx",
	"level": 3
}, {
	"code": "42B35",
	"title": " Function spaces arising in harmonic analysis",
	"parentcode": "42Bxx",
	"level": 3
}, {
	"code": "42B37",
	"title": " Harmonic analysis and PDE [See also 35-XX]",
	"parentcode": "42Bxx",
	"level": 3
}, {
	"code": "42B99",
	"title": " None of the above, but in this section",
	"parentcode": "42Bxx",
	"level": 3
}, {
	"code": "42Cxx",
	"title": " Nontrigonometric harmonic analysis",
	"parentcode": "42-XX",
	"level": 2
}, {
	"code": "42C05",
	"title": " Orthogonal functions and polynomials, general theory [See also 33C45, 33C50, 33D45]",
	"parentcode": "42Cxx",
	"level": 3
}, {
	"code": "42C10",
	"title": " Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)",
	"parentcode": "42Cxx",
	"level": 3
}, {
	"code": "42C15",
	"title": " General harmonic expansions, frames",
	"parentcode": "42Cxx",
	"level": 3
}, {
	"code": "42C20",
	"title": " Other transformations of harmonic type",
	"parentcode": "42Cxx",
	"level": 3
}, {
	"code": "42C25",
	"title": " Uniqueness and localization for orthogonal series",
	"parentcode": "42Cxx",
	"level": 3
}, {
	"code": "42C30",
	"title": " Completeness of sets of functions",
	"parentcode": "42Cxx",
	"level": 3
}, {
	"code": "42C40",
	"title": " Wavelets and other special systems",
	"parentcode": "42Cxx",
	"level": 3
}, {
	"code": "42C99",
	"title": " None of the above, but in this section",
	"parentcode": "42Cxx",
	"level": 3
}, {
	"code": "43-XX",
	"title": " Abstract harmonic analysis {For other analysis on topological and Lie groups, see 22Exx}",
	"parentcode": null,
	"level": 1
}, {
	"code": "43-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "43-XX",
	"level": 2
}, {
	"code": "43-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "43-XX",
	"level": 2
}, {
	"code": "43-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "43-XX",
	"level": 2
}, {
	"code": "43-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "43-XX",
	"level": 2
}, {
	"code": "43-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "43-XX",
	"level": 2
}, {
	"code": "43-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "43-XX",
	"level": 2
}, {
	"code": "43Axx",
	"title": " Abstract harmonic analysis {For other analysis on topological and Lie groups, see 22Exx}",
	"parentcode": "43-XX",
	"level": 2
}, {
	"code": "43A05",
	"title": " Measures on groups and semigroups, etc.",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A07",
	"title": " Means on groups, semigroups, etc.; amenable groups",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A10",
	"title": " Measure algebras on groups, semigroups, etc.",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A15",
	"title": " $L^p$-spaces and other function spaces on groups, semigroups, etc.",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A17",
	"title": " Analysis on ordered groups, $H^p$-theory",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A20",
	"title": " $L^1$-algebras on groups, semigroups, etc.",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A22",
	"title": " Homomorphisms and multipliers of function spaces on groups, semigroups, etc.",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A25",
	"title": " Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A30",
	"title": " Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A32",
	"title": " Other transforms and operators of Fourier type",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A35",
	"title": " Positive definite functions on groups, semigroups, etc.",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A40",
	"title": " Character groups and dual objects",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A45",
	"title": " Spectral synthesis on groups, semigroups, etc.",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A46",
	"title": " Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A50",
	"title": " Convergence of Fourier series and of inverse transforms",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A55",
	"title": " Summability methods on groups, semigroups, etc. [See also 40J05]",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A60",
	"title": " Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A62",
	"title": " Hypergroups",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A65",
	"title": " Representations of groups, semigroups, etc. [See also 22A10, 22A20, 22Dxx, 22E45]",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A70",
	"title": " Analysis on specific locally compact and other abelian groups [See also 11R56, 22B05]",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A75",
	"title": " Analysis on specific compact groups",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A77",
	"title": " Analysis on general compact groups",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A80",
	"title": " Analysis on other specific Lie groups [See also 22Exx]",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A85",
	"title": " Analysis on homogeneous spaces",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A90",
	"title": " Spherical functions [See also 22E45, 22E46, 33C55]",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A95",
	"title": " Categorical methods [See also 46Mxx]",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "43A99",
	"title": " None of the above, but in this section",
	"parentcode": "43Axx",
	"level": 3
}, {
	"code": "44-XX",
	"title": " Integral transforms, operational calculus {For fractional derivatives and integrals, see 26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. For numerical methods, see 65R10}",
	"parentcode": null,
	"level": 1
}, {
	"code": "44-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "44-XX",
	"level": 2
}, {
	"code": "44-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "44-XX",
	"level": 2
}, {
	"code": "44-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "44-XX",
	"level": 2
}, {
	"code": "44-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "44-XX",
	"level": 2
}, {
	"code": "44-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "44-XX",
	"level": 2
}, {
	"code": "44-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "44-XX",
	"level": 2
}, {
	"code": "44Axx",
	"title": " Integral transforms, operational calculus {For fractional derivatives and integrals, see 26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. For numerical methods, see 65R10}",
	"parentcode": "44-XX",
	"level": 2
}, {
	"code": "44A05",
	"title": " General transforms [See also 42A38]",
	"parentcode": "44Axx",
	"level": 3
}, {
	"code": "44A10",
	"title": " Laplace transform",
	"parentcode": "44Axx",
	"level": 3
}, {
	"code": "44A12",
	"title": " Radon transform [See also 92C55]",
	"parentcode": "44Axx",
	"level": 3
}, {
	"code": "44A15",
	"title": " Special transforms (Legendre, Hilbert, etc.)",
	"parentcode": "44Axx",
	"level": 3
}, {
	"code": "44A20",
	"title": " Transforms of special functions",
	"parentcode": "44Axx",
	"level": 3
}, {
	"code": "44A30",
	"title": " Multiple transforms",
	"parentcode": "44Axx",
	"level": 3
}, {
	"code": "44A35",
	"title": " Convolution",
	"parentcode": "44Axx",
	"level": 3
}, {
	"code": "44A40",
	"title": " Calculus of Mikusiński and other operational calculi",
	"parentcode": "44Axx",
	"level": 3
}, {
	"code": "44A45",
	"title": " Classical operational calculus",
	"parentcode": "44Axx",
	"level": 3
}, {
	"code": "44A55",
	"title": " Discrete operational calculus",
	"parentcode": "44Axx",
	"level": 3
}, {
	"code": "44A60",
	"title": " Moment problems",
	"parentcode": "44Axx",
	"level": 3
}, {
	"code": "44A99",
	"title": " None of the above, but in this section",
	"parentcode": "44Axx",
	"level": 3
}, {
	"code": "45-XX",
	"title": " Integral equations",
	"parentcode": null,
	"level": 1
}, {
	"code": "45-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45Axx",
	"title": " Linear integral equations",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45A05",
	"title": " Linear integral equations",
	"parentcode": "45Axx",
	"level": 3
}, {
	"code": "45A99",
	"title": " None of the above, but in this section",
	"parentcode": "45Axx",
	"level": 3
}, {
	"code": "45Bxx",
	"title": " Fredholm integral equations",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45B05",
	"title": " Fredholm integral equations",
	"parentcode": "45Bxx",
	"level": 3
}, {
	"code": "45B99",
	"title": " None of the above, but in this section",
	"parentcode": "45Bxx",
	"level": 3
}, {
	"code": "45Cxx",
	"title": " Eigenvalue problems [See also 34Lxx, 35Pxx, 45P05, 47A75]",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45C05",
	"title": " Eigenvalue problems [See also 34Lxx, 35Pxx, 45P05, 47A75]",
	"parentcode": "45Cxx",
	"level": 3
}, {
	"code": "45C99",
	"title": " None of the above, but in this section",
	"parentcode": "45Cxx",
	"level": 3
}, {
	"code": "45Dxx",
	"title": " Volterra integral equations [See also 34A12]",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45D05",
	"title": " Volterra integral equations [See also 34A12]",
	"parentcode": "45Dxx",
	"level": 3
}, {
	"code": "45D99",
	"title": " None of the above, but in this section",
	"parentcode": "45Dxx",
	"level": 3
}, {
	"code": "45Exx",
	"title": " Singular integral equations [See also 30E20, 30E25, 44A15, 44A35]",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45E05",
	"title": " Integral equations with kernels of Cauchy type [See also 35J15]",
	"parentcode": "45Exx",
	"level": 3
}, {
	"code": "45E10",
	"title": " Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) [See also 47B35]",
	"parentcode": "45Exx",
	"level": 3
}, {
	"code": "45E99",
	"title": " None of the above, but in this section",
	"parentcode": "45Exx",
	"level": 3
}, {
	"code": "45Fxx",
	"title": " Systems of linear integral equations",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45F05",
	"title": " Systems of nonsingular linear integral equations",
	"parentcode": "45Fxx",
	"level": 3
}, {
	"code": "45F10",
	"title": " Dual, triple, etc., integral and series equations",
	"parentcode": "45Fxx",
	"level": 3
}, {
	"code": "45F15",
	"title": " Systems of singular linear integral equations",
	"parentcode": "45Fxx",
	"level": 3
}, {
	"code": "45F99",
	"title": " None of the above, but in this section",
	"parentcode": "45Fxx",
	"level": 3
}, {
	"code": "45Gxx",
	"title": " Nonlinear integral equations [See also 47H30, 47Jxx]",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45G05",
	"title": " Singular nonlinear integral equations",
	"parentcode": "45Gxx",
	"level": 3
}, {
	"code": "45G10",
	"title": " Other nonlinear integral equations",
	"parentcode": "45Gxx",
	"level": 3
}, {
	"code": "45G15",
	"title": " Systems of nonlinear integral equations",
	"parentcode": "45Gxx",
	"level": 3
}, {
	"code": "45G99",
	"title": " None of the above, but in this section",
	"parentcode": "45Gxx",
	"level": 3
}, {
	"code": "45Hxx",
	"title": " Miscellaneous special kernels [See also 44A15]",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45H05",
	"title": " Miscellaneous special kernels [See also 44A15]",
	"parentcode": "45Hxx",
	"level": 3
}, {
	"code": "45H99",
	"title": " None of the above, but in this section",
	"parentcode": "45Hxx",
	"level": 3
}, {
	"code": "45Jxx",
	"title": " Integro-ordinary differential equations [See also 34K05, 34K30, 47G20]",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45J05",
	"title": " Integro-ordinary differential equations [See also 34K05, 34K30, 47G20]",
	"parentcode": "45Jxx",
	"level": 3
}, {
	"code": "45J99",
	"title": " None of the above, but in this section",
	"parentcode": "45Jxx",
	"level": 3
}, {
	"code": "45Kxx",
	"title": " Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45K05",
	"title": " Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]",
	"parentcode": "45Kxx",
	"level": 3
}, {
	"code": "45K99",
	"title": " None of the above, but in this section",
	"parentcode": "45Kxx",
	"level": 3
}, {
	"code": "45Lxx",
	"title": " Theoretical approximation of solutions {For numerical analysis, see 65Rxx}",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45L05",
	"title": " Theoretical approximation of solutions {For numerical analysis, see 65Rxx}",
	"parentcode": "45Lxx",
	"level": 3
}, {
	"code": "45L99",
	"title": " None of the above, but in this section",
	"parentcode": "45Lxx",
	"level": 3
}, {
	"code": "45Mxx",
	"title": " Qualitative behavior",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45M05",
	"title": " Asymptotics",
	"parentcode": "45Mxx",
	"level": 3
}, {
	"code": "45M10",
	"title": " Stability theory",
	"parentcode": "45Mxx",
	"level": 3
}, {
	"code": "45M15",
	"title": " Periodic solutions",
	"parentcode": "45Mxx",
	"level": 3
}, {
	"code": "45M20",
	"title": " Positive solutions",
	"parentcode": "45Mxx",
	"level": 3
}, {
	"code": "45M99",
	"title": " None of the above, but in this section",
	"parentcode": "45Mxx",
	"level": 3
}, {
	"code": "45Nxx",
	"title": " Abstract integral equations, integral equations in abstract spaces",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45N05",
	"title": " Abstract integral equations, integral equations in abstract spaces",
	"parentcode": "45Nxx",
	"level": 3
}, {
	"code": "45N99",
	"title": " None of the above, but in this section",
	"parentcode": "45Nxx",
	"level": 3
}, {
	"code": "45Pxx",
	"title": " Integral operators [See also 47B38, 47G10]",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45P05",
	"title": " Integral operators [See also 47B38, 47G10]",
	"parentcode": "45Pxx",
	"level": 3
}, {
	"code": "45P99",
	"title": " None of the above, but in this section",
	"parentcode": "45Pxx",
	"level": 3
}, {
	"code": "45Qxx",
	"title": " Inverse problems",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45Q05",
	"title": " Inverse problems",
	"parentcode": "45Qxx",
	"level": 3
}, {
	"code": "45Q99",
	"title": " None of the above, but in this section",
	"parentcode": "45Qxx",
	"level": 3
}, {
	"code": "45Rxx",
	"title": " Random integral equations [See also 60H20]",
	"parentcode": "45-XX",
	"level": 2
}, {
	"code": "45R05",
	"title": " Random integral equations [See also 60H20]",
	"parentcode": "45Rxx",
	"level": 3
}, {
	"code": "45R99",
	"title": " None of the above, but in this section",
	"parentcode": "45Rxx",
	"level": 3
}, {
	"code": "46-XX",
	"title": " Functional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx}",
	"parentcode": null,
	"level": 1
}, {
	"code": "46-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "46-XX",
	"level": 2
}, {
	"code": "46-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "46-XX",
	"level": 2
}, {
	"code": "46-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "46-XX",
	"level": 2
}, {
	"code": "46-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "46-XX",
	"level": 2
}, {
	"code": "46-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "46-XX",
	"level": 2
}, {
	"code": "46-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "46-XX",
	"level": 2
}, {
	"code": "46Axx",
	"title": " Topological linear spaces and related structures {For function spaces, see 46Exx}",
	"parentcode": "46-XX",
	"level": 2
}, {
	"code": "46A03",
	"title": " General theory of locally convex spaces",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A04",
	"title": " Locally convex Fréchet spaces and (DF)-spaces",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A08",
	"title": " Barrelled spaces, bornological spaces",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A11",
	"title": " Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A13",
	"title": " Spaces defined by inductive or projective limits (LB, LF, etc.) [See also 46M40]",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A16",
	"title": " Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A17",
	"title": " Bornologies and related structures; Mackey convergence, etc.",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A19",
	"title": " Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than ${\\bf R}$, etc.)",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A20",
	"title": " Duality theory",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A22",
	"title": " Theorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10]",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A25",
	"title": " Reflexivity and semi-reflexivity [See also 46B10]",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A30",
	"title": " Open mapping and closed graph theorems; completeness (including $B$-, $B_r$-completeness)",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A32",
	"title": " Spaces of linear operators; topological tensor products; approximation properties [See also 46B28, 46M05, 47L05, 47L20]",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A35",
	"title": " Summability and bases [See also 46B15]",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A40",
	"title": " Ordered topological linear spaces, vector lattices [See also 06F20, 46B40, 46B42]",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A45",
	"title": " Sequence spaces (including Köthe sequence spaces) [See also 46B45]",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A50",
	"title": " Compactness in topological linear spaces; angelic spaces, etc.",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A55",
	"title": " Convex sets in topological linear spaces; Choquet theory [See also 52A07]",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A61",
	"title": " Graded Fréchet spaces and tame operators",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A63",
	"title": " Topological invariants ((DN), ($\\Omega$), etc.)",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A70",
	"title": " Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A80",
	"title": " Modular spaces",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46A99",
	"title": " None of the above, but in this section",
	"parentcode": "46Axx",
	"level": 3
}, {
	"code": "46Bxx",
	"title": " Normed linear spaces and Banach spaces; Banach lattices {For function spaces, see 46Exx}",
	"parentcode": "46-XX",
	"level": 2
}, {
	"code": "46B03",
	"title": " Isomorphic theory (including renorming) of Banach spaces",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46B04",
	"title": " Isometric theory of Banach spaces",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46B06",
	"title": " Asymptotic theory of Banach spaces [See also 52A23]",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46B07",
	"title": " Local theory of Banach spaces",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46B08",
	"title": " Ultraproduct techniques in Banach space theory [See also 46M07]",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46B09",
	"title": " Probabilistic methods in Banach space theory [See also 60Bxx]",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46B10",
	"title": " Duality and reflexivity [See also 46A25]",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46B15",
	"title": " Summability and bases [See also 46A35]",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46B20",
	"title": " Geometry and structure of normed linear spaces",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46B22",
	"title": " Radon-Nikodým, Kreĭn-Milman and related properties [See also 46G10]",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46B25",
	"title": " Classical Banach spaces in the general theory",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46B26",
	"title": " Nonseparable Banach spaces",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46B28",
	"title": " Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46B40",
	"title": " Ordered normed spaces [See also 46A40, 46B42]",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46B42",
	"title": " Banach lattices [See also 46A40, 46B40]",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46B45",
	"title": " Banach sequence spaces [See also 46A45]",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46B50",
	"title": " Compactness in Banach (or normed) spaces",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46B70",
	"title": " Interpolation between normed linear spaces [See also 46M35]",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46B80",
	"title": " Nonlinear classification of Banach spaces; nonlinear quotients",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46B85",
	"title": " Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science [See also 05C12, 68Rxx]",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46B99",
	"title": " None of the above, but in this section",
	"parentcode": "46Bxx",
	"level": 3
}, {
	"code": "46Cxx",
	"title": " Inner product spaces and their generalizations, Hilbert spaces {For function spaces, see 46Exx}",
	"parentcode": "46-XX",
	"level": 2
}, {
	"code": "46C05",
	"title": " Hilbert and pre-Hilbert spaces",
	"parentcode": "46Cxx",
	"level": 3
}, {
	"code": "46C07",
	"title": " Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) [See also 46B70, 46M35]",
	"parentcode": "46Cxx",
	"level": 3
}, {
	"code": "46C15",
	"title": " Characterizations of Hilbert spaces",
	"parentcode": "46Cxx",
	"level": 3
}, {
	"code": "46C20",
	"title": " Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.) [See also 47B50]",
	"parentcode": "46Cxx",
	"level": 3
}, {
	"code": "46C50",
	"title": " Generalizations of inner products (semi-inner products, partial inner products, etc.)",
	"parentcode": "46Cxx",
	"level": 3
}, {
	"code": "46C99",
	"title": " None of the above, but in this section",
	"parentcode": "46Cxx",
	"level": 3
}, {
	"code": "46Exx",
	"title": " Linear function spaces and their duals [See also 30H05, 32A38, 46F05] {For function algebras, see 46J10}",
	"parentcode": "46-XX",
	"level": 2
}, {
	"code": "46E05",
	"title": " Lattices of continuous, differentiable or analytic functions",
	"parentcode": "46Exx",
	"level": 3
}, {
	"code": "46E10",
	"title": " Topological linear spaces of continuous, differentiable or analytic functions",
	"parentcode": "46Exx",
	"level": 3
}, {
	"code": "46E15",
	"title": " Banach spaces of continuous, differentiable or analytic functions",
	"parentcode": "46Exx",
	"level": 3
}, {
	"code": "46E20",
	"title": " Hilbert spaces of continuous, differentiable or analytic functions",
	"parentcode": "46Exx",
	"level": 3
}, {
	"code": "46E22",
	"title": " Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]",
	"parentcode": "46Exx",
	"level": 3
}, {
	"code": "46E25",
	"title": " Rings and algebras of continuous, differentiable or analytic functions {For Banach function algebras, see 46J10, 46J15}",
	"parentcode": "46Exx",
	"level": 3
}, {
	"code": "46E27",
	"title": " Spaces of measures [See also 28A33, 46Gxx]",
	"parentcode": "46Exx",
	"level": 3
}, {
	"code": "46E30",
	"title": " Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)",
	"parentcode": "46Exx",
	"level": 3
}, {
	"code": "46E35",
	"title": " Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems",
	"parentcode": "46Exx",
	"level": 3
}, {
	"code": "46E39",
	"title": " Sobolev (and similar kinds of) spaces of functions of discrete variables",
	"parentcode": "46Exx",
	"level": 3
}, {
	"code": "46E40",
	"title": " Spaces of vector- and operator-valued functions",
	"parentcode": "46Exx",
	"level": 3
}, {
	"code": "46E50",
	"title": " Spaces of differentiable or holomorphic functions on infinite-dimensional spaces [See also 46G20, 46G25, 47H60]",
	"parentcode": "46Exx",
	"level": 3
}, {
	"code": "46E99",
	"title": " None of the above, but in this section",
	"parentcode": "46Exx",
	"level": 3
}, {
	"code": "46Fxx",
	"title": " Distributions, generalized functions, distribution spaces [See also 46T30]",
	"parentcode": "46-XX",
	"level": 2
}, {
	"code": "46F05",
	"title": " Topological linear spaces of test functions, distributions and ultradistributions [See also 46E10, 46E35]",
	"parentcode": "46Fxx",
	"level": 3
}, {
	"code": "46F10",
	"title": " Operations with distributions",
	"parentcode": "46Fxx",
	"level": 3
}, {
	"code": "46F12",
	"title": " Integral transforms in distribution spaces [See also 42-XX, 44-XX]",
	"parentcode": "46Fxx",
	"level": 3
}, {
	"code": "46F15",
	"title": " Hyperfunctions, analytic functionals [See also 32A25, 32A45, 32C35, 58J15]",
	"parentcode": "46Fxx",
	"level": 3
}, {
	"code": "46F20",
	"title": " Distributions and ultradistributions as boundary values of analytic functions [See also 30D40, 30E25, 32A40]",
	"parentcode": "46Fxx",
	"level": 3
}, {
	"code": "46F25",
	"title": " Distributions on infinite-dimensional spaces [See also 58C35]",
	"parentcode": "46Fxx",
	"level": 3
}, {
	"code": "46F30",
	"title": " Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)",
	"parentcode": "46Fxx",
	"level": 3
}, {
	"code": "46F99",
	"title": " None of the above, but in this section",
	"parentcode": "46Fxx",
	"level": 3
}, {
	"code": "46Gxx",
	"title": " Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) [See also 28-XX, 46Txx]",
	"parentcode": "46-XX",
	"level": 2
}, {
	"code": "46G05",
	"title": " Derivatives [See also 46T20, 58C20, 58C25]",
	"parentcode": "46Gxx",
	"level": 3
}, {
	"code": "46G10",
	"title": " Vector-valued measures and integration [See also 28Bxx, 46B22]",
	"parentcode": "46Gxx",
	"level": 3
}, {
	"code": "46G12",
	"title": " Measures and integration on abstract linear spaces [See also 28C20, 46T12]",
	"parentcode": "46Gxx",
	"level": 3
}, {
	"code": "46G15",
	"title": " Functional analytic lifting theory [See also 28A51]",
	"parentcode": "46Gxx",
	"level": 3
}, {
	"code": "46G20",
	"title": " Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10]",
	"parentcode": "46Gxx",
	"level": 3
}, {
	"code": "46G25",
	"title": " (Spaces of) multilinear mappings, polynomials [See also 46E50, 46G20, 47H60]",
	"parentcode": "46Gxx",
	"level": 3
}, {
	"code": "46G99",
	"title": " None of the above, but in this section",
	"parentcode": "46Gxx",
	"level": 3
}, {
	"code": "46Hxx",
	"title": " Topological algebras, normed rings and algebras, Banach algebras {For group algebras, convolution algebras and measure algebras, see 43A10, 43A20}",
	"parentcode": "46-XX",
	"level": 2
}, {
	"code": "46H05",
	"title": " General theory of topological algebras",
	"parentcode": "46Hxx",
	"level": 3
}, {
	"code": "46H10",
	"title": " Ideals and subalgebras",
	"parentcode": "46Hxx",
	"level": 3
}, {
	"code": "46H15",
	"title": " Representations of topological algebras",
	"parentcode": "46Hxx",
	"level": 3
}, {
	"code": "46H20",
	"title": " Structure, classification of topological algebras",
	"parentcode": "46Hxx",
	"level": 3
}, {
	"code": "46H25",
	"title": " Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)",
	"parentcode": "46Hxx",
	"level": 3
}, {
	"code": "46H30",
	"title": " Functional calculus in topological algebras [See also 47A60]",
	"parentcode": "46Hxx",
	"level": 3
}, {
	"code": "46H35",
	"title": " Topological algebras of operators [See mainly 47Lxx]",
	"parentcode": "46Hxx",
	"level": 3
}, {
	"code": "46H40",
	"title": " Automatic continuity",
	"parentcode": "46Hxx",
	"level": 3
}, {
	"code": "46H70",
	"title": " Nonassociative topological algebras [See also 46K70, 46L70]",
	"parentcode": "46Hxx",
	"level": 3
}, {
	"code": "46H99",
	"title": " None of the above, but in this section",
	"parentcode": "46Hxx",
	"level": 3
}, {
	"code": "46Jxx",
	"title": " Commutative Banach algebras and commutative topological algebras [See also 46E25]",
	"parentcode": "46-XX",
	"level": 2
}, {
	"code": "46J05",
	"title": " General theory of commutative topological algebras",
	"parentcode": "46Jxx",
	"level": 3
}, {
	"code": "46J10",
	"title": " Banach algebras of continuous functions, function algebras [See also 46E25]",
	"parentcode": "46Jxx",
	"level": 3
}, {
	"code": "46J15",
	"title": " Banach algebras of differentiable or analytic functions, $H^p$-spaces [See also 30H10, 32A35, 32A37, 32A38, 42B30]",
	"parentcode": "46Jxx",
	"level": 3
}, {
	"code": "46J20",
	"title": " Ideals, maximal ideals, boundaries",
	"parentcode": "46Jxx",
	"level": 3
}, {
	"code": "46J25",
	"title": " Representations of commutative topological algebras",
	"parentcode": "46Jxx",
	"level": 3
}, {
	"code": "46J30",
	"title": " Subalgebras",
	"parentcode": "46Jxx",
	"level": 3
}, {
	"code": "46J40",
	"title": " Structure, classification of commutative topological algebras",
	"parentcode": "46Jxx",
	"level": 3
}, {
	"code": "46J45",
	"title": " Radical Banach algebras",
	"parentcode": "46Jxx",
	"level": 3
}, {
	"code": "46J99",
	"title": " None of the above, but in this section",
	"parentcode": "46Jxx",
	"level": 3
}, {
	"code": "46Kxx",
	"title": " Topological (rings and) algebras with an involution [See also 16W10]",
	"parentcode": "46-XX",
	"level": 2
}, {
	"code": "46K05",
	"title": " General theory of topological algebras with involution",
	"parentcode": "46Kxx",
	"level": 3
}, {
	"code": "46K10",
	"title": " Representations of topological algebras with involution",
	"parentcode": "46Kxx",
	"level": 3
}, {
	"code": "46K15",
	"title": " Hilbert algebras",
	"parentcode": "46Kxx",
	"level": 3
}, {
	"code": "46K50",
	"title": " Nonselfadjoint (sub)algebras in algebras with involution",
	"parentcode": "46Kxx",
	"level": 3
}, {
	"code": "46K70",
	"title": " Nonassociative topological algebras with an involution [See also 46H70, 46L70]",
	"parentcode": "46Kxx",
	"level": 3
}, {
	"code": "46K99",
	"title": " None of the above, but in this section",
	"parentcode": "46Kxx",
	"level": 3
}, {
	"code": "46Lxx",
	"title": " Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) [See also 22D25, 47Lxx]",
	"parentcode": "46-XX",
	"level": 2
}, {
	"code": "46L05",
	"title": " General theory of $C^*$-algebras",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L06",
	"title": " Tensor products of $C^*$-algebras",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L07",
	"title": " Operator spaces and completely bounded maps [See also 47L25]",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L08",
	"title": " $C^*$-modules",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L09",
	"title": " Free products of $C^*$-algebras",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L10",
	"title": " General theory of von Neumann algebras",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L30",
	"title": " States",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L35",
	"title": " Classifications of $C^*$-algebras",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L36",
	"title": " Classification of factors",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L37",
	"title": " Subfactors and their classification",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L40",
	"title": " Automorphisms",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L45",
	"title": " Decomposition theory for $C^*$-algebras",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L51",
	"title": " Noncommutative measure and integration",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L52",
	"title": " Noncommutative function spaces",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L53",
	"title": " Noncommutative probability and statistics",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L54",
	"title": " Free probability and free operator algebras",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L55",
	"title": " Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L57",
	"title": " Derivations, dissipations and positive semigroups in $C^*$-algebras",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L60",
	"title": " Applications of selfadjoint operator algebras to physics [See also 46N50, 46N55, 47L90, 81T05, 82B10, 82C10]",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L65",
	"title": " Quantizations, deformations",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L70",
	"title": " Nonassociative selfadjoint operator algebras [See also 46H70, 46K70]",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L80",
	"title": " $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L85",
	"title": " Noncommutative topology [See also 58B32, 58B34, 58J22]",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L87",
	"title": " Noncommutative differential geometry [See also 58B32, 58B34, 58J22]",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L89",
	"title": " Other “noncommutative” mathematics based on $C^*$-algebra theory [See also 58B32, 58B34, 58J22]",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46L99",
	"title": " None of the above, but in this section",
	"parentcode": "46Lxx",
	"level": 3
}, {
	"code": "46Mxx",
	"title": " Methods of category theory in functional analysis [See also 18-XX]",
	"parentcode": "46-XX",
	"level": 2
}, {
	"code": "46M05",
	"title": " Tensor products [See also 46A32, 46B28, 47A80]",
	"parentcode": "46Mxx",
	"level": 3
}, {
	"code": "46M07",
	"title": " Ultraproducts [See also 46B08, 46S20]",
	"parentcode": "46Mxx",
	"level": 3
}, {
	"code": "46M10",
	"title": " Projective and injective objects [See also 46A22]",
	"parentcode": "46Mxx",
	"level": 3
}, {
	"code": "46M15",
	"title": " Categories, functors {For $K$-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M20}",
	"parentcode": "46Mxx",
	"level": 3
}, {
	"code": "46M18",
	"title": " Homological methods (exact sequences, right inverses, lifting, etc.)",
	"parentcode": "46Mxx",
	"level": 3
}, {
	"code": "46M20",
	"title": " Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.) [See also 14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx]",
	"parentcode": "46Mxx",
	"level": 3
}, {
	"code": "46M35",
	"title": " Abstract interpolation of topological vector spaces [See also 46B70]",
	"parentcode": "46Mxx",
	"level": 3
}, {
	"code": "46M40",
	"title": " Inductive and projective limits [See also 46A13]",
	"parentcode": "46Mxx",
	"level": 3
}, {
	"code": "46M99",
	"title": " None of the above, but in this section",
	"parentcode": "46Mxx",
	"level": 3
}, {
	"code": "46Nxx",
	"title": " Miscellaneous applications of functional analysis [See also 47Nxx]",
	"parentcode": "46-XX",
	"level": 2
}, {
	"code": "46N10",
	"title": " Applications in optimization, convex analysis, mathematical programming, economics",
	"parentcode": "46Nxx",
	"level": 3
}, {
	"code": "46N20",
	"title": " Applications to differential and integral equations",
	"parentcode": "46Nxx",
	"level": 3
}, {
	"code": "46N30",
	"title": " Applications in probability theory and statistics",
	"parentcode": "46Nxx",
	"level": 3
}, {
	"code": "46N40",
	"title": " Applications in numerical analysis [See also 65Jxx]",
	"parentcode": "46Nxx",
	"level": 3
}, {
	"code": "46N50",
	"title": " Applications in quantum physics",
	"parentcode": "46Nxx",
	"level": 3
}, {
	"code": "46N55",
	"title": " Applications in statistical physics",
	"parentcode": "46Nxx",
	"level": 3
}, {
	"code": "46N60",
	"title": " Applications in biology and other sciences",
	"parentcode": "46Nxx",
	"level": 3
}, {
	"code": "46N99",
	"title": " None of the above, but in this section",
	"parentcode": "46Nxx",
	"level": 3
}, {
	"code": "46Sxx",
	"title": " Other (nonclassical) types of functional analysis [See also 47Sxx]",
	"parentcode": "46-XX",
	"level": 2
}, {
	"code": "46S10",
	"title": " Functional analysis over fields other than ${\\bf R}$ or ${\\bf C}$ or the quaternions; non-Archimedean functional analysis [See also 12J25, 32P05]",
	"parentcode": "46Sxx",
	"level": 3
}, {
	"code": "46S20",
	"title": " Nonstandard functional analysis [See also 03H05]",
	"parentcode": "46Sxx",
	"level": 3
}, {
	"code": "46S30",
	"title": " Constructive functional analysis [See also 03F60]",
	"parentcode": "46Sxx",
	"level": 3
}, {
	"code": "46S40",
	"title": " Fuzzy functional analysis [See also 03E72]",
	"parentcode": "46Sxx",
	"level": 3
}, {
	"code": "46S50",
	"title": " Functional analysis in probabilistic metric linear spaces",
	"parentcode": "46Sxx",
	"level": 3
}, {
	"code": "46S60",
	"title": " Functional analysis on superspaces (supermanifolds) or graded spaces [See also 58A50 and 58C50]",
	"parentcode": "46Sxx",
	"level": 3
}, {
	"code": "46S99",
	"title": " None of the above, but in this section",
	"parentcode": "46Sxx",
	"level": 3
}, {
	"code": "46Txx",
	"title": " Nonlinear functional analysis [See also 47Hxx, 47Jxx, 58Cxx, 58Dxx]",
	"parentcode": "46-XX",
	"level": 2
}, {
	"code": "46T05",
	"title": " Infinite-dimensional manifolds [See also 53Axx, 57N20, 58Bxx, 58Dxx]",
	"parentcode": "46Txx",
	"level": 3
}, {
	"code": "46T10",
	"title": " Manifolds of mappings",
	"parentcode": "46Txx",
	"level": 3
}, {
	"code": "46T12",
	"title": " Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds [See also 28Cxx, 46G12, 60-XX]",
	"parentcode": "46Txx",
	"level": 3
}, {
	"code": "46T20",
	"title": " Continuous and differentiable maps [See also 46G05]",
	"parentcode": "46Txx",
	"level": 3
}, {
	"code": "46T25",
	"title": " Holomorphic maps [See also 46G20]",
	"parentcode": "46Txx",
	"level": 3
}, {
	"code": "46T30",
	"title": " Distributions and generalized functions on nonlinear spaces [See also 46Fxx]",
	"parentcode": "46Txx",
	"level": 3
}, {
	"code": "46T99",
	"title": " None of the above, but in this section",
	"parentcode": "46Txx",
	"level": 3
}, {
	"code": "47-XX",
	"title": " Operator theory",
	"parentcode": null,
	"level": 1
}, {
	"code": "47-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "47-XX",
	"level": 2
}, {
	"code": "47-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "47-XX",
	"level": 2
}, {
	"code": "47-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "47-XX",
	"level": 2
}, {
	"code": "47-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "47-XX",
	"level": 2
}, {
	"code": "47-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "47-XX",
	"level": 2
}, {
	"code": "47-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "47-XX",
	"level": 2
}, {
	"code": "47Axx",
	"title": " General theory of linear operators",
	"parentcode": "47-XX",
	"level": 2
}, {
	"code": "47A05",
	"title": " General (adjoints, conjugates, products, inverses, domains, ranges, etc.)",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A06",
	"title": " Linear relations (multivalued linear operators)",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A07",
	"title": " Forms (bilinear, sesquilinear, multilinear)",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A10",
	"title": " Spectrum, resolvent",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A11",
	"title": " Local spectral properties",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A12",
	"title": " Numerical range, numerical radius",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A13",
	"title": " Several-variable operator theory (spectral, Fredholm, etc.)",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A15",
	"title": " Invariant subspaces [See also 47A46]",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A16",
	"title": " Cyclic vectors, hypercyclic and chaotic operators",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A20",
	"title": " Dilations, extensions, compressions",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A25",
	"title": " Spectral sets",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A30",
	"title": " Norms (inequalities, more than one norm, etc.)",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A35",
	"title": " Ergodic theory [See also 28Dxx, 37Axx]",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A40",
	"title": " Scattering theory [See also 34L25, 35P25, 37K15, 58J50, 81Uxx]",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A45",
	"title": " Canonical models for contractions and nonselfadjoint operators",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A46",
	"title": " Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A48",
	"title": " Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc.",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A50",
	"title": " Equations and inequalities involving linear operators, with vector unknowns",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A52",
	"title": " Ill-posed problems, regularization [See also 35R25, 47J06, 65F22, 65J20, 65L08, 65M30, 65R30]",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A53",
	"title": " (Semi-) Fredholm operators; index theories [See also 58B15, 58J20]",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A55",
	"title": " Perturbation theory  [See also 47H14, 58J37, 70H09, 81Q15]",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A56",
	"title": " Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones)",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A57",
	"title": " Operator methods in interpolation, moment and extension problems [See also 30E05, 42A70, 42A82, 44A60]",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A58",
	"title": " Operator approximation theory",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A60",
	"title": " Functional calculus",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A62",
	"title": " Equations involving linear operators, with operator unknowns",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A63",
	"title": " Operator inequalities",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A64",
	"title": " Operator means, shorted operators, etc.",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A65",
	"title": " Structure theory",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A66",
	"title": " Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operators",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A67",
	"title": " Representation theory",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A68",
	"title": " Factorization theory (including Wiener-Hopf and spectral factorizations)",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A70",
	"title": " (Generalized) eigenfunction expansions; rigged Hilbert spaces",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A75",
	"title": " Eigenvalue problems [See also 47J10, 49R05]",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A80",
	"title": " Tensor products of operators [See also 46M05]",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47A99",
	"title": " None of the above, but in this section",
	"parentcode": "47Axx",
	"level": 3
}, {
	"code": "47Bxx",
	"title": " Special classes of linear operators",
	"parentcode": "47-XX",
	"level": 2
}, {
	"code": "47B06",
	"title": " Riesz operators; eigenvalue distributions; approximation numbers, $s$-numbers, Kolmogorov numbers, entropy numbers, etc. of operators",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B07",
	"title": " Operators defined by compactness properties",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B10",
	"title": " Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B15",
	"title": " Hermitian and normal operators (spectral measures, functional calculus, etc.)",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B20",
	"title": " Subnormal operators, hyponormal operators, etc.",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B25",
	"title": " Symmetric and selfadjoint operators (unbounded)",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B32",
	"title": " Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) [See also 46E22]",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B33",
	"title": " Composition operators",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B34",
	"title": " Kernel operators",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B35",
	"title": " Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B36",
	"title": " Jacobi (tridiagonal) operators (matrices) and generalizations",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B37",
	"title": " Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B38",
	"title": " Operators on function spaces (general)",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B39",
	"title": " Difference operators [See also 39A70]",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B40",
	"title": " Spectral operators, decomposable operators, well-bounded operators, etc.",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B44",
	"title": " Accretive operators, dissipative operators, etc.",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B47",
	"title": " Commutators, derivations, elementary operators, etc.",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B48",
	"title": " Operators on Banach algebras",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B49",
	"title": " Transformers, preservers (operators on spaces of operators)",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B50",
	"title": " Operators on spaces with an indefinite metric [See also 46C50]",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B60",
	"title": " Operators on ordered spaces",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B65",
	"title": " Positive operators and order-bounded operators",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B80",
	"title": " Random operators [See also 47H40, 60H25]",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47B99",
	"title": " None of the above, but in this section",
	"parentcode": "47Bxx",
	"level": 3
}, {
	"code": "47Cxx",
	"title": " Individual linear operators as elements of algebraic systems",
	"parentcode": "47-XX",
	"level": 2
}, {
	"code": "47C05",
	"title": " Operators in algebras",
	"parentcode": "47Cxx",
	"level": 3
}, {
	"code": "47C10",
	"title": " Operators in ${}^*$-algebras",
	"parentcode": "47Cxx",
	"level": 3
}, {
	"code": "47C15",
	"title": " Operators in $C^*$- or von Neumann algebras",
	"parentcode": "47Cxx",
	"level": 3
}, {
	"code": "47C99",
	"title": " None of the above, but in this section",
	"parentcode": "47Cxx",
	"level": 3
}, {
	"code": "47Dxx",
	"title": " Groups and semigroups of linear operators, their generalizations and applications",
	"parentcode": "47-XX",
	"level": 2
}, {
	"code": "47D03",
	"title": " Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20}",
	"parentcode": "47Dxx",
	"level": 3
}, {
	"code": "47D06",
	"title": " One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]",
	"parentcode": "47Dxx",
	"level": 3
}, {
	"code": "47D07",
	"title": " Markov semigroups and applications to diffusion processes {For Markov processes, see 60Jxx}",
	"parentcode": "47Dxx",
	"level": 3
}, {
	"code": "47D08",
	"title": " Schrödinger and Feynman-Kac semigroups",
	"parentcode": "47Dxx",
	"level": 3
}, {
	"code": "47D09",
	"title": " Operator sine and cosine functions and higher-order Cauchy problems [See also 34G10]",
	"parentcode": "47Dxx",
	"level": 3
}, {
	"code": "47D60",
	"title": " $C$-semigroups, regularized semigroups",
	"parentcode": "47Dxx",
	"level": 3
}, {
	"code": "47D62",
	"title": " Integrated semigroups",
	"parentcode": "47Dxx",
	"level": 3
}, {
	"code": "47D99",
	"title": " None of the above, but in this section",
	"parentcode": "47Dxx",
	"level": 3
}, {
	"code": "47Exx",
	"title": " Ordinary differential operators [See also 34Bxx, 34Lxx]",
	"parentcode": "47-XX",
	"level": 2
}, {
	"code": "47E05",
	"title": " Ordinary differential operators [See also 34Bxx, 34Lxx] (should also be assigned at least one other classification number in section 47)",
	"parentcode": "47Exx",
	"level": 3
}, {
	"code": "47E99",
	"title": " None of the above, but in this section",
	"parentcode": "47Exx",
	"level": 3
}, {
	"code": "47Fxx",
	"title": " Partial differential operators [See also 35Pxx, 58Jxx]",
	"parentcode": "47-XX",
	"level": 2
}, {
	"code": "47F05",
	"title": " Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47)",
	"parentcode": "47Fxx",
	"level": 3
}, {
	"code": "47F99",
	"title": " None of the above, but in this section",
	"parentcode": "47Fxx",
	"level": 3
}, {
	"code": "47Gxx",
	"title": " Integral, integro-differential, and pseudodifferential operators [See also 58Jxx]",
	"parentcode": "47-XX",
	"level": 2
}, {
	"code": "47G10",
	"title": " Integral operators [See also 45P05]",
	"parentcode": "47Gxx",
	"level": 3
}, {
	"code": "47G20",
	"title": " Integro-differential operators [See also 34K30, 35R09, 35R10, 45Jxx, 45Kxx]",
	"parentcode": "47Gxx",
	"level": 3
}, {
	"code": "47G30",
	"title": " Pseudodifferential operators [See also 35Sxx, 58Jxx]",
	"parentcode": "47Gxx",
	"level": 3
}, {
	"code": "47G40",
	"title": " Potential operators [See also 31-XX]",
	"parentcode": "47Gxx",
	"level": 3
}, {
	"code": "47G99",
	"title": " None of the above, but in this section",
	"parentcode": "47Gxx",
	"level": 3
}, {
	"code": "47Hxx",
	"title": " Nonlinear operators and their properties {For global and geometric aspects, see 49J53, 58-XX, especially 58Cxx}",
	"parentcode": "47-XX",
	"level": 2
}, {
	"code": "47H04",
	"title": " Set-valued operators [See also 28B20, 54C60, 58C06]",
	"parentcode": "47Hxx",
	"level": 3
}, {
	"code": "47H05",
	"title": " Monotone operators and generalizations",
	"parentcode": "47Hxx",
	"level": 3
}, {
	"code": "47H06",
	"title": " Accretive operators, dissipative operators, etc.",
	"parentcode": "47Hxx",
	"level": 3
}, {
	"code": "47H07",
	"title": " Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces",
	"parentcode": "47Hxx",
	"level": 3
}, {
	"code": "47H08",
	"title": " Measures of noncompactness and condensing mappings, $K$-set contractions, etc.",
	"parentcode": "47Hxx",
	"level": 3
}, {
	"code": "47H09",
	"title": " Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc.",
	"parentcode": "47Hxx",
	"level": 3
}, {
	"code": "47H10",
	"title": " Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]",
	"parentcode": "47Hxx",
	"level": 3
}, {
	"code": "47H11",
	"title": " Degree theory [See also 55M25, 58C30]",
	"parentcode": "47Hxx",
	"level": 3
}, {
	"code": "47H14",
	"title": " Perturbations of nonlinear operators [See also 47A55, 58J37, 70H09, 70K60, 81Q15]",
	"parentcode": "47Hxx",
	"level": 3
}, {
	"code": "47H20",
	"title": " Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07]",
	"parentcode": "47Hxx",
	"level": 3
}, {
	"code": "47H25",
	"title": " Nonlinear ergodic theorems [See also 28Dxx, 37Axx, 47A35]",
	"parentcode": "47Hxx",
	"level": 3
}, {
	"code": "47H30",
	"title": " Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) [See also 45Gxx, 45P05]",
	"parentcode": "47Hxx",
	"level": 3
}, {
	"code": "47H40",
	"title": " Random operators  [See also 47B80, 60H25]",
	"parentcode": "47Hxx",
	"level": 3
}, {
	"code": "47H60",
	"title": " Multilinear and polynomial operators [See also 46G25]",
	"parentcode": "47Hxx",
	"level": 3
}, {
	"code": "47H99",
	"title": " None of the above, but in this section",
	"parentcode": "47Hxx",
	"level": 3
}, {
	"code": "47Jxx",
	"title": " Equations and inequalities involving nonlinear operators [See also 46Txx] {For global and geometric aspects, see 58-XX}",
	"parentcode": "47-XX",
	"level": 2
}, {
	"code": "47J05",
	"title": " Equations involving nonlinear operators (general) [See also 47H10, 47J25]",
	"parentcode": "47Jxx",
	"level": 3
}, {
	"code": "47J06",
	"title": " Nonlinear ill-posed problems [See also 35R25, 47A52, 65F22, 65J20, 65L08, 65M30, 65R30]",
	"parentcode": "47Jxx",
	"level": 3
}, {
	"code": "47J07",
	"title": " Abstract inverse mapping and implicit function theorems [See also 46T20 and 58C15]",
	"parentcode": "47Jxx",
	"level": 3
}, {
	"code": "47J10",
	"title": " Nonlinear spectral theory, nonlinear eigenvalue problems [See also 49R05]",
	"parentcode": "47Jxx",
	"level": 3
}, {
	"code": "47J15",
	"title": " Abstract bifurcation theory [See also 34C23, 37Gxx, 58E07, 58E09]",
	"parentcode": "47Jxx",
	"level": 3
}, {
	"code": "47J20",
	"title": " Variational and other types of inequalities involving nonlinear operators (general) [See also 49J40]",
	"parentcode": "47Jxx",
	"level": 3
}, {
	"code": "47J22",
	"title": " Variational and other types of inclusions [See also 34A60, 49J21, 49K21]",
	"parentcode": "47Jxx",
	"level": 3
}, {
	"code": "47J25",
	"title": " Iterative procedures [See also 65J15]",
	"parentcode": "47Jxx",
	"level": 3
}, {
	"code": "47J30",
	"title": " Variational methods [See also 58Exx]",
	"parentcode": "47Jxx",
	"level": 3
}, {
	"code": "47J35",
	"title": " Nonlinear evolution equations [See also 34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx,  47H20, 58D25]",
	"parentcode": "47Jxx",
	"level": 3
}, {
	"code": "47J40",
	"title": " Equations with hysteresis operators [See also 34C55, 74N30]",
	"parentcode": "47Jxx",
	"level": 3
}, {
	"code": "47J99",
	"title": " None of the above, but in this section",
	"parentcode": "47Jxx",
	"level": 3
}, {
	"code": "47Lxx",
	"title": " Linear spaces and algebras of operators [See also 46Lxx]",
	"parentcode": "47-XX",
	"level": 2
}, {
	"code": "47L05",
	"title": " Linear spaces of operators [See also 46A32 and 46B28]",
	"parentcode": "47Lxx",
	"level": 3
}, {
	"code": "47L07",
	"title": " Convex sets and cones of operators [See also 46A55]",
	"parentcode": "47Lxx",
	"level": 3
}, {
	"code": "47L10",
	"title": " Algebras of operators on Banach spaces and other topological linear spaces",
	"parentcode": "47Lxx",
	"level": 3
}, {
	"code": "47L15",
	"title": " Operator algebras with symbol structure",
	"parentcode": "47Lxx",
	"level": 3
}, {
	"code": "47L20",
	"title": " Operator ideals  [See also 47B10]",
	"parentcode": "47Lxx",
	"level": 3
}, {
	"code": "47L22",
	"title": " Ideals of polynomials and of multilinear mappings",
	"parentcode": "47Lxx",
	"level": 3
}, {
	"code": "47L25",
	"title": " Operator spaces (= matricially normed spaces) [See also 46L07]",
	"parentcode": "47Lxx",
	"level": 3
}, {
	"code": "47L30",
	"title": " Abstract operator algebras on Hilbert spaces",
	"parentcode": "47Lxx",
	"level": 3
}, {
	"code": "47L35",
	"title": " Nest algebras, CSL algebras",
	"parentcode": "47Lxx",
	"level": 3
}, {
	"code": "47L40",
	"title": " Limit algebras, subalgebras of $C^*$-algebras",
	"parentcode": "47Lxx",
	"level": 3
}, {
	"code": "47L45",
	"title": " Dual algebras; weakly closed singly generated operator algebras",
	"parentcode": "47Lxx",
	"level": 3
}, {
	"code": "47L50",
	"title": " Dual spaces of operator algebras",
	"parentcode": "47Lxx",
	"level": 3
}, {
	"code": "47L55",
	"title": " Representations of (nonselfadjoint) operator algebras",
	"parentcode": "47Lxx",
	"level": 3
}, {
	"code": "47L60",
	"title": " Algebras of unbounded operators; partial algebras of operators",
	"parentcode": "47Lxx",
	"level": 3
}, {
	"code": "47L65",
	"title": " Crossed product algebras (analytic crossed products)",
	"parentcode": "47Lxx",
	"level": 3
}, {
	"code": "47L70",
	"title": " Nonassociative nonselfadjoint operator algebras",
	"parentcode": "47Lxx",
	"level": 3
}, {
	"code": "47L75",
	"title": " Other nonselfadjoint operator algebras",
	"parentcode": "47Lxx",
	"level": 3
}, {
	"code": "47L80",
	"title": " Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)",
	"parentcode": "47Lxx",
	"level": 3
}, {
	"code": "47L90",
	"title": " Applications of operator algebras to physics",
	"parentcode": "47Lxx",
	"level": 3
}, {
	"code": "47L99",
	"title": " None of the above, but in this section",
	"parentcode": "47Lxx",
	"level": 3
}, {
	"code": "47Nxx",
	"title": " Miscellaneous applications of operator theory [See also 46Nxx]",
	"parentcode": "47-XX",
	"level": 2
}, {
	"code": "47N10",
	"title": " Applications in optimization, convex analysis, mathematical programming, economics",
	"parentcode": "47Nxx",
	"level": 3
}, {
	"code": "47N20",
	"title": " Applications to differential and integral equations",
	"parentcode": "47Nxx",
	"level": 3
}, {
	"code": "47N30",
	"title": " Applications in probability theory and statistics",
	"parentcode": "47Nxx",
	"level": 3
}, {
	"code": "47N40",
	"title": " Applications in numerical analysis [See also 65Jxx]",
	"parentcode": "47Nxx",
	"level": 3
}, {
	"code": "47N50",
	"title": " Applications in the physical sciences",
	"parentcode": "47Nxx",
	"level": 3
}, {
	"code": "47N60",
	"title": " Applications in chemistry and life sciences",
	"parentcode": "47Nxx",
	"level": 3
}, {
	"code": "47N70",
	"title": " Applications in systems theory, circuits, and control theory",
	"parentcode": "47Nxx",
	"level": 3
}, {
	"code": "47N99",
	"title": " None of the above, but in this section",
	"parentcode": "47Nxx",
	"level": 3
}, {
	"code": "47Sxx",
	"title": " Other (nonclassical) types of operator theory [See also 46Sxx]",
	"parentcode": "47-XX",
	"level": 2
}, {
	"code": "47S10",
	"title": " Operator theory over fields other than ${\\bf R}$, ${\\bf C}$ or the quaternions; non-Archimedean operator theory",
	"parentcode": "47Sxx",
	"level": 3
}, {
	"code": "47S20",
	"title": " Nonstandard operator theory [See also 03H05]",
	"parentcode": "47Sxx",
	"level": 3
}, {
	"code": "47S30",
	"title": " Constructive operator theory [See also 03F60]",
	"parentcode": "47Sxx",
	"level": 3
}, {
	"code": "47S40",
	"title": " Fuzzy operator theory [See also 03E72]",
	"parentcode": "47Sxx",
	"level": 3
}, {
	"code": "47S50",
	"title": " Operator theory in probabilistic metric linear spaces [See also 54E70]",
	"parentcode": "47Sxx",
	"level": 3
}, {
	"code": "47S99",
	"title": " None of the above, but in this section",
	"parentcode": "47Sxx",
	"level": 3
}, {
	"code": "49-XX",
	"title": " Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]",
	"parentcode": null,
	"level": 1
}, {
	"code": "49-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "49-XX",
	"level": 2
}, {
	"code": "49-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "49-XX",
	"level": 2
}, {
	"code": "49-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "49-XX",
	"level": 2
}, {
	"code": "49-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "49-XX",
	"level": 2
}, {
	"code": "49-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "49-XX",
	"level": 2
}, {
	"code": "49-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "49-XX",
	"level": 2
}, {
	"code": "49Jxx",
	"title": " Existence theories",
	"parentcode": "49-XX",
	"level": 2
}, {
	"code": "49J05",
	"title": " Free problems in one independent variable",
	"parentcode": "49Jxx",
	"level": 3
}, {
	"code": "49J10",
	"title": " Free problems in two or more independent variables",
	"parentcode": "49Jxx",
	"level": 3
}, {
	"code": "49J15",
	"title": " Optimal control problems involving ordinary differential equations",
	"parentcode": "49Jxx",
	"level": 3
}, {
	"code": "49J20",
	"title": " Optimal control problems involving partial differential equations",
	"parentcode": "49Jxx",
	"level": 3
}, {
	"code": "49J21",
	"title": " Optimal control problems involving relations other than differential equations",
	"parentcode": "49Jxx",
	"level": 3
}, {
	"code": "49J27",
	"title": " Problems in abstract spaces [See also 90C48, 93C25]",
	"parentcode": "49Jxx",
	"level": 3
}, {
	"code": "49J30",
	"title": " Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)",
	"parentcode": "49Jxx",
	"level": 3
}, {
	"code": "49J35",
	"title": " Minimax problems",
	"parentcode": "49Jxx",
	"level": 3
}, {
	"code": "49J40",
	"title": " Variational methods including variational inequalities [See also 47J20]",
	"parentcode": "49Jxx",
	"level": 3
}, {
	"code": "49J45",
	"title": " Methods involving semicontinuity and convergence; relaxation",
	"parentcode": "49Jxx",
	"level": 3
}, {
	"code": "49J50",
	"title": " Fréchet and Gateaux differentiability [See also 46G05, 58C20]",
	"parentcode": "49Jxx",
	"level": 3
}, {
	"code": "49J52",
	"title": " Nonsmooth analysis [See also 46G05, 58C50, 90C56]",
	"parentcode": "49Jxx",
	"level": 3
}, {
	"code": "49J53",
	"title": " Set-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06]",
	"parentcode": "49Jxx",
	"level": 3
}, {
	"code": "49J55",
	"title": " Problems involving randomness [See also 93E20]",
	"parentcode": "49Jxx",
	"level": 3
}, {
	"code": "49J99",
	"title": " None of the above, but in this section",
	"parentcode": "49Jxx",
	"level": 3
}, {
	"code": "49Kxx",
	"title": " Optimality conditions",
	"parentcode": "49-XX",
	"level": 2
}, {
	"code": "49K05",
	"title": " Free problems in one independent variable",
	"parentcode": "49Kxx",
	"level": 3
}, {
	"code": "49K10",
	"title": " Free problems in two or more independent variables",
	"parentcode": "49Kxx",
	"level": 3
}, {
	"code": "49K15",
	"title": " Problems involving ordinary differential equations",
	"parentcode": "49Kxx",
	"level": 3
}, {
	"code": "49K20",
	"title": " Problems involving partial differential equations",
	"parentcode": "49Kxx",
	"level": 3
}, {
	"code": "49K21",
	"title": " Problems involving relations other than differential equations",
	"parentcode": "49Kxx",
	"level": 3
}, {
	"code": "49K27",
	"title": " Problems in abstract spaces [See also 90C48, 93C25]",
	"parentcode": "49Kxx",
	"level": 3
}, {
	"code": "49K30",
	"title": " Optimal solutions belonging to restricted classes",
	"parentcode": "49Kxx",
	"level": 3
}, {
	"code": "49K35",
	"title": " Minimax problems",
	"parentcode": "49Kxx",
	"level": 3
}, {
	"code": "49K40",
	"title": " Sensitivity, stability, well-posedness [See also 90C31]",
	"parentcode": "49Kxx",
	"level": 3
}, {
	"code": "49K45",
	"title": " Problems involving randomness [See also 93E20]",
	"parentcode": "49Kxx",
	"level": 3
}, {
	"code": "49K99",
	"title": " None of the above, but in this section",
	"parentcode": "49Kxx",
	"level": 3
}, {
	"code": "49Lxx",
	"title": " Hamilton-Jacobi theories, including dynamic programming",
	"parentcode": "49-XX",
	"level": 2
}, {
	"code": "49L20",
	"title": " Dynamic programming method",
	"parentcode": "49Lxx",
	"level": 3
}, {
	"code": "49L25",
	"title": " Viscosity solutions",
	"parentcode": "49Lxx",
	"level": 3
}, {
	"code": "49L99",
	"title": " None of the above, but in this section",
	"parentcode": "49Lxx",
	"level": 3
}, {
	"code": "49Mxx",
	"title": " Numerical methods [See also 90Cxx, 65Kxx]",
	"parentcode": "49-XX",
	"level": 2
}, {
	"code": "49M05",
	"title": " Methods based on necessary conditions",
	"parentcode": "49Mxx",
	"level": 3
}, {
	"code": "49M15",
	"title": " Newton-type methods",
	"parentcode": "49Mxx",
	"level": 3
}, {
	"code": "49M20",
	"title": " Methods of relaxation type",
	"parentcode": "49Mxx",
	"level": 3
}, {
	"code": "49M25",
	"title": " Discrete approximations",
	"parentcode": "49Mxx",
	"level": 3
}, {
	"code": "49M27",
	"title": " Decomposition methods",
	"parentcode": "49Mxx",
	"level": 3
}, {
	"code": "49M29",
	"title": " Methods involving duality",
	"parentcode": "49Mxx",
	"level": 3
}, {
	"code": "49M30",
	"title": " Other methods",
	"parentcode": "49Mxx",
	"level": 3
}, {
	"code": "49M37",
	"title": " Methods of nonlinear programming type [See also 90C30, 65Kxx]",
	"parentcode": "49Mxx",
	"level": 3
}, {
	"code": "49M99",
	"title": " None of the above, but in this section",
	"parentcode": "49Mxx",
	"level": 3
}, {
	"code": "49Nxx",
	"title": " Miscellaneous topics",
	"parentcode": "49-XX",
	"level": 2
}, {
	"code": "49N05",
	"title": " Linear optimal control problems [See also 93C05]",
	"parentcode": "49Nxx",
	"level": 3
}, {
	"code": "49N10",
	"title": " Linear-quadratic problems",
	"parentcode": "49Nxx",
	"level": 3
}, {
	"code": "49N15",
	"title": " Duality theory",
	"parentcode": "49Nxx",
	"level": 3
}, {
	"code": "49N20",
	"title": " Periodic optimization",
	"parentcode": "49Nxx",
	"level": 3
}, {
	"code": "49N25",
	"title": " Impulsive optimal control problems",
	"parentcode": "49Nxx",
	"level": 3
}, {
	"code": "49N30",
	"title": " Problems with incomplete information [See also 93C41]",
	"parentcode": "49Nxx",
	"level": 3
}, {
	"code": "49N35",
	"title": " Optimal feedback synthesis [See also 93B52]",
	"parentcode": "49Nxx",
	"level": 3
}, {
	"code": "49N45",
	"title": " Inverse problems",
	"parentcode": "49Nxx",
	"level": 3
}, {
	"code": "49N60",
	"title": " Regularity of solutions",
	"parentcode": "49Nxx",
	"level": 3
}, {
	"code": "49N70",
	"title": " Differential games",
	"parentcode": "49Nxx",
	"level": 3
}, {
	"code": "49N75",
	"title": " Pursuit and evasion games",
	"parentcode": "49Nxx",
	"level": 3
}, {
	"code": "49N90",
	"title": " Applications of optimal control and differential games [See also 90C90, 93C95]",
	"parentcode": "49Nxx",
	"level": 3
}, {
	"code": "49N99",
	"title": " None of the above, but in this section",
	"parentcode": "49Nxx",
	"level": 3
}, {
	"code": "49Qxx",
	"title": " Manifolds [See also 58Exx]",
	"parentcode": "49-XX",
	"level": 2
}, {
	"code": "49Q05",
	"title": " Minimal surfaces [See also 53A10, 58E12]",
	"parentcode": "49Qxx",
	"level": 3
}, {
	"code": "49Q10",
	"title": " Optimization of shapes other than minimal surfaces [See also 90C90]",
	"parentcode": "49Qxx",
	"level": 3
}, {
	"code": "49Q12",
	"title": " Sensitivity analysis",
	"parentcode": "49Qxx",
	"level": 3
}, {
	"code": "49Q15",
	"title": " Geometric measure and integration theory, integral and normal currents [See also 28A75, 32C30, 58A25, 58C35]",
	"parentcode": "49Qxx",
	"level": 3
}, {
	"code": "49Q20",
	"title": " Variational problems in a geometric measure-theoretic setting",
	"parentcode": "49Qxx",
	"level": 3
}, {
	"code": "49Q99",
	"title": " None of the above, but in this section",
	"parentcode": "49Qxx",
	"level": 3
}, {
	"code": "49Rxx",
	"title": " Variational methods for eigenvalues of operators [See also 47A75]",
	"parentcode": "49-XX",
	"level": 2
}, {
	"code": "49R05",
	"title": " Variational methods for eigenvalues of operators [See also 47A75] (should also be assigned at least one other classification number in Section 49)",
	"parentcode": "49Rxx",
	"level": 3
}, {
	"code": "49R99",
	"title": " None of the above, but in this section",
	"parentcode": "49Rxx",
	"level": 3
}, {
	"code": "49Sxx",
	"title": " Variational principles of physics",
	"parentcode": "49-XX",
	"level": 2
}, {
	"code": "49S05",
	"title": " Variational principles of physics (should also be assigned at least one other classification number in  section 49)",
	"parentcode": "49Sxx",
	"level": 3
}, {
	"code": "49S99",
	"title": " None of the above, but in this section",
	"parentcode": "49Sxx",
	"level": 3
}, {
	"code": "51-XX",
	"title": " Geometry {For algebraic geometry, see 14-XX}",
	"parentcode": null,
	"level": 1
}, {
	"code": "51-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "51-XX",
	"level": 2
}, {
	"code": "51-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "51-XX",
	"level": 2
}, {
	"code": "51-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "51-XX",
	"level": 2
}, {
	"code": "51-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "51-XX",
	"level": 2
}, {
	"code": "51-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "51-XX",
	"level": 2
}, {
	"code": "51-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "51-XX",
	"level": 2
}, {
	"code": "51Axx",
	"title": " Linear incidence geometry",
	"parentcode": "51-XX",
	"level": 2
}, {
	"code": "51A05",
	"title": " General theory and projective geometries",
	"parentcode": "51Axx",
	"level": 3
}, {
	"code": "51A10",
	"title": " Homomorphism, automorphism and dualities",
	"parentcode": "51Axx",
	"level": 3
}, {
	"code": "51A15",
	"title": " Structures with parallelism",
	"parentcode": "51Axx",
	"level": 3
}, {
	"code": "51A20",
	"title": " Configuration theorems",
	"parentcode": "51Axx",
	"level": 3
}, {
	"code": "51A25",
	"title": " Algebraization [See also 12Kxx, 20N05]",
	"parentcode": "51Axx",
	"level": 3
}, {
	"code": "51A30",
	"title": " Desarguesian and Pappian geometries",
	"parentcode": "51Axx",
	"level": 3
}, {
	"code": "51A35",
	"title": " Non-Desarguesian affine and projective planes",
	"parentcode": "51Axx",
	"level": 3
}, {
	"code": "51A40",
	"title": " Translation planes and spreads",
	"parentcode": "51Axx",
	"level": 3
}, {
	"code": "51A45",
	"title": " Incidence structures imbeddable into projective geometries",
	"parentcode": "51Axx",
	"level": 3
}, {
	"code": "51A50",
	"title": " Polar geometry, symplectic spaces, orthogonal spaces",
	"parentcode": "51Axx",
	"level": 3
}, {
	"code": "51A99",
	"title": " None of the above, but in this section",
	"parentcode": "51Axx",
	"level": 3
}, {
	"code": "51Bxx",
	"title": " Nonlinear incidence geometry",
	"parentcode": "51-XX",
	"level": 2
}, {
	"code": "51B05",
	"title": " General theory",
	"parentcode": "51Bxx",
	"level": 3
}, {
	"code": "51B10",
	"title": " Möbius geometries",
	"parentcode": "51Bxx",
	"level": 3
}, {
	"code": "51B15",
	"title": " Laguerre geometries",
	"parentcode": "51Bxx",
	"level": 3
}, {
	"code": "51B20",
	"title": " Minkowski geometries",
	"parentcode": "51Bxx",
	"level": 3
}, {
	"code": "51B25",
	"title": " Lie geometries",
	"parentcode": "51Bxx",
	"level": 3
}, {
	"code": "51B99",
	"title": " None of the above, but in this section",
	"parentcode": "51Bxx",
	"level": 3
}, {
	"code": "51Cxx",
	"title": " Ring geometry (Hjelmslev, Barbilian, etc.)",
	"parentcode": "51-XX",
	"level": 2
}, {
	"code": "51C05",
	"title": " Ring geometry (Hjelmslev, Barbilian, etc.)",
	"parentcode": "51Cxx",
	"level": 3
}, {
	"code": "51C99",
	"title": " None of the above, but in this section",
	"parentcode": "51Cxx",
	"level": 3
}, {
	"code": "51Dxx",
	"title": " Geometric closure systems",
	"parentcode": "51-XX",
	"level": 2
}, {
	"code": "51D05",
	"title": " Abstract (Maeda) geometries",
	"parentcode": "51Dxx",
	"level": 3
}, {
	"code": "51D10",
	"title": " Abstract geometries with exchange axiom",
	"parentcode": "51Dxx",
	"level": 3
}, {
	"code": "51D15",
	"title": " Abstract geometries with parallelism",
	"parentcode": "51Dxx",
	"level": 3
}, {
	"code": "51D20",
	"title": " Combinatorial geometries [See also 05B25, 05B35]",
	"parentcode": "51Dxx",
	"level": 3
}, {
	"code": "51D25",
	"title": " Lattices of subspaces [See also 05B35]",
	"parentcode": "51Dxx",
	"level": 3
}, {
	"code": "51D30",
	"title": " Continuous geometries and related topics [See also 06Cxx]",
	"parentcode": "51Dxx",
	"level": 3
}, {
	"code": "51D99",
	"title": " None of the above, but in this section",
	"parentcode": "51Dxx",
	"level": 3
}, {
	"code": "51Exx",
	"title": " Finite geometry and special incidence structures",
	"parentcode": "51-XX",
	"level": 2
}, {
	"code": "51E05",
	"title": " General block designs [See also 05B05]",
	"parentcode": "51Exx",
	"level": 3
}, {
	"code": "51E10",
	"title": " Steiner systems",
	"parentcode": "51Exx",
	"level": 3
}, {
	"code": "51E12",
	"title": " Generalized quadrangles, generalized polygons",
	"parentcode": "51Exx",
	"level": 3
}, {
	"code": "51E14",
	"title": " Finite partial geometries (general), nets, partial spreads",
	"parentcode": "51Exx",
	"level": 3
}, {
	"code": "51E15",
	"title": " Affine and projective planes",
	"parentcode": "51Exx",
	"level": 3
}, {
	"code": "51E20",
	"title": " Combinatorial structures in finite projective spaces [See also 05Bxx]",
	"parentcode": "51Exx",
	"level": 3
}, {
	"code": "51E21",
	"title": " Blocking sets, ovals, $k$-arcs",
	"parentcode": "51Exx",
	"level": 3
}, {
	"code": "51E22",
	"title": " Linear codes and caps in Galois spaces [See also 94B05]",
	"parentcode": "51Exx",
	"level": 3
}, {
	"code": "51E23",
	"title": " Spreads and packing problems",
	"parentcode": "51Exx",
	"level": 3
}, {
	"code": "51E24",
	"title": " Buildings and the geometry of diagrams",
	"parentcode": "51Exx",
	"level": 3
}, {
	"code": "51E25",
	"title": " Other finite nonlinear geometries",
	"parentcode": "51Exx",
	"level": 3
}, {
	"code": "51E26",
	"title": " Other finite linear geometries",
	"parentcode": "51Exx",
	"level": 3
}, {
	"code": "51E30",
	"title": " Other finite incidence structures [See also 05B30]",
	"parentcode": "51Exx",
	"level": 3
}, {
	"code": "51E99",
	"title": " None of the above, but in this section",
	"parentcode": "51Exx",
	"level": 3
}, {
	"code": "51Fxx",
	"title": " Metric geometry",
	"parentcode": "51-XX",
	"level": 2
}, {
	"code": "51F05",
	"title": " Absolute planes",
	"parentcode": "51Fxx",
	"level": 3
}, {
	"code": "51F10",
	"title": " Absolute spaces",
	"parentcode": "51Fxx",
	"level": 3
}, {
	"code": "51F15",
	"title": " Reflection groups, reflection geometries [See also 20H10, 20H15; for Coxeter groups, see 20F55]",
	"parentcode": "51Fxx",
	"level": 3
}, {
	"code": "51F20",
	"title": " Congruence and orthogonality [See also 20H05]",
	"parentcode": "51Fxx",
	"level": 3
}, {
	"code": "51F25",
	"title": " Orthogonal and unitary groups [See also 20H05]",
	"parentcode": "51Fxx",
	"level": 3
}, {
	"code": "51F99",
	"title": " None of the above, but in this section",
	"parentcode": "51Fxx",
	"level": 3
}, {
	"code": "51Gxx",
	"title": " Ordered geometries (ordered incidence structures, etc.)",
	"parentcode": "51-XX",
	"level": 2
}, {
	"code": "51G05",
	"title": " Ordered geometries (ordered incidence structures, etc.)",
	"parentcode": "51Gxx",
	"level": 3
}, {
	"code": "51G99",
	"title": " None of the above, but in this section",
	"parentcode": "51Gxx",
	"level": 3
}, {
	"code": "51Hxx",
	"title": " Topological geometry",
	"parentcode": "51-XX",
	"level": 2
}, {
	"code": "51H05",
	"title": " General theory",
	"parentcode": "51Hxx",
	"level": 3
}, {
	"code": "51H10",
	"title": " Topological linear incidence structures",
	"parentcode": "51Hxx",
	"level": 3
}, {
	"code": "51H15",
	"title": " Topological nonlinear incidence structures",
	"parentcode": "51Hxx",
	"level": 3
}, {
	"code": "51H20",
	"title": " Topological geometries on manifolds [See also 57-XX]",
	"parentcode": "51Hxx",
	"level": 3
}, {
	"code": "51H25",
	"title": " Geometries with differentiable structure [See also 53Cxx, 53C70]",
	"parentcode": "51Hxx",
	"level": 3
}, {
	"code": "51H30",
	"title": " Geometries with algebraic manifold structure [See also 14-XX]",
	"parentcode": "51Hxx",
	"level": 3
}, {
	"code": "51H99",
	"title": " None of the above, but in this section",
	"parentcode": "51Hxx",
	"level": 3
}, {
	"code": "51Jxx",
	"title": " Incidence groups",
	"parentcode": "51-XX",
	"level": 2
}, {
	"code": "51J05",
	"title": " General theory",
	"parentcode": "51Jxx",
	"level": 3
}, {
	"code": "51J10",
	"title": " Projective incidence groups",
	"parentcode": "51Jxx",
	"level": 3
}, {
	"code": "51J15",
	"title": " Kinematic spaces",
	"parentcode": "51Jxx",
	"level": 3
}, {
	"code": "51J20",
	"title": " Representation by near-fields and near-algebras [See also 12K05, 16Y30]",
	"parentcode": "51Jxx",
	"level": 3
}, {
	"code": "51J99",
	"title": " None of the above, but in this section",
	"parentcode": "51Jxx",
	"level": 3
}, {
	"code": "51Kxx",
	"title": " Distance geometry",
	"parentcode": "51-XX",
	"level": 2
}, {
	"code": "51K05",
	"title": " General theory",
	"parentcode": "51Kxx",
	"level": 3
}, {
	"code": "51K10",
	"title": " Synthetic differential geometry",
	"parentcode": "51Kxx",
	"level": 3
}, {
	"code": "51K99",
	"title": " None of the above, but in this section",
	"parentcode": "51Kxx",
	"level": 3
}, {
	"code": "51Lxx",
	"title": " Geometric order structures [See also 53C75]",
	"parentcode": "51-XX",
	"level": 2
}, {
	"code": "51L05",
	"title": " Geometry of orders of nondifferentiable curves",
	"parentcode": "51Lxx",
	"level": 3
}, {
	"code": "51L10",
	"title": " Directly differentiable curves",
	"parentcode": "51Lxx",
	"level": 3
}, {
	"code": "51L15",
	"title": " $n$-vertex theorems via direct methods",
	"parentcode": "51Lxx",
	"level": 3
}, {
	"code": "51L20",
	"title": " Geometry of orders of surfaces",
	"parentcode": "51Lxx",
	"level": 3
}, {
	"code": "51L99",
	"title": " None of the above, but in this section",
	"parentcode": "51Lxx",
	"level": 3
}, {
	"code": "51Mxx",
	"title": " Real and complex geometry",
	"parentcode": "51-XX",
	"level": 2
}, {
	"code": "51M04",
	"title": " Elementary problems in Euclidean geometries",
	"parentcode": "51Mxx",
	"level": 3
}, {
	"code": "51M05",
	"title": " Euclidean geometries (general) and generalizations",
	"parentcode": "51Mxx",
	"level": 3
}, {
	"code": "51M09",
	"title": " Elementary problems in hyperbolic and elliptic geometries",
	"parentcode": "51Mxx",
	"level": 3
}, {
	"code": "51M10",
	"title": " Hyperbolic and elliptic geometries (general) and generalizations",
	"parentcode": "51Mxx",
	"level": 3
}, {
	"code": "51M15",
	"title": " Geometric constructions",
	"parentcode": "51Mxx",
	"level": 3
}, {
	"code": "51M16",
	"title": " Inequalities and extremum problems {For convex problems, see 52A40}",
	"parentcode": "51Mxx",
	"level": 3
}, {
	"code": "51M20",
	"title": " Polyhedra and polytopes; regular figures, division of spaces [See also 51F15]",
	"parentcode": "51Mxx",
	"level": 3
}, {
	"code": "51M25",
	"title": " Length, area and volume [See also 26B15]",
	"parentcode": "51Mxx",
	"level": 3
}, {
	"code": "51M30",
	"title": " Line geometries and their generalizations [See also 53A25]",
	"parentcode": "51Mxx",
	"level": 3
}, {
	"code": "51M35",
	"title": " Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) [See also 14M15]",
	"parentcode": "51Mxx",
	"level": 3
}, {
	"code": "51M99",
	"title": " None of the above, but in this section",
	"parentcode": "51Mxx",
	"level": 3
}, {
	"code": "51Nxx",
	"title": " Analytic and descriptive geometry",
	"parentcode": "51-XX",
	"level": 2
}, {
	"code": "51N05",
	"title": " Descriptive geometry [See also 65D17, 68U07]",
	"parentcode": "51Nxx",
	"level": 3
}, {
	"code": "51N10",
	"title": " Affine analytic geometry",
	"parentcode": "51Nxx",
	"level": 3
}, {
	"code": "51N15",
	"title": " Projective analytic geometry",
	"parentcode": "51Nxx",
	"level": 3
}, {
	"code": "51N20",
	"title": " Euclidean analytic geometry",
	"parentcode": "51Nxx",
	"level": 3
}, {
	"code": "51N25",
	"title": " Analytic geometry with other transformation groups",
	"parentcode": "51Nxx",
	"level": 3
}, {
	"code": "51N30",
	"title": " Geometry of classical groups [See also 20Gxx, 14L35]",
	"parentcode": "51Nxx",
	"level": 3
}, {
	"code": "51N35",
	"title": " Questions of classical algebraic geometry [See also 14Nxx]",
	"parentcode": "51Nxx",
	"level": 3
}, {
	"code": "51N99",
	"title": " None of the above, but in this section",
	"parentcode": "51Nxx",
	"level": 3
}, {
	"code": "51Pxx",
	"title": " Geometry and physics (should also be assigned at least one other classification number from Sections 70--86)",
	"parentcode": "51-XX",
	"level": 2
}, {
	"code": "51P05",
	"title": " Geometry and physics (should also be assigned at least one other classification number from Sections 70--86)",
	"parentcode": "51Pxx",
	"level": 3
}, {
	"code": "51P99",
	"title": " None of the above, but in this section",
	"parentcode": "51Pxx",
	"level": 3
}, {
	"code": "52-XX",
	"title": " Convex and discrete geometry",
	"parentcode": null,
	"level": 1
}, {
	"code": "52-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "52-XX",
	"level": 2
}, {
	"code": "52-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "52-XX",
	"level": 2
}, {
	"code": "52-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "52-XX",
	"level": 2
}, {
	"code": "52-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "52-XX",
	"level": 2
}, {
	"code": "52-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "52-XX",
	"level": 2
}, {
	"code": "52-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "52-XX",
	"level": 2
}, {
	"code": "52Axx",
	"title": " General convexity",
	"parentcode": "52-XX",
	"level": 2
}, {
	"code": "52A01",
	"title": " Axiomatic and generalized convexity",
	"parentcode": "52Axx",
	"level": 3
}, {
	"code": "52A05",
	"title": " Convex sets without dimension restrictions",
	"parentcode": "52Axx",
	"level": 3
}, {
	"code": "52A07",
	"title": " Convex sets in topological vector spaces [See also 46A55]",
	"parentcode": "52Axx",
	"level": 3
}, {
	"code": "52A10",
	"title": " Convex sets in $2$ dimensions (including convex curves) [See also 53A04]",
	"parentcode": "52Axx",
	"level": 3
}, {
	"code": "52A15",
	"title": " Convex sets in $3$ dimensions (including convex surfaces) [See also 53A05, 53C45]",
	"parentcode": "52Axx",
	"level": 3
}, {
	"code": "52A20",
	"title": " Convex sets in $n$ dimensions (including convex hypersurfaces) [See also 53A07, 53C45]",
	"parentcode": "52Axx",
	"level": 3
}, {
	"code": "52A21",
	"title": " Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also 46Bxx]",
	"parentcode": "52Axx",
	"level": 3
}, {
	"code": "52A22",
	"title": " Random convex sets and integral geometry [See also 53C65, 60D05]",
	"parentcode": "52Axx",
	"level": 3
}, {
	"code": "52A23",
	"title": " Asymptotic theory of convex bodies [See also 46B06]",
	"parentcode": "52Axx",
	"level": 3
}, {
	"code": "52A27",
	"title": " Approximation by convex sets",
	"parentcode": "52Axx",
	"level": 3
}, {
	"code": "52A30",
	"title": " Variants of convex sets (star-shaped, ($m, n$)-convex, etc.)",
	"parentcode": "52Axx",
	"level": 3
}, {
	"code": "52A35",
	"title": " Helly-type theorems and geometric transversal theory",
	"parentcode": "52Axx",
	"level": 3
}, {
	"code": "52A37",
	"title": " Other problems of combinatorial convexity",
	"parentcode": "52Axx",
	"level": 3
}, {
	"code": "52A38",
	"title": " Length, area, volume [See also 26B15, 28A75, 49Q20]",
	"parentcode": "52Axx",
	"level": 3
}, {
	"code": "52A39",
	"title": " Mixed volumes and related topics",
	"parentcode": "52Axx",
	"level": 3
}, {
	"code": "52A40",
	"title": " Inequalities and extremum problems",
	"parentcode": "52Axx",
	"level": 3
}, {
	"code": "52A41",
	"title": " Convex functions and convex programs [See also 26B25, 90C25]",
	"parentcode": "52Axx",
	"level": 3
}, {
	"code": "52A55",
	"title": " Spherical and hyperbolic convexity",
	"parentcode": "52Axx",
	"level": 3
}, {
	"code": "52A99",
	"title": " None of the above, but in this section",
	"parentcode": "52Axx",
	"level": 3
}, {
	"code": "52Bxx",
	"title": " Polytopes and polyhedra",
	"parentcode": "52-XX",
	"level": 2
}, {
	"code": "52B05",
	"title": " Combinatorial properties (number of faces, shortest paths, etc.) [See also 05Cxx]",
	"parentcode": "52Bxx",
	"level": 3
}, {
	"code": "52B10",
	"title": " Three-dimensional polytopes",
	"parentcode": "52Bxx",
	"level": 3
}, {
	"code": "52B11",
	"title": " $n$-dimensional polytopes",
	"parentcode": "52Bxx",
	"level": 3
}, {
	"code": "52B12",
	"title": " Special polytopes (linear programming, centrally symmetric, etc.)",
	"parentcode": "52Bxx",
	"level": 3
}, {
	"code": "52B15",
	"title": " Symmetry properties of polytopes",
	"parentcode": "52Bxx",
	"level": 3
}, {
	"code": "52B20",
	"title": " Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]",
	"parentcode": "52Bxx",
	"level": 3
}, {
	"code": "52B22",
	"title": " Shellability",
	"parentcode": "52Bxx",
	"level": 3
}, {
	"code": "52B35",
	"title": " Gale and other diagrams",
	"parentcode": "52Bxx",
	"level": 3
}, {
	"code": "52B40",
	"title": " Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) [See also 05B35, 52Cxx]",
	"parentcode": "52Bxx",
	"level": 3
}, {
	"code": "52B45",
	"title": " Dissections and valuations (Hilbert's third problem, etc.)",
	"parentcode": "52Bxx",
	"level": 3
}, {
	"code": "52B55",
	"title": " Computational aspects related to convexity {For computational geometry and algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx} [See also 68Uxx]",
	"parentcode": "52Bxx",
	"level": 3
}, {
	"code": "52B60",
	"title": " Isoperimetric problems for polytopes",
	"parentcode": "52Bxx",
	"level": 3
}, {
	"code": "52B70",
	"title": " Polyhedral manifolds",
	"parentcode": "52Bxx",
	"level": 3
}, {
	"code": "52B99",
	"title": " None of the above, but in this section",
	"parentcode": "52Bxx",
	"level": 3
}, {
	"code": "52Cxx",
	"title": " Discrete geometry",
	"parentcode": "52-XX",
	"level": 2
}, {
	"code": "52C05",
	"title": " Lattices and convex bodies in $2$ dimensions [See also 11H06, 11H31, 11P21]",
	"parentcode": "52Cxx",
	"level": 3
}, {
	"code": "52C07",
	"title": " Lattices and convex bodies in $n$ dimensions [See also 11H06, 11H31, 11P21]",
	"parentcode": "52Cxx",
	"level": 3
}, {
	"code": "52C10",
	"title": " Erdős problems and related topics of discrete geometry [See also 11Hxx]",
	"parentcode": "52Cxx",
	"level": 3
}, {
	"code": "52C15",
	"title": " Packing and covering in $2$ dimensions [See also 05B40, 11H31]",
	"parentcode": "52Cxx",
	"level": 3
}, {
	"code": "52C17",
	"title": " Packing and covering in $n$ dimensions [See also 05B40, 11H31]",
	"parentcode": "52Cxx",
	"level": 3
}, {
	"code": "52C20",
	"title": " Tilings in $2$ dimensions [See also 05B45, 51M20]",
	"parentcode": "52Cxx",
	"level": 3
}, {
	"code": "52C22",
	"title": " Tilings in $n$ dimensions [See also 05B45, 51M20]",
	"parentcode": "52Cxx",
	"level": 3
}, {
	"code": "52C23",
	"title": " Quasicrystals, aperiodic tilings",
	"parentcode": "52Cxx",
	"level": 3
}, {
	"code": "52C25",
	"title": " Rigidity and flexibility of structures [See also 70B15]",
	"parentcode": "52Cxx",
	"level": 3
}, {
	"code": "52C26",
	"title": " Circle packings and discrete conformal geometry",
	"parentcode": "52Cxx",
	"level": 3
}, {
	"code": "52C30",
	"title": " Planar arrangements of lines and pseudolines",
	"parentcode": "52Cxx",
	"level": 3
}, {
	"code": "52C35",
	"title": " Arrangements of points, flats, hyperplanes [See also 32S22]",
	"parentcode": "52Cxx",
	"level": 3
}, {
	"code": "52C40",
	"title": " Oriented matroids",
	"parentcode": "52Cxx",
	"level": 3
}, {
	"code": "52C45",
	"title": " Combinatorial complexity of geometric structures [See also 68U05]",
	"parentcode": "52Cxx",
	"level": 3
}, {
	"code": "52C99",
	"title": " None of the above, but in this section",
	"parentcode": "52Cxx",
	"level": 3
}, {
	"code": "53-XX",
	"title": " Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx}",
	"parentcode": null,
	"level": 1
}, {
	"code": "53-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "53-XX",
	"level": 2
}, {
	"code": "53-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "53-XX",
	"level": 2
}, {
	"code": "53-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "53-XX",
	"level": 2
}, {
	"code": "53-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "53-XX",
	"level": 2
}, {
	"code": "53-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "53-XX",
	"level": 2
}, {
	"code": "53-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "53-XX",
	"level": 2
}, {
	"code": "53Axx",
	"title": " Classical differential geometry",
	"parentcode": "53-XX",
	"level": 2
}, {
	"code": "53A04",
	"title": " Curves in Euclidean space",
	"parentcode": "53Axx",
	"level": 3
}, {
	"code": "53A05",
	"title": " Surfaces in Euclidean space",
	"parentcode": "53Axx",
	"level": 3
}, {
	"code": "53A07",
	"title": " Higher-dimensional and -codimensional surfaces in Euclidean $n$-space",
	"parentcode": "53Axx",
	"level": 3
}, {
	"code": "53A10",
	"title": " Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]",
	"parentcode": "53Axx",
	"level": 3
}, {
	"code": "53A15",
	"title": " Affine differential geometry",
	"parentcode": "53Axx",
	"level": 3
}, {
	"code": "53A17",
	"title": " Kinematics",
	"parentcode": "53Axx",
	"level": 3
}, {
	"code": "53A20",
	"title": " Projective differential geometry",
	"parentcode": "53Axx",
	"level": 3
}, {
	"code": "53A25",
	"title": " Differential line geometry",
	"parentcode": "53Axx",
	"level": 3
}, {
	"code": "53A30",
	"title": " Conformal differential geometry",
	"parentcode": "53Axx",
	"level": 3
}, {
	"code": "53A35",
	"title": " Non-Euclidean differential geometry",
	"parentcode": "53Axx",
	"level": 3
}, {
	"code": "53A40",
	"title": " Other special differential geometries",
	"parentcode": "53Axx",
	"level": 3
}, {
	"code": "53A45",
	"title": " Vector and tensor analysis",
	"parentcode": "53Axx",
	"level": 3
}, {
	"code": "53A55",
	"title": " Differential invariants (local theory), geometric objects",
	"parentcode": "53Axx",
	"level": 3
}, {
	"code": "53A60",
	"title": " Geometry of webs [See also 14C21, 20N05]",
	"parentcode": "53Axx",
	"level": 3
}, {
	"code": "53A99",
	"title": " None of the above, but in this section",
	"parentcode": "53Axx",
	"level": 3
}, {
	"code": "53Bxx",
	"title": " Local differential geometry",
	"parentcode": "53-XX",
	"level": 2
}, {
	"code": "53B05",
	"title": " Linear and affine connections",
	"parentcode": "53Bxx",
	"level": 3
}, {
	"code": "53B10",
	"title": " Projective connections",
	"parentcode": "53Bxx",
	"level": 3
}, {
	"code": "53B15",
	"title": " Other connections",
	"parentcode": "53Bxx",
	"level": 3
}, {
	"code": "53B20",
	"title": " Local Riemannian geometry",
	"parentcode": "53Bxx",
	"level": 3
}, {
	"code": "53B21",
	"title": " Methods of Riemannian geometry",
	"parentcode": "53Bxx",
	"level": 3
}, {
	"code": "53B25",
	"title": " Local submanifolds [See also 53C40]",
	"parentcode": "53Bxx",
	"level": 3
}, {
	"code": "53B30",
	"title": " Lorentz metrics, indefinite metrics",
	"parentcode": "53Bxx",
	"level": 3
}, {
	"code": "53B35",
	"title": " Hermitian and Kählerian structures [See also 32Cxx]",
	"parentcode": "53Bxx",
	"level": 3
}, {
	"code": "53B40",
	"title": " Finsler spaces and generalizations (areal metrics)",
	"parentcode": "53Bxx",
	"level": 3
}, {
	"code": "53B50",
	"title": " Applications to physics",
	"parentcode": "53Bxx",
	"level": 3
}, {
	"code": "53B99",
	"title": " None of the above, but in this section",
	"parentcode": "53Bxx",
	"level": 3
}, {
	"code": "53Cxx",
	"title": " Global differential geometry [See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx]",
	"parentcode": "53-XX",
	"level": 2
}, {
	"code": "53C05",
	"title": " Connections, general theory",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C07",
	"title": " Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills) [See also 32Q20]",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C08",
	"title": " Gerbes, differential characters",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C10",
	"title": " $G$-structures",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C12",
	"title": " Foliations (differential geometric aspects) [See also 57R30, 57R32]",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C15",
	"title": " General geometric structures on manifolds (almost complex, almost product structures, etc.)",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C17",
	"title": " Sub-Riemannian geometry",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C20",
	"title": " Global Riemannian geometry, including pinching [See also 31C12, 58B20]",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C21",
	"title": " Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C22",
	"title": " Geodesics [See also 58E10]",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C23",
	"title": " Global geometric and  topological methods (à la Gromov); differential geometric analysis on metric spaces",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C24",
	"title": " Rigidity results",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C25",
	"title": " Special Riemannian manifolds (Einstein, Sasakian, etc.)",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C26",
	"title": " Hyper-Kähler and quaternionic Kähler geometry, “special” geometry",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C27",
	"title": " Spin and Spin${}^c$ geometry",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C28",
	"title": " Twistor methods [See also 32L25]",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C29",
	"title": " Issues of holonomy",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C30",
	"title": " Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C35",
	"title": " Symmetric spaces [See also 32M15, 57T15]",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C38",
	"title": " Calibrations and calibrated geometries",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C40",
	"title": " Global submanifolds [See also 53B25]",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C42",
	"title": " Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C43",
	"title": " Differential geometric aspects of harmonic maps [See also 58E20]",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C44",
	"title": " Geometric evolution equations (mean curvature flow, Ricci flow, etc.)",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C45",
	"title": " Global surface theory (convex surfaces à la A. D. Aleksandrov)",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C50",
	"title": " Lorentz manifolds, manifolds with indefinite metrics",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C55",
	"title": " Hermitian and Kählerian manifolds [See also 32Cxx]",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C56",
	"title": " Other complex differential geometry [See also 32Cxx]",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C60",
	"title": " Finsler spaces and generalizations (areal metrics) [See also 58B20]",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C65",
	"title": " Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx]",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C70",
	"title": " Direct methods ($G$-spaces of Busemann, etc.)",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C75",
	"title": " Geometric orders, order geometry [See also 51Lxx]",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C80",
	"title": " Applications to physics",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53C99",
	"title": " None of the above, but in this section",
	"parentcode": "53Cxx",
	"level": 3
}, {
	"code": "53Dxx",
	"title": " Symplectic geometry, contact geometry [See also 37Jxx, 70Gxx, 70Hxx]",
	"parentcode": "53-XX",
	"level": 2
}, {
	"code": "53D05",
	"title": " Symplectic manifolds, general",
	"parentcode": "53Dxx",
	"level": 3
}, {
	"code": "53D10",
	"title": " Contact manifolds, general",
	"parentcode": "53Dxx",
	"level": 3
}, {
	"code": "53D12",
	"title": " Lagrangian submanifolds; Maslov index",
	"parentcode": "53Dxx",
	"level": 3
}, {
	"code": "53D15",
	"title": " Almost contact and almost symplectic manifolds",
	"parentcode": "53Dxx",
	"level": 3
}, {
	"code": "53D17",
	"title": " Poisson manifolds; Poisson groupoids and algebroids",
	"parentcode": "53Dxx",
	"level": 3
}, {
	"code": "53D18",
	"title": "  Generalized geometries (à la Hitchin)",
	"parentcode": "53Dxx",
	"level": 3
}, {
	"code": "53D20",
	"title": " Momentum maps; symplectic reduction",
	"parentcode": "53Dxx",
	"level": 3
}, {
	"code": "53D22",
	"title": " Canonical transformations",
	"parentcode": "53Dxx",
	"level": 3
}, {
	"code": "53D25",
	"title": " Geodesic flows",
	"parentcode": "53Dxx",
	"level": 3
}, {
	"code": "53D30",
	"title": " Symplectic structures of moduli spaces",
	"parentcode": "53Dxx",
	"level": 3
}, {
	"code": "53D35",
	"title": " Global theory of symplectic and contact manifolds [See also 57Rxx]",
	"parentcode": "53Dxx",
	"level": 3
}, {
	"code": "53D37",
	"title": " Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category [See also 14J33]",
	"parentcode": "53Dxx",
	"level": 3
}, {
	"code": "53D40",
	"title": " Floer homology and cohomology, symplectic aspects",
	"parentcode": "53Dxx",
	"level": 3
}, {
	"code": "53D42",
	"title": " Symplectic field theory; contact homology",
	"parentcode": "53Dxx",
	"level": 3
}, {
	"code": "53D45",
	"title": " Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]",
	"parentcode": "53Dxx",
	"level": 3
}, {
	"code": "53D50",
	"title": " Geometric quantization",
	"parentcode": "53Dxx",
	"level": 3
}, {
	"code": "53D55",
	"title": " Deformation quantization, star products",
	"parentcode": "53Dxx",
	"level": 3
}, {
	"code": "53D99",
	"title": " None of the above, but in this section",
	"parentcode": "53Dxx",
	"level": 3
}, {
	"code": "53Zxx",
	"title": " Applications to physics",
	"parentcode": "53-XX",
	"level": 2
}, {
	"code": "53Z05",
	"title": " Applications to physics",
	"parentcode": "53Zxx",
	"level": 3
}, {
	"code": "53Z99",
	"title": " None of the above, but in this section",
	"parentcode": "53Zxx",
	"level": 3
}, {
	"code": "54-XX",
	"title": " General topology {For the topology of manifolds of all dimensions, see 57Nxx}",
	"parentcode": null,
	"level": 1
}, {
	"code": "54-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "54-XX",
	"level": 2
}, {
	"code": "54-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "54-XX",
	"level": 2
}, {
	"code": "54-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "54-XX",
	"level": 2
}, {
	"code": "54-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "54-XX",
	"level": 2
}, {
	"code": "54-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "54-XX",
	"level": 2
}, {
	"code": "54-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "54-XX",
	"level": 2
}, {
	"code": "54Axx",
	"title": " Generalities",
	"parentcode": "54-XX",
	"level": 2
}, {
	"code": "54A05",
	"title": " Topological spaces and generalizations (closure spaces, etc.)",
	"parentcode": "54Axx",
	"level": 3
}, {
	"code": "54A10",
	"title": " Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)",
	"parentcode": "54Axx",
	"level": 3
}, {
	"code": "54A15",
	"title": " Syntopogeneous structures",
	"parentcode": "54Axx",
	"level": 3
}, {
	"code": "54A20",
	"title": " Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)",
	"parentcode": "54Axx",
	"level": 3
}, {
	"code": "54A25",
	"title": " Cardinality properties (cardinal functions and inequalities, discrete subsets) [See also 03Exx] {For ultrafilters, see 54D80}",
	"parentcode": "54Axx",
	"level": 3
}, {
	"code": "54A35",
	"title": " Consistency and independence results [See also 03E35]",
	"parentcode": "54Axx",
	"level": 3
}, {
	"code": "54A40",
	"title": " Fuzzy topology [See also 03E72]",
	"parentcode": "54Axx",
	"level": 3
}, {
	"code": "54A99",
	"title": " None of the above, but in this section",
	"parentcode": "54Axx",
	"level": 3
}, {
	"code": "54Bxx",
	"title": " Basic constructions",
	"parentcode": "54-XX",
	"level": 2
}, {
	"code": "54B05",
	"title": " Subspaces",
	"parentcode": "54Bxx",
	"level": 3
}, {
	"code": "54B10",
	"title": " Product spaces",
	"parentcode": "54Bxx",
	"level": 3
}, {
	"code": "54B15",
	"title": " Quotient spaces, decompositions",
	"parentcode": "54Bxx",
	"level": 3
}, {
	"code": "54B17",
	"title": " Adjunction spaces and similar constructions",
	"parentcode": "54Bxx",
	"level": 3
}, {
	"code": "54B20",
	"title": " Hyperspaces",
	"parentcode": "54Bxx",
	"level": 3
}, {
	"code": "54B30",
	"title": " Categorical methods [See also 18B30]",
	"parentcode": "54Bxx",
	"level": 3
}, {
	"code": "54B35",
	"title": " Spectra",
	"parentcode": "54Bxx",
	"level": 3
}, {
	"code": "54B40",
	"title": " Presheaves and sheaves [See also 18F20]",
	"parentcode": "54Bxx",
	"level": 3
}, {
	"code": "54B99",
	"title": " None of the above, but in this section",
	"parentcode": "54Bxx",
	"level": 3
}, {
	"code": "54Cxx",
	"title": " Maps and general types of spaces defined by maps",
	"parentcode": "54-XX",
	"level": 2
}, {
	"code": "54C05",
	"title": " Continuous maps",
	"parentcode": "54Cxx",
	"level": 3
}, {
	"code": "54C08",
	"title": " Weak and generalized continuity",
	"parentcode": "54Cxx",
	"level": 3
}, {
	"code": "54C10",
	"title": " Special maps on topological spaces (open, closed, perfect, etc.)",
	"parentcode": "54Cxx",
	"level": 3
}, {
	"code": "54C15",
	"title": " Retraction",
	"parentcode": "54Cxx",
	"level": 3
}, {
	"code": "54C20",
	"title": " Extension of maps",
	"parentcode": "54Cxx",
	"level": 3
}, {
	"code": "54C25",
	"title": " Embedding",
	"parentcode": "54Cxx",
	"level": 3
}, {
	"code": "54C30",
	"title": " Real-valued functions [See also 26-XX]",
	"parentcode": "54Cxx",
	"level": 3
}, {
	"code": "54C35",
	"title": " Function spaces [See also 46Exx, 58D15]",
	"parentcode": "54Cxx",
	"level": 3
}, {
	"code": "54C40",
	"title": " Algebraic properties of function spaces [See also 46J10]",
	"parentcode": "54Cxx",
	"level": 3
}, {
	"code": "54C45",
	"title": " $C$- and $C^*$-embedding",
	"parentcode": "54Cxx",
	"level": 3
}, {
	"code": "54C50",
	"title": " Special sets defined by functions [See also 26A21]",
	"parentcode": "54Cxx",
	"level": 3
}, {
	"code": "54C55",
	"title": " Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) [See also 55M15]",
	"parentcode": "54Cxx",
	"level": 3
}, {
	"code": "54C56",
	"title": " Shape theory [See also 55P55, 57N25]",
	"parentcode": "54Cxx",
	"level": 3
}, {
	"code": "54C60",
	"title": " Set-valued maps [See also 26E25, 28B20, 47H04, 58C06]",
	"parentcode": "54Cxx",
	"level": 3
}, {
	"code": "54C65",
	"title": " Selections [See also 28B20]",
	"parentcode": "54Cxx",
	"level": 3
}, {
	"code": "54C70",
	"title": " Entropy",
	"parentcode": "54Cxx",
	"level": 3
}, {
	"code": "54C99",
	"title": " None of the above, but in this section",
	"parentcode": "54Cxx",
	"level": 3
}, {
	"code": "54Dxx",
	"title": " Fairly general properties",
	"parentcode": "54-XX",
	"level": 2
}, {
	"code": "54D05",
	"title": " Connected and locally connected spaces (general aspects)",
	"parentcode": "54Dxx",
	"level": 3
}, {
	"code": "54D10",
	"title": " Lower separation axioms ($T_0$--$T_3$, etc.)",
	"parentcode": "54Dxx",
	"level": 3
}, {
	"code": "54D15",
	"title": " Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)",
	"parentcode": "54Dxx",
	"level": 3
}, {
	"code": "54D20",
	"title": " Noncompact covering properties (paracompact, Lindelöf, etc.)",
	"parentcode": "54Dxx",
	"level": 3
}, {
	"code": "54D25",
	"title": " “$P$-minimal” and “$P$-closed” spaces",
	"parentcode": "54Dxx",
	"level": 3
}, {
	"code": "54D30",
	"title": " Compactness",
	"parentcode": "54Dxx",
	"level": 3
}, {
	"code": "54D35",
	"title": " Extensions of spaces (compactifications, supercompactifications, completions, etc.)",
	"parentcode": "54Dxx",
	"level": 3
}, {
	"code": "54D40",
	"title": " Remainders",
	"parentcode": "54Dxx",
	"level": 3
}, {
	"code": "54D45",
	"title": " Local compactness, $\\sigma$-compactness",
	"parentcode": "54Dxx",
	"level": 3
}, {
	"code": "54D50",
	"title": " $k$-spaces",
	"parentcode": "54Dxx",
	"level": 3
}, {
	"code": "54D55",
	"title": " Sequential spaces",
	"parentcode": "54Dxx",
	"level": 3
}, {
	"code": "54D60",
	"title": " Realcompactness and realcompactification",
	"parentcode": "54Dxx",
	"level": 3
}, {
	"code": "54D65",
	"title": " Separability",
	"parentcode": "54Dxx",
	"level": 3
}, {
	"code": "54D70",
	"title": " Base properties",
	"parentcode": "54Dxx",
	"level": 3
}, {
	"code": "54D80",
	"title": " Special constructions of spaces (spaces of ultrafilters, etc.)",
	"parentcode": "54Dxx",
	"level": 3
}, {
	"code": "54D99",
	"title": " None of the above, but in this section",
	"parentcode": "54Dxx",
	"level": 3
}, {
	"code": "54Exx",
	"title": " Spaces with richer structures",
	"parentcode": "54-XX",
	"level": 2
}, {
	"code": "54E05",
	"title": " Proximity structures and generalizations",
	"parentcode": "54Exx",
	"level": 3
}, {
	"code": "54E15",
	"title": " Uniform structures and generalizations",
	"parentcode": "54Exx",
	"level": 3
}, {
	"code": "54E17",
	"title": " Nearness spaces",
	"parentcode": "54Exx",
	"level": 3
}, {
	"code": "54E18",
	"title": " $p$-spaces, $M$-spaces, $\\sigma$-spaces, etc.",
	"parentcode": "54Exx",
	"level": 3
}, {
	"code": "54E20",
	"title": " Stratifiable spaces, cosmic spaces, etc.",
	"parentcode": "54Exx",
	"level": 3
}, {
	"code": "54E25",
	"title": " Semimetric spaces",
	"parentcode": "54Exx",
	"level": 3
}, {
	"code": "54E30",
	"title": " Moore spaces",
	"parentcode": "54Exx",
	"level": 3
}, {
	"code": "54E35",
	"title": " Metric spaces, metrizability",
	"parentcode": "54Exx",
	"level": 3
}, {
	"code": "54E40",
	"title": " Special maps on metric spaces",
	"parentcode": "54Exx",
	"level": 3
}, {
	"code": "54E45",
	"title": " Compact (locally compact) metric spaces",
	"parentcode": "54Exx",
	"level": 3
}, {
	"code": "54E50",
	"title": " Complete metric spaces",
	"parentcode": "54Exx",
	"level": 3
}, {
	"code": "54E52",
	"title": " Baire category, Baire spaces",
	"parentcode": "54Exx",
	"level": 3
}, {
	"code": "54E55",
	"title": " Bitopologies",
	"parentcode": "54Exx",
	"level": 3
}, {
	"code": "54E70",
	"title": " Probabilistic metric spaces",
	"parentcode": "54Exx",
	"level": 3
}, {
	"code": "54E99",
	"title": " None of the above, but in this section",
	"parentcode": "54Exx",
	"level": 3
}, {
	"code": "54Fxx",
	"title": " Special properties",
	"parentcode": "54-XX",
	"level": 2
}, {
	"code": "54F05",
	"title": " Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces [See also 06B30, 06F30]",
	"parentcode": "54Fxx",
	"level": 3
}, {
	"code": "54F15",
	"title": " Continua and generalizations",
	"parentcode": "54Fxx",
	"level": 3
}, {
	"code": "54F35",
	"title": " Higher-dimensional local connectedness [See also 55Mxx, 55Nxx]",
	"parentcode": "54Fxx",
	"level": 3
}, {
	"code": "54F45",
	"title": " Dimension theory [See also 55M10]",
	"parentcode": "54Fxx",
	"level": 3
}, {
	"code": "54F50",
	"title": " Spaces of dimension $\\leq 1$; curves, dendrites [See also 26A03]",
	"parentcode": "54Fxx",
	"level": 3
}, {
	"code": "54F55",
	"title": " Unicoherence, multicoherence",
	"parentcode": "54Fxx",
	"level": 3
}, {
	"code": "54F65",
	"title": " Topological characterizations of particular spaces",
	"parentcode": "54Fxx",
	"level": 3
}, {
	"code": "54F99",
	"title": " None of the above, but in this section",
	"parentcode": "54Fxx",
	"level": 3
}, {
	"code": "54Gxx",
	"title": " Peculiar spaces",
	"parentcode": "54-XX",
	"level": 2
}, {
	"code": "54G05",
	"title": " Extremally disconnected spaces, $F$-spaces, etc.",
	"parentcode": "54Gxx",
	"level": 3
}, {
	"code": "54G10",
	"title": " $P$-spaces",
	"parentcode": "54Gxx",
	"level": 3
}, {
	"code": "54G12",
	"title": " Scattered spaces",
	"parentcode": "54Gxx",
	"level": 3
}, {
	"code": "54G15",
	"title": " Pathological spaces",
	"parentcode": "54Gxx",
	"level": 3
}, {
	"code": "54G20",
	"title": " Counterexamples",
	"parentcode": "54Gxx",
	"level": 3
}, {
	"code": "54G99",
	"title": " None of the above, but in this section",
	"parentcode": "54Gxx",
	"level": 3
}, {
	"code": "54Hxx",
	"title": " Connections with other structures, applications",
	"parentcode": "54-XX",
	"level": 2
}, {
	"code": "54H05",
	"title": " Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05]",
	"parentcode": "54Hxx",
	"level": 3
}, {
	"code": "54H10",
	"title": " Topological representations of algebraic systems [See also 22-XX]",
	"parentcode": "54Hxx",
	"level": 3
}, {
	"code": "54H11",
	"title": " Topological groups [See also 22A05]",
	"parentcode": "54Hxx",
	"level": 3
}, {
	"code": "54H12",
	"title": " Topological lattices, etc. [See also 06B30, 06F30]",
	"parentcode": "54Hxx",
	"level": 3
}, {
	"code": "54H13",
	"title": " Topological fields, rings, etc. [See also 12Jxx] {For algebraic aspects, see 13Jxx, 16W80}",
	"parentcode": "54Hxx",
	"level": 3
}, {
	"code": "54H15",
	"title": " Transformation groups and semigroups [See also 20M20, 22-XX, 57Sxx]",
	"parentcode": "54Hxx",
	"level": 3
}, {
	"code": "54H20",
	"title": " Topological dynamics [See also 28Dxx, 37Bxx]",
	"parentcode": "54Hxx",
	"level": 3
}, {
	"code": "54H25",
	"title": " Fixed-point and coincidence theorems [See also 47H10, 55M20]",
	"parentcode": "54Hxx",
	"level": 3
}, {
	"code": "54H99",
	"title": " None of the above, but in this section",
	"parentcode": "54Hxx",
	"level": 3
}, {
	"code": "54Jxx",
	"title": " Nonstandard topology [See also 03H05]",
	"parentcode": "54-XX",
	"level": 2
}, {
	"code": "54J05",
	"title": " Nonstandard topology [See also 03H05]",
	"parentcode": "54Jxx",
	"level": 3
}, {
	"code": "54J99",
	"title": " None of the above, but in this section",
	"parentcode": "54Jxx",
	"level": 3
}, {
	"code": "55-XX",
	"title": " Algebraic topology",
	"parentcode": null,
	"level": 1
}, {
	"code": "55-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "55-XX",
	"level": 2
}, {
	"code": "55-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "55-XX",
	"level": 2
}, {
	"code": "55-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "55-XX",
	"level": 2
}, {
	"code": "55-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "55-XX",
	"level": 2
}, {
	"code": "55-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "55-XX",
	"level": 2
}, {
	"code": "55-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "55-XX",
	"level": 2
}, {
	"code": "55Mxx",
	"title": " Classical topics {For the topology of Euclidean spaces and manifolds, see 57Nxx}",
	"parentcode": "55-XX",
	"level": 2
}, {
	"code": "55M05",
	"title": " Duality",
	"parentcode": "55Mxx",
	"level": 3
}, {
	"code": "55M10",
	"title": " Dimension theory [See also 54F45]",
	"parentcode": "55Mxx",
	"level": 3
}, {
	"code": "55M15",
	"title": " Absolute neighborhood retracts [See also 54C55]",
	"parentcode": "55Mxx",
	"level": 3
}, {
	"code": "55M20",
	"title": " Fixed points and coincidences [See also 54H25]",
	"parentcode": "55Mxx",
	"level": 3
}, {
	"code": "55M25",
	"title": " Degree, winding number",
	"parentcode": "55Mxx",
	"level": 3
}, {
	"code": "55M30",
	"title": " Ljusternik-Schnirelman (Lyusternik-Shnirel'man) category of a space",
	"parentcode": "55Mxx",
	"level": 3
}, {
	"code": "55M35",
	"title": " Finite groups of transformations (including Smith theory) [See also 57S17]",
	"parentcode": "55Mxx",
	"level": 3
}, {
	"code": "55M99",
	"title": " None of the above, but in this section",
	"parentcode": "55Mxx",
	"level": 3
}, {
	"code": "55Nxx",
	"title": " Homology and cohomology theories [See also 57Txx]",
	"parentcode": "55-XX",
	"level": 2
}, {
	"code": "55N05",
	"title": " Čech types",
	"parentcode": "55Nxx",
	"level": 3
}, {
	"code": "55N07",
	"title": " Steenrod-Sitnikov homologies",
	"parentcode": "55Nxx",
	"level": 3
}, {
	"code": "55N10",
	"title": " Singular theory",
	"parentcode": "55Nxx",
	"level": 3
}, {
	"code": "55N15",
	"title": " $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19-XX}",
	"parentcode": "55Nxx",
	"level": 3
}, {
	"code": "55N20",
	"title": " Generalized (extraordinary) homology and cohomology theories",
	"parentcode": "55Nxx",
	"level": 3
}, {
	"code": "55N22",
	"title": " Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90]",
	"parentcode": "55Nxx",
	"level": 3
}, {
	"code": "55N25",
	"title": " Homology with local coefficients, equivariant cohomology",
	"parentcode": "55Nxx",
	"level": 3
}, {
	"code": "55N30",
	"title": " Sheaf cohomology [See also 18F20, 32C35, 32L10]",
	"parentcode": "55Nxx",
	"level": 3
}, {
	"code": "55N32",
	"title": " Orbifold cohomology",
	"parentcode": "55Nxx",
	"level": 3
}, {
	"code": "55N33",
	"title": " Intersection homology and cohomology",
	"parentcode": "55Nxx",
	"level": 3
}, {
	"code": "55N34",
	"title": " Elliptic cohomology",
	"parentcode": "55Nxx",
	"level": 3
}, {
	"code": "55N35",
	"title": " Other homology theories",
	"parentcode": "55Nxx",
	"level": 3
}, {
	"code": "55N40",
	"title": " Axioms for homology theory and uniqueness theorems",
	"parentcode": "55Nxx",
	"level": 3
}, {
	"code": "55N45",
	"title": " Products and intersections",
	"parentcode": "55Nxx",
	"level": 3
}, {
	"code": "55N91",
	"title": " Equivariant homology and cohomology [See also 19L47]",
	"parentcode": "55Nxx",
	"level": 3
}, {
	"code": "55N99",
	"title": " None of the above, but in this section",
	"parentcode": "55Nxx",
	"level": 3
}, {
	"code": "55Pxx",
	"title": " Homotopy theory {For simple homotopy type, see 57Q10}",
	"parentcode": "55-XX",
	"level": 2
}, {
	"code": "55P05",
	"title": " Homotopy extension properties, cofibrations",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P10",
	"title": " Homotopy equivalences",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P15",
	"title": " Classification of homotopy type",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P20",
	"title": " Eilenberg-Mac Lane spaces",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P25",
	"title": " Spanier-Whitehead duality",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P30",
	"title": " Eckmann-Hilton duality",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P35",
	"title": " Loop spaces",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P40",
	"title": " Suspensions",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P42",
	"title": " Stable homotopy theory, spectra",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P43",
	"title": " Spectra with additional structure ($E_\\infty$, $A_\\infty$, ring spectra, etc.)",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P45",
	"title": " $H$-spaces and duals",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P47",
	"title": " Infinite loop spaces",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P48",
	"title": " Loop space machines, operads [See also 18D50]",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P50",
	"title": " String topology",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P55",
	"title": " Shape theory [See also 54C56, 55Q07]",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P57",
	"title": " Proper homotopy theory",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P60",
	"title": " Localization and completion",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P62",
	"title": " Rational homotopy theory",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P65",
	"title": " Homotopy functors",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P91",
	"title": " Equivariant homotopy theory [See also 19L47]",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P92",
	"title": " Relations between equivariant and nonequivariant homotopy theory",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55P99",
	"title": " None of the above, but in this section",
	"parentcode": "55Pxx",
	"level": 3
}, {
	"code": "55Qxx",
	"title": " Homotopy groups",
	"parentcode": "55-XX",
	"level": 2
}, {
	"code": "55Q05",
	"title": " Homotopy groups, general; sets of homotopy classes",
	"parentcode": "55Qxx",
	"level": 3
}, {
	"code": "55Q07",
	"title": " Shape groups",
	"parentcode": "55Qxx",
	"level": 3
}, {
	"code": "55Q10",
	"title": " Stable homotopy groups",
	"parentcode": "55Qxx",
	"level": 3
}, {
	"code": "55Q15",
	"title": " Whitehead products and generalizations",
	"parentcode": "55Qxx",
	"level": 3
}, {
	"code": "55Q20",
	"title": " Homotopy groups of wedges, joins, and simple spaces",
	"parentcode": "55Qxx",
	"level": 3
}, {
	"code": "55Q25",
	"title": " Hopf invariants",
	"parentcode": "55Qxx",
	"level": 3
}, {
	"code": "55Q35",
	"title": " Operations in homotopy groups",
	"parentcode": "55Qxx",
	"level": 3
}, {
	"code": "55Q40",
	"title": " Homotopy groups of spheres",
	"parentcode": "55Qxx",
	"level": 3
}, {
	"code": "55Q45",
	"title": " Stable homotopy of spheres",
	"parentcode": "55Qxx",
	"level": 3
}, {
	"code": "55Q50",
	"title": " $J$-morphism [See also 19L20]",
	"parentcode": "55Qxx",
	"level": 3
}, {
	"code": "55Q51",
	"title": " $v_n$-periodicity",
	"parentcode": "55Qxx",
	"level": 3
}, {
	"code": "55Q52",
	"title": " Homotopy groups of special spaces",
	"parentcode": "55Qxx",
	"level": 3
}, {
	"code": "55Q55",
	"title": " Cohomotopy groups",
	"parentcode": "55Qxx",
	"level": 3
}, {
	"code": "55Q70",
	"title": " Homotopy groups of special types [See also 55N05, 55N07]",
	"parentcode": "55Qxx",
	"level": 3
}, {
	"code": "55Q91",
	"title": " Equivariant homotopy groups [See also 19L47]",
	"parentcode": "55Qxx",
	"level": 3
}, {
	"code": "55Q99",
	"title": " None of the above, but in this section",
	"parentcode": "55Qxx",
	"level": 3
}, {
	"code": "55Rxx",
	"title": " Fiber spaces and bundles [See also 18F15, 32Lxx, 46M20, 57R20, 57R22, 57R25]",
	"parentcode": "55-XX",
	"level": 2
}, {
	"code": "55R05",
	"title": " Fiber spaces",
	"parentcode": "55Rxx",
	"level": 3
}, {
	"code": "55R10",
	"title": " Fiber bundles",
	"parentcode": "55Rxx",
	"level": 3
}, {
	"code": "55R12",
	"title": " Transfer",
	"parentcode": "55Rxx",
	"level": 3
}, {
	"code": "55R15",
	"title": " Classification",
	"parentcode": "55Rxx",
	"level": 3
}, {
	"code": "55R20",
	"title": " Spectral sequences and homology of fiber spaces [See also 55Txx]",
	"parentcode": "55Rxx",
	"level": 3
}, {
	"code": "55R25",
	"title": " Sphere bundles and vector bundles",
	"parentcode": "55Rxx",
	"level": 3
}, {
	"code": "55R35",
	"title": " Classifying spaces of groups and $H$-spaces",
	"parentcode": "55Rxx",
	"level": 3
}, {
	"code": "55R37",
	"title": " Maps between classifying spaces",
	"parentcode": "55Rxx",
	"level": 3
}, {
	"code": "55R40",
	"title": " Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20]",
	"parentcode": "55Rxx",
	"level": 3
}, {
	"code": "55R45",
	"title": " Homology and homotopy of $B{\\rm O}$ and $B{\\rm U}$; Bott periodicity",
	"parentcode": "55Rxx",
	"level": 3
}, {
	"code": "55R50",
	"title": " Stable classes of vector space bundles, $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19-XX}",
	"parentcode": "55Rxx",
	"level": 3
}, {
	"code": "55R55",
	"title": " Fiberings with singularities",
	"parentcode": "55Rxx",
	"level": 3
}, {
	"code": "55R60",
	"title": " Microbundles and block bundles [See also 57N55, 57Q50]",
	"parentcode": "55Rxx",
	"level": 3
}, {
	"code": "55R65",
	"title": " Generalizations of fiber spaces and bundles",
	"parentcode": "55Rxx",
	"level": 3
}, {
	"code": "55R70",
	"title": " Fibrewise topology",
	"parentcode": "55Rxx",
	"level": 3
}, {
	"code": "55R80",
	"title": " Discriminantal varieties, configuration spaces",
	"parentcode": "55Rxx",
	"level": 3
}, {
	"code": "55R91",
	"title": " Equivariant fiber spaces and bundles [See also 19L47]",
	"parentcode": "55Rxx",
	"level": 3
}, {
	"code": "55R99",
	"title": " None of the above, but in this section",
	"parentcode": "55Rxx",
	"level": 3
}, {
	"code": "55Sxx",
	"title": " Operations and obstructions",
	"parentcode": "55-XX",
	"level": 2
}, {
	"code": "55S05",
	"title": " Primary cohomology operations",
	"parentcode": "55Sxx",
	"level": 3
}, {
	"code": "55S10",
	"title": " Steenrod algebra",
	"parentcode": "55Sxx",
	"level": 3
}, {
	"code": "55S12",
	"title": " Dyer-Lashof operations",
	"parentcode": "55Sxx",
	"level": 3
}, {
	"code": "55S15",
	"title": " Symmetric products, cyclic products",
	"parentcode": "55Sxx",
	"level": 3
}, {
	"code": "55S20",
	"title": " Secondary and higher cohomology operations",
	"parentcode": "55Sxx",
	"level": 3
}, {
	"code": "55S25",
	"title": " $K$-theory operations and generalized cohomology operations [See also 19D55, 19Lxx]",
	"parentcode": "55Sxx",
	"level": 3
}, {
	"code": "55S30",
	"title": " Massey products",
	"parentcode": "55Sxx",
	"level": 3
}, {
	"code": "55S35",
	"title": " Obstruction theory",
	"parentcode": "55Sxx",
	"level": 3
}, {
	"code": "55S36",
	"title": " Extension and compression of mappings",
	"parentcode": "55Sxx",
	"level": 3
}, {
	"code": "55S37",
	"title": " Classification of mappings",
	"parentcode": "55Sxx",
	"level": 3
}, {
	"code": "55S40",
	"title": " Sectioning fiber spaces and bundles",
	"parentcode": "55Sxx",
	"level": 3
}, {
	"code": "55S45",
	"title": " Postnikov systems, $k$-invariants",
	"parentcode": "55Sxx",
	"level": 3
}, {
	"code": "55S91",
	"title": " Equivariant operations and obstructions [See also 19L47]",
	"parentcode": "55Sxx",
	"level": 3
}, {
	"code": "55S99",
	"title": " None of the above, but in this section",
	"parentcode": "55Sxx",
	"level": 3
}, {
	"code": "55Txx",
	"title": " Spectral sequences [See also 18G40, 55R20]",
	"parentcode": "55-XX",
	"level": 2
}, {
	"code": "55T05",
	"title": " General",
	"parentcode": "55Txx",
	"level": 3
}, {
	"code": "55T10",
	"title": " Serre spectral sequences",
	"parentcode": "55Txx",
	"level": 3
}, {
	"code": "55T15",
	"title": " Adams spectral sequences",
	"parentcode": "55Txx",
	"level": 3
}, {
	"code": "55T20",
	"title": " Eilenberg-Moore spectral sequences [See also 57T35]",
	"parentcode": "55Txx",
	"level": 3
}, {
	"code": "55T25",
	"title": " Generalized cohomology",
	"parentcode": "55Txx",
	"level": 3
}, {
	"code": "55T99",
	"title": " None of the above, but in this section",
	"parentcode": "55Txx",
	"level": 3
}, {
	"code": "55Uxx",
	"title": " Applied homological algebra and category theory [See also 18Gxx]",
	"parentcode": "55-XX",
	"level": 2
}, {
	"code": "55U05",
	"title": " Abstract complexes",
	"parentcode": "55Uxx",
	"level": 3
}, {
	"code": "55U10",
	"title": " Simplicial sets and complexes",
	"parentcode": "55Uxx",
	"level": 3
}, {
	"code": "55U15",
	"title": " Chain complexes",
	"parentcode": "55Uxx",
	"level": 3
}, {
	"code": "55U20",
	"title": " Universal coefficient theorems, Bockstein operator",
	"parentcode": "55Uxx",
	"level": 3
}, {
	"code": "55U25",
	"title": " Homology of a product, Künneth formula",
	"parentcode": "55Uxx",
	"level": 3
}, {
	"code": "55U30",
	"title": " Duality",
	"parentcode": "55Uxx",
	"level": 3
}, {
	"code": "55U35",
	"title": " Abstract and axiomatic homotopy theory",
	"parentcode": "55Uxx",
	"level": 3
}, {
	"code": "55U40",
	"title": " Topological categories, foundations of homotopy theory",
	"parentcode": "55Uxx",
	"level": 3
}, {
	"code": "55U99",
	"title": " None of the above, but in this section",
	"parentcode": "55Uxx",
	"level": 3
}, {
	"code": "57-XX",
	"title": " Manifolds and cell complexes {For complex manifolds, see 32Qxx}",
	"parentcode": null,
	"level": 1
}, {
	"code": "57-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "57-XX",
	"level": 2
}, {
	"code": "57-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "57-XX",
	"level": 2
}, {
	"code": "57-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "57-XX",
	"level": 2
}, {
	"code": "57-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "57-XX",
	"level": 2
}, {
	"code": "57-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "57-XX",
	"level": 2
}, {
	"code": "57-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "57-XX",
	"level": 2
}, {
	"code": "57Mxx",
	"title": " Low-dimensional topology",
	"parentcode": "57-XX",
	"level": 2
}, {
	"code": "57M05",
	"title": " Fundamental group, presentations, free differential calculus",
	"parentcode": "57Mxx",
	"level": 3
}, {
	"code": "57M07",
	"title": " Topological methods in group theory",
	"parentcode": "57Mxx",
	"level": 3
}, {
	"code": "57M10",
	"title": " Covering spaces",
	"parentcode": "57Mxx",
	"level": 3
}, {
	"code": "57M12",
	"title": " Special coverings, e.g. branched",
	"parentcode": "57Mxx",
	"level": 3
}, {
	"code": "57M15",
	"title": " Relations with graph theory [See also 05Cxx]",
	"parentcode": "57Mxx",
	"level": 3
}, {
	"code": "57M20",
	"title": " Two-dimensional complexes",
	"parentcode": "57Mxx",
	"level": 3
}, {
	"code": "57M25",
	"title": " Knots and links in $S^3$ {For higher dimensions, see 57Q45}",
	"parentcode": "57Mxx",
	"level": 3
}, {
	"code": "57M27",
	"title": " Invariants of knots and 3-manifolds",
	"parentcode": "57Mxx",
	"level": 3
}, {
	"code": "57M30",
	"title": " Wild knots and surfaces, etc., wild embeddings",
	"parentcode": "57Mxx",
	"level": 3
}, {
	"code": "57M35",
	"title": " Dehn's lemma, sphere theorem, loop theorem, asphericity",
	"parentcode": "57Mxx",
	"level": 3
}, {
	"code": "57M40",
	"title": " Characterizations of $E^3$ and $S^3$ (Poincaré conjecture) [See also 57N12]",
	"parentcode": "57Mxx",
	"level": 3
}, {
	"code": "57M50",
	"title": " Geometric structures on low-dimensional manifolds",
	"parentcode": "57Mxx",
	"level": 3
}, {
	"code": "57M60",
	"title": " Group actions in low dimensions",
	"parentcode": "57Mxx",
	"level": 3
}, {
	"code": "57M99",
	"title": " None of the above, but in this section",
	"parentcode": "57Mxx",
	"level": 3
}, {
	"code": "57Nxx",
	"title": " Topological manifolds",
	"parentcode": "57-XX",
	"level": 2
}, {
	"code": "57N05",
	"title": " Topology of $E^2$, $2$-manifolds",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N10",
	"title": " Topology of general $3$-manifolds [See also 57Mxx]",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N12",
	"title": " Topology of $E^3$ and $S^3$ [See also 57M40]",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N13",
	"title": " Topology of $E^4$, $4$-manifolds [See also 14Jxx, 32Jxx]",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N15",
	"title": " Topology of $E^n$, $n$-manifolds ($4 \\less n \\less \\infty$)",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N16",
	"title": " Geometric structures on manifolds [See also 57M50]",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N17",
	"title": " Topology of topological vector spaces",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N20",
	"title": " Topology of infinite-dimensional manifolds [See also 58Bxx]",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N25",
	"title": " Shapes [See also 54C56, 55P55, 55Q07]",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N30",
	"title": " Engulfing",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N35",
	"title": " Embeddings and immersions",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N37",
	"title": " Isotopy and pseudo-isotopy",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N40",
	"title": " Neighborhoods of submanifolds",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N45",
	"title": " Flatness and tameness",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N50",
	"title": " $S^{n-1}\\subset E^n$, Schoenflies problem",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N55",
	"title": " Microbundles and block bundles [See also 55R60, 57Q50]",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N60",
	"title": " Cellularity",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N65",
	"title": " Algebraic topology of manifolds",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N70",
	"title": " Cobordism and concordance",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N75",
	"title": " General position and transversality",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N80",
	"title": " Stratifications",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57N99",
	"title": " None of the above, but in this section",
	"parentcode": "57Nxx",
	"level": 3
}, {
	"code": "57Pxx",
	"title": " Generalized manifolds [See also 18F15]",
	"parentcode": "57-XX",
	"level": 2
}, {
	"code": "57P05",
	"title": " Local properties of generalized manifolds",
	"parentcode": "57Pxx",
	"level": 3
}, {
	"code": "57P10",
	"title": " Poincaré duality spaces",
	"parentcode": "57Pxx",
	"level": 3
}, {
	"code": "57P99",
	"title": " None of the above, but in this section",
	"parentcode": "57Pxx",
	"level": 3
}, {
	"code": "57Qxx",
	"title": " PL-topology",
	"parentcode": "57-XX",
	"level": 2
}, {
	"code": "57Q05",
	"title": " General topology of complexes",
	"parentcode": "57Qxx",
	"level": 3
}, {
	"code": "57Q10",
	"title": " Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28]",
	"parentcode": "57Qxx",
	"level": 3
}, {
	"code": "57Q12",
	"title": " Wall finiteness obstruction for CW-complexes",
	"parentcode": "57Qxx",
	"level": 3
}, {
	"code": "57Q15",
	"title": " Triangulating manifolds",
	"parentcode": "57Qxx",
	"level": 3
}, {
	"code": "57Q20",
	"title": " Cobordism",
	"parentcode": "57Qxx",
	"level": 3
}, {
	"code": "57Q25",
	"title": " Comparison of PL-structures",
	"parentcode": "57Qxx",
	"level": 3
}, {
	"code": "57Q30",
	"title": " Engulfing",
	"parentcode": "57Qxx",
	"level": 3
}, {
	"code": "57Q35",
	"title": " Embeddings and immersions",
	"parentcode": "57Qxx",
	"level": 3
}, {
	"code": "57Q37",
	"title": " Isotopy",
	"parentcode": "57Qxx",
	"level": 3
}, {
	"code": "57Q40",
	"title": " Regular neighborhoods",
	"parentcode": "57Qxx",
	"level": 3
}, {
	"code": "57Q45",
	"title": " Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}",
	"parentcode": "57Qxx",
	"level": 3
}, {
	"code": "57Q50",
	"title": " Microbundles and block bundles [See also 55R60, 57N55]",
	"parentcode": "57Qxx",
	"level": 3
}, {
	"code": "57Q55",
	"title": " Approximations",
	"parentcode": "57Qxx",
	"level": 3
}, {
	"code": "57Q60",
	"title": " Cobordism and concordance",
	"parentcode": "57Qxx",
	"level": 3
}, {
	"code": "57Q65",
	"title": " General position and transversality",
	"parentcode": "57Qxx",
	"level": 3
}, {
	"code": "57Q91",
	"title": " Equivariant PL-topology",
	"parentcode": "57Qxx",
	"level": 3
}, {
	"code": "57Q99",
	"title": " None of the above, but in this section",
	"parentcode": "57Qxx",
	"level": 3
}, {
	"code": "57Rxx",
	"title": " Differential topology {For foundational questions of differentiable manifolds, see 58Axx; for infinite-dimensional manifolds, see 58Bxx}",
	"parentcode": "57-XX",
	"level": 2
}, {
	"code": "57R05",
	"title": " Triangulating",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R10",
	"title": " Smoothing",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R12",
	"title": " Smooth approximations",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R15",
	"title": " Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R17",
	"title": " Symplectic and contact topology",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R18",
	"title": " Topology and geometry of orbifolds",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R19",
	"title": " Algebraic topology on manifolds",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R20",
	"title": " Characteristic classes and numbers",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R22",
	"title": " Topology of vector bundles and fiber bundles [See also 55Rxx]",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R25",
	"title": " Vector fields, frame fields",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R27",
	"title": " Controllability of vector fields on $C^\\infty$ and real-analytic manifolds [See also 49Qxx, 37C10, 93B05]",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R30",
	"title": " Foliations; geometric theory",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R32",
	"title": " Classifying spaces for foliations; Gelfand-Fuks cohomology [See also 58H10]",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R35",
	"title": " Differentiable mappings",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R40",
	"title": " Embeddings",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R42",
	"title": " Immersions",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R45",
	"title": " Singularities of differentiable mappings",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R50",
	"title": " Diffeomorphisms",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R52",
	"title": " Isotopy",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R55",
	"title": " Differentiable structures",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R56",
	"title": " Topological quantum field theories",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R57",
	"title": " Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R58",
	"title": " Floer homology",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R60",
	"title": " Homotopy spheres, Poincaré conjecture",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R65",
	"title": " Surgery and handlebodies",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R67",
	"title": " Surgery obstructions, Wall groups [See also 19J25]",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R70",
	"title": " Critical points and critical submanifolds",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R75",
	"title": " ${\\rm O}$- and ${\\rm SO}$-cobordism",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R77",
	"title": " Complex cobordism (${\\rm U}$- and ${\\rm SU}$-cobordism) [See also 55N22]",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R80",
	"title": " $h$- and $s$-cobordism",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R85",
	"title": " Equivariant cobordism",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R90",
	"title": " Other types of cobordism [See also 55N22]",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R91",
	"title": " Equivariant algebraic topology of manifolds",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R95",
	"title": " Realizing cycles by submanifolds",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57R99",
	"title": " None of the above, but in this section",
	"parentcode": "57Rxx",
	"level": 3
}, {
	"code": "57Sxx",
	"title": " Topological transformation groups [See also 20F34, 22-XX, 37-XX, 54H15, 58D05]",
	"parentcode": "57-XX",
	"level": 2
}, {
	"code": "57S05",
	"title": " Topological properties of groups of homeomorphisms or diffeomorphisms",
	"parentcode": "57Sxx",
	"level": 3
}, {
	"code": "57S10",
	"title": " Compact groups of homeomorphisms",
	"parentcode": "57Sxx",
	"level": 3
}, {
	"code": "57S15",
	"title": " Compact Lie groups of differentiable transformations",
	"parentcode": "57Sxx",
	"level": 3
}, {
	"code": "57S17",
	"title": " Finite transformation groups",
	"parentcode": "57Sxx",
	"level": 3
}, {
	"code": "57S20",
	"title": " Noncompact Lie groups of transformations",
	"parentcode": "57Sxx",
	"level": 3
}, {
	"code": "57S25",
	"title": " Groups acting on specific manifolds",
	"parentcode": "57Sxx",
	"level": 3
}, {
	"code": "57S30",
	"title": " Discontinuous groups of transformations",
	"parentcode": "57Sxx",
	"level": 3
}, {
	"code": "57S99",
	"title": " None of the above, but in this section",
	"parentcode": "57Sxx",
	"level": 3
}, {
	"code": "57Txx",
	"title": " Homology and homotopy of topological groups and related structures",
	"parentcode": "57-XX",
	"level": 2
}, {
	"code": "57T05",
	"title": " Hopf algebras [See also 16T05]",
	"parentcode": "57Txx",
	"level": 3
}, {
	"code": "57T10",
	"title": " Homology and cohomology of Lie groups",
	"parentcode": "57Txx",
	"level": 3
}, {
	"code": "57T15",
	"title": " Homology and cohomology of homogeneous spaces of Lie groups",
	"parentcode": "57Txx",
	"level": 3
}, {
	"code": "57T20",
	"title": " Homotopy groups of topological groups and homogeneous spaces",
	"parentcode": "57Txx",
	"level": 3
}, {
	"code": "57T25",
	"title": " Homology and cohomology of $H$-spaces",
	"parentcode": "57Txx",
	"level": 3
}, {
	"code": "57T30",
	"title": " Bar and cobar constructions [See also 18G55, 55Uxx]",
	"parentcode": "57Txx",
	"level": 3
}, {
	"code": "57T35",
	"title": " Applications of Eilenberg-Moore spectral sequences [See also 55R20, 55T20]",
	"parentcode": "57Txx",
	"level": 3
}, {
	"code": "57T99",
	"title": " None of the above, but in this section",
	"parentcode": "57Txx",
	"level": 3
}, {
	"code": "58-XX",
	"title": " Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15}",
	"parentcode": null,
	"level": 1
}, {
	"code": "58-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "58-XX",
	"level": 2
}, {
	"code": "58-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "58-XX",
	"level": 2
}, {
	"code": "58-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "58-XX",
	"level": 2
}, {
	"code": "58-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "58-XX",
	"level": 2
}, {
	"code": "58-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "58-XX",
	"level": 2
}, {
	"code": "58-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "58-XX",
	"level": 2
}, {
	"code": "58Axx",
	"title": " General theory of differentiable manifolds [See also 32Cxx]",
	"parentcode": "58-XX",
	"level": 2
}, {
	"code": "58A03",
	"title": " Topos-theoretic approach to differentiable manifolds",
	"parentcode": "58Axx",
	"level": 3
}, {
	"code": "58A05",
	"title": " Differentiable manifolds, foundations",
	"parentcode": "58Axx",
	"level": 3
}, {
	"code": "58A07",
	"title": " Real-analytic and Nash manifolds [See also 14P20, 32C07]",
	"parentcode": "58Axx",
	"level": 3
}, {
	"code": "58A10",
	"title": " Differential forms",
	"parentcode": "58Axx",
	"level": 3
}, {
	"code": "58A12",
	"title": " de Rham theory [See also 14Fxx]",
	"parentcode": "58Axx",
	"level": 3
}, {
	"code": "58A14",
	"title": " Hodge theory [See also 14C30, 14Fxx, 32J25, 32S35]",
	"parentcode": "58Axx",
	"level": 3
}, {
	"code": "58A15",
	"title": " Exterior differential systems (Cartan theory)",
	"parentcode": "58Axx",
	"level": 3
}, {
	"code": "58A17",
	"title": " Pfaffian systems",
	"parentcode": "58Axx",
	"level": 3
}, {
	"code": "58A20",
	"title": " Jets",
	"parentcode": "58Axx",
	"level": 3
}, {
	"code": "58A25",
	"title": " Currents [See also 32C30, 53C65]",
	"parentcode": "58Axx",
	"level": 3
}, {
	"code": "58A30",
	"title": " Vector distributions (subbundles of the tangent bundles)",
	"parentcode": "58Axx",
	"level": 3
}, {
	"code": "58A32",
	"title": " Natural bundles",
	"parentcode": "58Axx",
	"level": 3
}, {
	"code": "58A35",
	"title": " Stratified sets [See also 32S60]",
	"parentcode": "58Axx",
	"level": 3
}, {
	"code": "58A40",
	"title": " Differential spaces",
	"parentcode": "58Axx",
	"level": 3
}, {
	"code": "58A50",
	"title": " Supermanifolds and graded manifolds [See also 14A22, 32C11]",
	"parentcode": "58Axx",
	"level": 3
}, {
	"code": "58A99",
	"title": " None of the above, but in this section",
	"parentcode": "58Axx",
	"level": 3
}, {
	"code": "58Bxx",
	"title": " Infinite-dimensional manifolds",
	"parentcode": "58-XX",
	"level": 2
}, {
	"code": "58B05",
	"title": " Homotopy and topological questions",
	"parentcode": "58Bxx",
	"level": 3
}, {
	"code": "58B10",
	"title": " Differentiability questions",
	"parentcode": "58Bxx",
	"level": 3
}, {
	"code": "58B12",
	"title": " Questions of holomorphy [See also 32-XX, 46G20]",
	"parentcode": "58Bxx",
	"level": 3
}, {
	"code": "58B15",
	"title": " Fredholm structures [See also 47A53]",
	"parentcode": "58Bxx",
	"level": 3
}, {
	"code": "58B20",
	"title": " Riemannian, Finsler and other geometric structures [See also 53C20, 53C60]",
	"parentcode": "58Bxx",
	"level": 3
}, {
	"code": "58B25",
	"title": " Group structures and generalizations on infinite-dimensional manifolds [See also 22E65, 58D05]",
	"parentcode": "58Bxx",
	"level": 3
}, {
	"code": "58B32",
	"title": " Geometry of quantum groups",
	"parentcode": "58Bxx",
	"level": 3
}, {
	"code": "58B34",
	"title": " Noncommutative geometry (à la Connes)",
	"parentcode": "58Bxx",
	"level": 3
}, {
	"code": "58B99",
	"title": " None of the above, but in this section",
	"parentcode": "58Bxx",
	"level": 3
}, {
	"code": "58Cxx",
	"title": " Calculus on manifolds; nonlinear operators [See also 46Txx, 47Hxx, 47Jxx]",
	"parentcode": "58-XX",
	"level": 2
}, {
	"code": "58C05",
	"title": " Real-valued functions",
	"parentcode": "58Cxx",
	"level": 3
}, {
	"code": "58C06",
	"title": " Set valued and function-space valued mappings [See also 47H04, 54C60]",
	"parentcode": "58Cxx",
	"level": 3
}, {
	"code": "58C07",
	"title": " Continuity properties of mappings",
	"parentcode": "58Cxx",
	"level": 3
}, {
	"code": "58C10",
	"title": " Holomorphic maps [See also 32-XX]",
	"parentcode": "58Cxx",
	"level": 3
}, {
	"code": "58C15",
	"title": " Implicit function theorems; global Newton methods",
	"parentcode": "58Cxx",
	"level": 3
}, {
	"code": "58C20",
	"title": " Differentiation theory (Gateaux, Fréchet, etc.) [See also 26Exx, 46G05]",
	"parentcode": "58Cxx",
	"level": 3
}, {
	"code": "58C25",
	"title": " Differentiable maps",
	"parentcode": "58Cxx",
	"level": 3
}, {
	"code": "58C30",
	"title": " Fixed point theorems on manifolds [See also 47H10]",
	"parentcode": "58Cxx",
	"level": 3
}, {
	"code": "58C35",
	"title": " Integration on manifolds; measures on manifolds [See also 28Cxx]",
	"parentcode": "58Cxx",
	"level": 3
}, {
	"code": "58C40",
	"title": " Spectral theory; eigenvalue problems [See also 47J10, 58E07]",
	"parentcode": "58Cxx",
	"level": 3
}, {
	"code": "58C50",
	"title": " Analysis on supermanifolds or graded manifolds",
	"parentcode": "58Cxx",
	"level": 3
}, {
	"code": "58C99",
	"title": " None of the above, but in this section",
	"parentcode": "58Cxx",
	"level": 3
}, {
	"code": "58Dxx",
	"title": " Spaces and manifolds of mappings (including nonlinear versions of 46Exx) [See also 46Txx, 53Cxx]",
	"parentcode": "58-XX",
	"level": 2
}, {
	"code": "58D05",
	"title": " Groups of diffeomorphisms and homeomorphisms as manifolds [See also 22E65, 57S05]",
	"parentcode": "58Dxx",
	"level": 3
}, {
	"code": "58D07",
	"title": " Groups and semigroups of nonlinear operators [See also 17B65, 47H20]",
	"parentcode": "58Dxx",
	"level": 3
}, {
	"code": "58D10",
	"title": " Spaces of imbeddings and immersions",
	"parentcode": "58Dxx",
	"level": 3
}, {
	"code": "58D15",
	"title": " Manifolds of mappings [See also 46T10, 54C35]",
	"parentcode": "58Dxx",
	"level": 3
}, {
	"code": "58D17",
	"title": " Manifolds of metrics (esp. Riemannian)",
	"parentcode": "58Dxx",
	"level": 3
}, {
	"code": "58D19",
	"title": " Group actions and symmetry properties",
	"parentcode": "58Dxx",
	"level": 3
}, {
	"code": "58D20",
	"title": " Measures (Gaussian, cylindrical, etc.) on manifolds of maps [See also 28Cxx, 46T12]",
	"parentcode": "58Dxx",
	"level": 3
}, {
	"code": "58D25",
	"title": " Equations in function spaces; evolution equations [See also 34Gxx, 35K90, 35L90, 35R15, 37Lxx, 47Jxx]",
	"parentcode": "58Dxx",
	"level": 3
}, {
	"code": "58D27",
	"title": " Moduli problems for differential geometric structures",
	"parentcode": "58Dxx",
	"level": 3
}, {
	"code": "58D29",
	"title": " Moduli problems for topological structures",
	"parentcode": "58Dxx",
	"level": 3
}, {
	"code": "58D30",
	"title": " Applications (in quantum mechanics (Feynman path integrals), relativity, fluid dynamics, etc.)",
	"parentcode": "58Dxx",
	"level": 3
}, {
	"code": "58D99",
	"title": " None of the above, but in this section",
	"parentcode": "58Dxx",
	"level": 3
}, {
	"code": "58Exx",
	"title": " Variational problems in infinite-dimensional spaces",
	"parentcode": "58-XX",
	"level": 2
}, {
	"code": "58E05",
	"title": " Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel'man) theory, etc.)",
	"parentcode": "58Exx",
	"level": 3
}, {
	"code": "58E07",
	"title": " Abstract bifurcation theory",
	"parentcode": "58Exx",
	"level": 3
}, {
	"code": "58E09",
	"title": " Group-invariant bifurcation theory",
	"parentcode": "58Exx",
	"level": 3
}, {
	"code": "58E10",
	"title": " Applications to the theory of geodesics (problems in one independent variable)",
	"parentcode": "58Exx",
	"level": 3
}, {
	"code": "58E11",
	"title": " Critical metrics",
	"parentcode": "58Exx",
	"level": 3
}, {
	"code": "58E12",
	"title": " Applications to minimal surfaces (problems in two independent variables) [See also 49Q05]",
	"parentcode": "58Exx",
	"level": 3
}, {
	"code": "58E15",
	"title": " Application to extremal problems in several variables; Yang-Mills functionals [See also 81T13], etc.",
	"parentcode": "58Exx",
	"level": 3
}, {
	"code": "58E17",
	"title": " Pareto optimality, etc., applications to economics [See also 90C29]",
	"parentcode": "58Exx",
	"level": 3
}, {
	"code": "58E20",
	"title": " Harmonic maps [See also 53C43], etc.",
	"parentcode": "58Exx",
	"level": 3
}, {
	"code": "58E25",
	"title": " Applications to control theory [See also 49-XX, 93-XX]",
	"parentcode": "58Exx",
	"level": 3
}, {
	"code": "58E30",
	"title": " Variational principles",
	"parentcode": "58Exx",
	"level": 3
}, {
	"code": "58E35",
	"title": " Variational inequalities (global problems)",
	"parentcode": "58Exx",
	"level": 3
}, {
	"code": "58E40",
	"title": " Group actions",
	"parentcode": "58Exx",
	"level": 3
}, {
	"code": "58E50",
	"title": " Applications",
	"parentcode": "58Exx",
	"level": 3
}, {
	"code": "58E99",
	"title": " None of the above, but in this section",
	"parentcode": "58Exx",
	"level": 3
}, {
	"code": "58Hxx",
	"title": " Pseudogroups, differentiable groupoids and general structures on manifolds",
	"parentcode": "58-XX",
	"level": 2
}, {
	"code": "58H05",
	"title": " Pseudogroups and differentiable groupoids [See also 22A22, 22E65]",
	"parentcode": "58Hxx",
	"level": 3
}, {
	"code": "58H10",
	"title": " Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) [See also 57R32]",
	"parentcode": "58Hxx",
	"level": 3
}, {
	"code": "58H15",
	"title": " Deformations of structures [See also 32Gxx, 58J10]",
	"parentcode": "58Hxx",
	"level": 3
}, {
	"code": "58H99",
	"title": " None of the above, but in this section",
	"parentcode": "58Hxx",
	"level": 3
}, {
	"code": "58Jxx",
	"title": " Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx]",
	"parentcode": "58-XX",
	"level": 2
}, {
	"code": "58J05",
	"title": " Elliptic equations on manifolds, general theory [See also 35-XX]",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J10",
	"title": " Differential complexes [See also 35Nxx]; elliptic complexes",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J15",
	"title": " Relations with hyperfunctions",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J20",
	"title": " Index theory and related fixed point theorems [See also 19K56, 46L80]",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J22",
	"title": " Exotic index theories [See also 19K56, 46L05, 46L10, 46L80, 46M20]",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J26",
	"title": " Elliptic genera",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J28",
	"title": " Eta-invariants, Chern-Simons invariants",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J30",
	"title": " Spectral flows",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J32",
	"title": " Boundary value problems on manifolds",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J35",
	"title": " Heat and other parabolic equation methods",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J37",
	"title": " Perturbations; asymptotics",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J40",
	"title": " Pseudodifferential and Fourier integral operators on manifolds [See also 35Sxx]",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J42",
	"title": " Noncommutative global analysis, noncommutative residues",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J45",
	"title": " Hyperbolic equations [See also 35Lxx]",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J47",
	"title": " Propagation of singularities; initial value problems",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J50",
	"title": " Spectral problems; spectral geometry; scattering theory [See also 35Pxx]",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J51",
	"title": " Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J52",
	"title": " Determinants and determinant bundles, analytic torsion",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J53",
	"title": " Isospectrality",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J55",
	"title": " Bifurcation [See also 35B32]",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J60",
	"title": " Relations with special manifold structures (Riemannian, Finsler, etc.)",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J65",
	"title": " Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60]",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J70",
	"title": " Invariance and symmetry properties [See also 35A30]",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J72",
	"title": " Correspondences and other transformation methods (e.g. Lie-Bäcklund) [See also 35A22]",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J90",
	"title": " Applications",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58J99",
	"title": " None of the above, but in this section",
	"parentcode": "58Jxx",
	"level": 3
}, {
	"code": "58Kxx",
	"title": " Theory of singularities and catastrophe theory [See also 32Sxx, 37-XX]",
	"parentcode": "58-XX",
	"level": 2
}, {
	"code": "58K05",
	"title": " Critical points of functions and mappings",
	"parentcode": "58Kxx",
	"level": 3
}, {
	"code": "58K10",
	"title": " Monodromy",
	"parentcode": "58Kxx",
	"level": 3
}, {
	"code": "58K15",
	"title": " Topological properties of mappings",
	"parentcode": "58Kxx",
	"level": 3
}, {
	"code": "58K20",
	"title": " Algebraic and analytic properties of mappings",
	"parentcode": "58Kxx",
	"level": 3
}, {
	"code": "58K25",
	"title": " Stability",
	"parentcode": "58Kxx",
	"level": 3
}, {
	"code": "58K30",
	"title": " Global theory",
	"parentcode": "58Kxx",
	"level": 3
}, {
	"code": "58K35",
	"title": " Catastrophe theory",
	"parentcode": "58Kxx",
	"level": 3
}, {
	"code": "58K40",
	"title": " Classification; finite determinacy of map germs",
	"parentcode": "58Kxx",
	"level": 3
}, {
	"code": "58K45",
	"title": " Singularities of vector fields, topological aspects",
	"parentcode": "58Kxx",
	"level": 3
}, {
	"code": "58K50",
	"title": " Normal forms",
	"parentcode": "58Kxx",
	"level": 3
}, {
	"code": "58K55",
	"title": " Asymptotic behavior",
	"parentcode": "58Kxx",
	"level": 3
}, {
	"code": "58K60",
	"title": " Deformation of singularities",
	"parentcode": "58Kxx",
	"level": 3
}, {
	"code": "58K65",
	"title": " Topological invariants",
	"parentcode": "58Kxx",
	"level": 3
}, {
	"code": "58K70",
	"title": " Symmetries, equivariance",
	"parentcode": "58Kxx",
	"level": 3
}, {
	"code": "58K99",
	"title": " None of the above, but in this section",
	"parentcode": "58Kxx",
	"level": 3
}, {
	"code": "58Zxx",
	"title": " Applications to physics",
	"parentcode": "58-XX",
	"level": 2
}, {
	"code": "58Z05",
	"title": " Applications to physics",
	"parentcode": "58Zxx",
	"level": 3
}, {
	"code": "58Z99",
	"title": " None of the above, but in this section",
	"parentcode": "58Zxx",
	"level": 3
}, {
	"code": "60-XX",
	"title": " Probability theory and stochastic processes {For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX}",
	"parentcode": null,
	"level": 1
}, {
	"code": "60-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "60-XX",
	"level": 2
}, {
	"code": "60-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "60-XX",
	"level": 2
}, {
	"code": "60-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "60-XX",
	"level": 2
}, {
	"code": "60-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "60-XX",
	"level": 2
}, {
	"code": "60-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "60-XX",
	"level": 2
}, {
	"code": "60-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "60-XX",
	"level": 2
}, {
	"code": "60-08",
	"title": " Computational methods (not classified at a more specific level) [See also 65C50]",
	"parentcode": "60-XX",
	"level": 2
}, {
	"code": "60Axx",
	"title": " Foundations of probability theory",
	"parentcode": "60-XX",
	"level": 2
}, {
	"code": "60A05",
	"title": " Axioms; other general questions",
	"parentcode": "60Axx",
	"level": 3
}, {
	"code": "60A10",
	"title": " Probabilistic measure theory {For ergodic theory, see 28Dxx and 60Fxx}",
	"parentcode": "60Axx",
	"level": 3
}, {
	"code": "60A86",
	"title": " Fuzzy probability",
	"parentcode": "60Axx",
	"level": 3
}, {
	"code": "60A99",
	"title": " None of the above, but in this section",
	"parentcode": "60Axx",
	"level": 3
}, {
	"code": "60Bxx",
	"title": " Probability theory on algebraic and topological structures",
	"parentcode": "60-XX",
	"level": 2
}, {
	"code": "60B05",
	"title": " Probability measures on topological spaces",
	"parentcode": "60Bxx",
	"level": 3
}, {
	"code": "60B10",
	"title": " Convergence of probability measures",
	"parentcode": "60Bxx",
	"level": 3
}, {
	"code": "60B11",
	"title": " Probability theory on linear topological spaces [See also 28C20]",
	"parentcode": "60Bxx",
	"level": 3
}, {
	"code": "60B12",
	"title": " Limit theorems for vector-valued random variables (infinite-dimensional case)",
	"parentcode": "60Bxx",
	"level": 3
}, {
	"code": "60B15",
	"title": " Probability measures on groups or semigroups, Fourier transforms, factorization",
	"parentcode": "60Bxx",
	"level": 3
}, {
	"code": "60B20",
	"title": " Random matrices (probabilistic aspects; for algebraic aspects see 15B52)",
	"parentcode": "60Bxx",
	"level": 3
}, {
	"code": "60B99",
	"title": " None of the above, but in this section",
	"parentcode": "60Bxx",
	"level": 3
}, {
	"code": "60Cxx",
	"title": " Combinatorial probability",
	"parentcode": "60-XX",
	"level": 2
}, {
	"code": "60C05",
	"title": " Combinatorial probability",
	"parentcode": "60Cxx",
	"level": 3
}, {
	"code": "60C99",
	"title": " None of the above, but in this section",
	"parentcode": "60Cxx",
	"level": 3
}, {
	"code": "60Dxx",
	"title": " Geometric probability and stochastic geometry [See also 52A22, 53C65]",
	"parentcode": "60-XX",
	"level": 2
}, {
	"code": "60D05",
	"title": " Geometric probability and stochastic geometry [See also 52A22, 53C65]",
	"parentcode": "60Dxx",
	"level": 3
}, {
	"code": "60D99",
	"title": " None of the above, but in this section",
	"parentcode": "60Dxx",
	"level": 3
}, {
	"code": "60Exx",
	"title": " Distribution theory [See also 62Exx, 62Hxx]",
	"parentcode": "60-XX",
	"level": 2
}, {
	"code": "60E05",
	"title": " Distributions",
	"parentcode": "60Exx",
	"level": 3
}, {
	"code": "60E07",
	"title": " Infinitely divisible distributions; stable distributions",
	"parentcode": "60Exx",
	"level": 3
}, {
	"code": "60E10",
	"title": " Characteristic functions; other transforms",
	"parentcode": "60Exx",
	"level": 3
}, {
	"code": "60E15",
	"title": " Inequalities; stochastic orderings",
	"parentcode": "60Exx",
	"level": 3
}, {
	"code": "60E99",
	"title": " None of the above, but in this section",
	"parentcode": "60Exx",
	"level": 3
}, {
	"code": "60Fxx",
	"title": " Limit theorems [See also 28Dxx, 60B12]",
	"parentcode": "60-XX",
	"level": 2
}, {
	"code": "60F05",
	"title": " Central limit and other weak theorems",
	"parentcode": "60Fxx",
	"level": 3
}, {
	"code": "60F10",
	"title": " Large deviations",
	"parentcode": "60Fxx",
	"level": 3
}, {
	"code": "60F15",
	"title": " Strong theorems",
	"parentcode": "60Fxx",
	"level": 3
}, {
	"code": "60F17",
	"title": " Functional limit theorems; invariance principles",
	"parentcode": "60Fxx",
	"level": 3
}, {
	"code": "60F20",
	"title": " Zero-one laws",
	"parentcode": "60Fxx",
	"level": 3
}, {
	"code": "60F25",
	"title": " $L^p$-limit theorems",
	"parentcode": "60Fxx",
	"level": 3
}, {
	"code": "60F99",
	"title": " None of the above, but in this section",
	"parentcode": "60Fxx",
	"level": 3
}, {
	"code": "60Gxx",
	"title": " Stochastic processes",
	"parentcode": "60-XX",
	"level": 2
}, {
	"code": "60G05",
	"title": " Foundations of stochastic processes",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G07",
	"title": " General theory of processes",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G09",
	"title": " Exchangeability",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G10",
	"title": " Stationary processes",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G12",
	"title": " General second-order processes",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G15",
	"title": " Gaussian processes",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G17",
	"title": " Sample path properties",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G18",
	"title": " Self-similar processes",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G20",
	"title": " Generalized stochastic processes",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G22",
	"title": " Fractional processes, including fractional Brownian motion",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G25",
	"title": " Prediction theory [See also 62M20]",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G30",
	"title": " Continuity and singularity of induced measures",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G35",
	"title": " Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G40",
	"title": " Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G42",
	"title": " Martingales with discrete parameter",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G44",
	"title": " Martingales with continuous parameter",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G46",
	"title": " Martingales and classical analysis",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G48",
	"title": " Generalizations of martingales",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G50",
	"title": " Sums of independent random variables; random walks",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G51",
	"title": " Processes with independent increments; L\\'evy processes",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G52",
	"title": " Stable processes",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G55",
	"title": " Point processes",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G57",
	"title": " Random measures",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G60",
	"title": " Random fields",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G70",
	"title": " Extreme value theory; extremal processes",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60G99",
	"title": " None of the above, but in this section",
	"parentcode": "60Gxx",
	"level": 3
}, {
	"code": "60Hxx",
	"title": " Stochastic analysis [See also 58J65]",
	"parentcode": "60-XX",
	"level": 2
}, {
	"code": "60H05",
	"title": " Stochastic integrals",
	"parentcode": "60Hxx",
	"level": 3
}, {
	"code": "60H07",
	"title": " Stochastic calculus of variations and the Malliavin calculus",
	"parentcode": "60Hxx",
	"level": 3
}, {
	"code": "60H10",
	"title": " Stochastic ordinary differential equations [See also 34F05]",
	"parentcode": "60Hxx",
	"level": 3
}, {
	"code": "60H15",
	"title": " Stochastic partial differential equations [See also 35R60]",
	"parentcode": "60Hxx",
	"level": 3
}, {
	"code": "60H20",
	"title": " Stochastic integral equations",
	"parentcode": "60Hxx",
	"level": 3
}, {
	"code": "60H25",
	"title": " Random operators and equations [See also 47B80]",
	"parentcode": "60Hxx",
	"level": 3
}, {
	"code": "60H30",
	"title": " Applications of stochastic analysis (to PDE, etc.)",
	"parentcode": "60Hxx",
	"level": 3
}, {
	"code": "60H35",
	"title": " Computational methods for stochastic equations [See also 65C30]",
	"parentcode": "60Hxx",
	"level": 3
}, {
	"code": "60H40",
	"title": " White noise theory",
	"parentcode": "60Hxx",
	"level": 3
}, {
	"code": "60H99",
	"title": " None of the above, but in this section",
	"parentcode": "60Hxx",
	"level": 3
}, {
	"code": "60Jxx",
	"title": " Markov processes",
	"parentcode": "60-XX",
	"level": 2
}, {
	"code": "60J05",
	"title": " Discrete-time Markov processes on general state spaces",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J10",
	"title": " Markov chains (discrete-time Markov processes on discrete state spaces)",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J20",
	"title": " Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J22",
	"title": " Computational methods in Markov chains [See also 65C40]",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J25",
	"title": " Continuous-time Markov processes on general state spaces",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J27",
	"title": " Continuous-time Markov processes on discrete state spaces",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J28",
	"title": " Applications of continuous-time Markov processes on discrete state spaces",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J35",
	"title": " Transition functions, generators and resolvents [See also 47D03, 47D07]",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J40",
	"title": " Right processes",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J45",
	"title": " Probabilistic potential theory [See also 31Cxx, 31D05]",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J50",
	"title": " Boundary theory",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J55",
	"title": " Local time and additive functionals",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J57",
	"title": " Multiplicative functionals",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J60",
	"title": " Diffusion processes [See also 58J65]",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J65",
	"title": " Brownian motion [See also 58J65]",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J67",
	"title": " Stochastic (Schramm-)Loewner evolution (SLE)",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J68",
	"title": " Superprocesses",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J70",
	"title": " Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J75",
	"title": " Jump processes",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J80",
	"title": " Branching processes (Galton-Watson, birth-and-death, etc.)",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J85",
	"title": " Applications of branching processes [See also 92Dxx]",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60J99",
	"title": " None of the above, but in this section",
	"parentcode": "60Jxx",
	"level": 3
}, {
	"code": "60Kxx",
	"title": " Special processes",
	"parentcode": "60-XX",
	"level": 2
}, {
	"code": "60K05",
	"title": " Renewal theory",
	"parentcode": "60Kxx",
	"level": 3
}, {
	"code": "60K10",
	"title": " Applications (reliability, demand theory, etc.)",
	"parentcode": "60Kxx",
	"level": 3
}, {
	"code": "60K15",
	"title": " Markov renewal processes, semi-Markov processes",
	"parentcode": "60Kxx",
	"level": 3
}, {
	"code": "60K20",
	"title": " Applications of Markov renewal processes (reliability, queueing networks, etc.) [See also 90Bxx]",
	"parentcode": "60Kxx",
	"level": 3
}, {
	"code": "60K25",
	"title": " Queueing theory [See also 68M20, 90B22]",
	"parentcode": "60Kxx",
	"level": 3
}, {
	"code": "60K30",
	"title": " Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx]",
	"parentcode": "60Kxx",
	"level": 3
}, {
	"code": "60K35",
	"title": " Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]",
	"parentcode": "60Kxx",
	"level": 3
}, {
	"code": "60K37",
	"title": " Processes in random environments",
	"parentcode": "60Kxx",
	"level": 3
}, {
	"code": "60K40",
	"title": " Other physical applications of random processes",
	"parentcode": "60Kxx",
	"level": 3
}, {
	"code": "60K99",
	"title": " None of the above, but in this section",
	"parentcode": "60Kxx",
	"level": 3
}, {
	"code": "62-XX",
	"title": " Statistics",
	"parentcode": null,
	"level": 1
}, {
	"code": "62-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62-07",
	"title": " Data analysis",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62-09",
	"title": " Graphical methods",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62Axx",
	"title": " Foundational and philosophical topics",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62A01",
	"title": " Foundations and philosophical topics",
	"parentcode": "62Axx",
	"level": 3
}, {
	"code": "62A86",
	"title": " Fuzzy analysis in statistics",
	"parentcode": "62Axx",
	"level": 3
}, {
	"code": "62A99",
	"title": " None of the above, but in this section",
	"parentcode": "62Axx",
	"level": 3
}, {
	"code": "62Bxx",
	"title": " Sufficiency and information",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62B05",
	"title": " Sufficient statistics and fields",
	"parentcode": "62Bxx",
	"level": 3
}, {
	"code": "62B10",
	"title": " Information-theoretic topics [See also 94A17]",
	"parentcode": "62Bxx",
	"level": 3
}, {
	"code": "62B15",
	"title": " Theory of statistical experiments",
	"parentcode": "62Bxx",
	"level": 3
}, {
	"code": "62B86",
	"title": " Fuzziness, sufficiency, and information",
	"parentcode": "62Bxx",
	"level": 3
}, {
	"code": "62B99",
	"title": " None of the above, but in this section",
	"parentcode": "62Bxx",
	"level": 3
}, {
	"code": "62Cxx",
	"title": " Decision theory [See also 90B50, 91B06; for game theory, see 91A35]",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62C05",
	"title": " General considerations",
	"parentcode": "62Cxx",
	"level": 3
}, {
	"code": "62C07",
	"title": " Complete class results",
	"parentcode": "62Cxx",
	"level": 3
}, {
	"code": "62C10",
	"title": " Bayesian problems; characterization of Bayes procedures",
	"parentcode": "62Cxx",
	"level": 3
}, {
	"code": "62C12",
	"title": " Empirical decision procedures; empirical Bayes procedures",
	"parentcode": "62Cxx",
	"level": 3
}, {
	"code": "62C15",
	"title": " Admissibility",
	"parentcode": "62Cxx",
	"level": 3
}, {
	"code": "62C20",
	"title": " Minimax procedures",
	"parentcode": "62Cxx",
	"level": 3
}, {
	"code": "62C25",
	"title": " Compound decision problems",
	"parentcode": "62Cxx",
	"level": 3
}, {
	"code": "62C86",
	"title": " Decision theory and fuzziness",
	"parentcode": "62Cxx",
	"level": 3
}, {
	"code": "62C99",
	"title": " None of the above, but in this section",
	"parentcode": "62Cxx",
	"level": 3
}, {
	"code": "62Dxx",
	"title": " Sampling theory, sample surveys",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62D05",
	"title": " Sampling theory, sample surveys",
	"parentcode": "62Dxx",
	"level": 3
}, {
	"code": "62D99",
	"title": " None of the above, but in this section",
	"parentcode": "62Dxx",
	"level": 3
}, {
	"code": "62Exx",
	"title": " Distribution theory [See also 60Exx]",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62E10",
	"title": " Characterization and structure theory",
	"parentcode": "62Exx",
	"level": 3
}, {
	"code": "62E15",
	"title": " Exact distribution theory",
	"parentcode": "62Exx",
	"level": 3
}, {
	"code": "62E17",
	"title": " Approximations to distributions (nonasymptotic)",
	"parentcode": "62Exx",
	"level": 3
}, {
	"code": "62E20",
	"title": " Asymptotic distribution theory",
	"parentcode": "62Exx",
	"level": 3
}, {
	"code": "62E86",
	"title": " Fuzziness in connection with the topics on distributions in this section",
	"parentcode": "62Exx",
	"level": 3
}, {
	"code": "62E99",
	"title": " None of the above, but in this section",
	"parentcode": "62Exx",
	"level": 3
}, {
	"code": "62Fxx",
	"title": " Parametric inference",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62F03",
	"title": " Hypothesis testing",
	"parentcode": "62Fxx",
	"level": 3
}, {
	"code": "62F05",
	"title": " Asymptotic properties of tests",
	"parentcode": "62Fxx",
	"level": 3
}, {
	"code": "62F07",
	"title": " Ranking and selection",
	"parentcode": "62Fxx",
	"level": 3
}, {
	"code": "62F10",
	"title": " Point estimation",
	"parentcode": "62Fxx",
	"level": 3
}, {
	"code": "62F12",
	"title": " Asymptotic properties of estimators",
	"parentcode": "62Fxx",
	"level": 3
}, {
	"code": "62F15",
	"title": " Bayesian inference",
	"parentcode": "62Fxx",
	"level": 3
}, {
	"code": "62F25",
	"title": " Tolerance and confidence regions",
	"parentcode": "62Fxx",
	"level": 3
}, {
	"code": "62F30",
	"title": " Inference under constraints",
	"parentcode": "62Fxx",
	"level": 3
}, {
	"code": "62F35",
	"title": " Robustness and adaptive procedures",
	"parentcode": "62Fxx",
	"level": 3
}, {
	"code": "62F40",
	"title": " Bootstrap, jackknife and other resampling methods",
	"parentcode": "62Fxx",
	"level": 3
}, {
	"code": "62F86",
	"title": " Parametric inference and fuzziness",
	"parentcode": "62Fxx",
	"level": 3
}, {
	"code": "62F99",
	"title": " None of the above, but in this section",
	"parentcode": "62Fxx",
	"level": 3
}, {
	"code": "62Gxx",
	"title": " Nonparametric inference",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62G05",
	"title": " Estimation",
	"parentcode": "62Gxx",
	"level": 3
}, {
	"code": "62G07",
	"title": " Density estimation",
	"parentcode": "62Gxx",
	"level": 3
}, {
	"code": "62G08",
	"title": " Nonparametric regression",
	"parentcode": "62Gxx",
	"level": 3
}, {
	"code": "62G09",
	"title": " Resampling methods",
	"parentcode": "62Gxx",
	"level": 3
}, {
	"code": "62G10",
	"title": " Hypothesis testing",
	"parentcode": "62Gxx",
	"level": 3
}, {
	"code": "62G15",
	"title": " Tolerance and confidence regions",
	"parentcode": "62Gxx",
	"level": 3
}, {
	"code": "62G20",
	"title": " Asymptotic properties",
	"parentcode": "62Gxx",
	"level": 3
}, {
	"code": "62G30",
	"title": " Order statistics; empirical distribution functions",
	"parentcode": "62Gxx",
	"level": 3
}, {
	"code": "62G32",
	"title": " Statistics of extreme values; tail inference",
	"parentcode": "62Gxx",
	"level": 3
}, {
	"code": "62G35",
	"title": " Robustness",
	"parentcode": "62Gxx",
	"level": 3
}, {
	"code": "62G86",
	"title": " Nonparametric inference and fuzziness",
	"parentcode": "62Gxx",
	"level": 3
}, {
	"code": "62G99",
	"title": " None of the above, but in this section",
	"parentcode": "62Gxx",
	"level": 3
}, {
	"code": "62Hxx",
	"title": " Multivariate analysis [See also 60Exx]",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62H05",
	"title": " Characterization and structure theory",
	"parentcode": "62Hxx",
	"level": 3
}, {
	"code": "62H10",
	"title": " Distribution of statistics",
	"parentcode": "62Hxx",
	"level": 3
}, {
	"code": "62H11",
	"title": " Directional data; spatial statistics",
	"parentcode": "62Hxx",
	"level": 3
}, {
	"code": "62H12",
	"title": " Estimation",
	"parentcode": "62Hxx",
	"level": 3
}, {
	"code": "62H15",
	"title": " Hypothesis testing",
	"parentcode": "62Hxx",
	"level": 3
}, {
	"code": "62H17",
	"title": " Contingency tables",
	"parentcode": "62Hxx",
	"level": 3
}, {
	"code": "62H20",
	"title": " Measures of association (correlation, canonical correlation, etc.)",
	"parentcode": "62Hxx",
	"level": 3
}, {
	"code": "62H25",
	"title": " Factor analysis and principal components; correspondence analysis",
	"parentcode": "62Hxx",
	"level": 3
}, {
	"code": "62H30",
	"title": " Classification and discrimination; cluster analysis [See also 68T10, 91C20]",
	"parentcode": "62Hxx",
	"level": 3
}, {
	"code": "62H35",
	"title": " Image analysis",
	"parentcode": "62Hxx",
	"level": 3
}, {
	"code": "62H86",
	"title": " Multivariate analysis and fuzziness",
	"parentcode": "62Hxx",
	"level": 3
}, {
	"code": "62H99",
	"title": " None of the above, but in this section",
	"parentcode": "62Hxx",
	"level": 3
}, {
	"code": "62Jxx",
	"title": " Linear inference, regression",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62J02",
	"title": " General nonlinear regression",
	"parentcode": "62Jxx",
	"level": 3
}, {
	"code": "62J05",
	"title": " Linear regression",
	"parentcode": "62Jxx",
	"level": 3
}, {
	"code": "62J07",
	"title": " Ridge regression; shrinkage estimators",
	"parentcode": "62Jxx",
	"level": 3
}, {
	"code": "62J10",
	"title": " Analysis of variance and covariance",
	"parentcode": "62Jxx",
	"level": 3
}, {
	"code": "62J12",
	"title": " Generalized linear models",
	"parentcode": "62Jxx",
	"level": 3
}, {
	"code": "62J15",
	"title": " Paired and multiple comparisons",
	"parentcode": "62Jxx",
	"level": 3
}, {
	"code": "62J20",
	"title": " Diagnostics",
	"parentcode": "62Jxx",
	"level": 3
}, {
	"code": "62J86",
	"title": " Fuzziness, and linear inference and regression",
	"parentcode": "62Jxx",
	"level": 3
}, {
	"code": "62J99",
	"title": " None of the above, but in this section",
	"parentcode": "62Jxx",
	"level": 3
}, {
	"code": "62Kxx",
	"title": " Design of experiments [See also 05Bxx]",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62K05",
	"title": " Optimal designs",
	"parentcode": "62Kxx",
	"level": 3
}, {
	"code": "62K10",
	"title": " Block designs",
	"parentcode": "62Kxx",
	"level": 3
}, {
	"code": "62K15",
	"title": " Factorial designs",
	"parentcode": "62Kxx",
	"level": 3
}, {
	"code": "62K20",
	"title": " Response surface designs",
	"parentcode": "62Kxx",
	"level": 3
}, {
	"code": "62K25",
	"title": " Robust parameter designs",
	"parentcode": "62Kxx",
	"level": 3
}, {
	"code": "62K86",
	"title": " Fuzziness and design of experiments",
	"parentcode": "62Kxx",
	"level": 3
}, {
	"code": "62K99",
	"title": " None of the above, but in this section",
	"parentcode": "62Kxx",
	"level": 3
}, {
	"code": "62Lxx",
	"title": " Sequential methods",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62L05",
	"title": " Sequential design",
	"parentcode": "62Lxx",
	"level": 3
}, {
	"code": "62L10",
	"title": " Sequential analysis",
	"parentcode": "62Lxx",
	"level": 3
}, {
	"code": "62L12",
	"title": " Sequential estimation",
	"parentcode": "62Lxx",
	"level": 3
}, {
	"code": "62L15",
	"title": " Optimal stopping [See also 60G40, 91A60]",
	"parentcode": "62Lxx",
	"level": 3
}, {
	"code": "62L20",
	"title": " Stochastic approximation",
	"parentcode": "62Lxx",
	"level": 3
}, {
	"code": "62L86",
	"title": " Fuzziness and sequential methods",
	"parentcode": "62Lxx",
	"level": 3
}, {
	"code": "62L99",
	"title": " None of the above, but in this section",
	"parentcode": "62Lxx",
	"level": 3
}, {
	"code": "62Mxx",
	"title": " Inference from stochastic processes",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62M02",
	"title": " Markov processes",
	"parentcode": "62Mxx",
	"level": 3
}, {
	"code": "62M05",
	"title": " Markov processes",
	"parentcode": "62Mxx",
	"level": 3
}, {
	"code": "62M07",
	"title": " Non-Markovian processes",
	"parentcode": "62Mxx",
	"level": 3
}, {
	"code": "62M09",
	"title": " Non-Markovian processes",
	"parentcode": "62Mxx",
	"level": 3
}, {
	"code": "62M10",
	"title": " Time series, auto-correlation, regression, etc. [See also 91B84]",
	"parentcode": "62Mxx",
	"level": 3
}, {
	"code": "62M15",
	"title": " Spectral analysis",
	"parentcode": "62Mxx",
	"level": 3
}, {
	"code": "62M20",
	"title": " Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]",
	"parentcode": "62Mxx",
	"level": 3
}, {
	"code": "62M30",
	"title": " Spatial processes",
	"parentcode": "62Mxx",
	"level": 3
}, {
	"code": "62M40",
	"title": " Random fields; image analysis",
	"parentcode": "62Mxx",
	"level": 3
}, {
	"code": "62M45",
	"title": " Neural nets and related approaches",
	"parentcode": "62Mxx",
	"level": 3
}, {
	"code": "62M86",
	"title": " Inference from stochastic processes and fuzziness",
	"parentcode": "62Mxx",
	"level": 3
}, {
	"code": "62M99",
	"title": " None of the above, but in this section",
	"parentcode": "62Mxx",
	"level": 3
}, {
	"code": "62Nxx",
	"title": " Survival analysis and censored data",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62N01",
	"title": " Censored data models",
	"parentcode": "62Nxx",
	"level": 3
}, {
	"code": "62N02",
	"title": " Estimation",
	"parentcode": "62Nxx",
	"level": 3
}, {
	"code": "62N03",
	"title": " Testing",
	"parentcode": "62Nxx",
	"level": 3
}, {
	"code": "62N05",
	"title": " Reliability and life testing [See also 90B25]",
	"parentcode": "62Nxx",
	"level": 3
}, {
	"code": "62N86",
	"title": " Fuzziness, and survival analysis and censored data",
	"parentcode": "62Nxx",
	"level": 3
}, {
	"code": "62N99",
	"title": " None of the above, but in this section",
	"parentcode": "62Nxx",
	"level": 3
}, {
	"code": "62Pxx",
	"title": " Applications [See also 90-XX, 91-XX, 92-XX]",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62P05",
	"title": " Applications to actuarial sciences and financial mathematics",
	"parentcode": "62Pxx",
	"level": 3
}, {
	"code": "62P10",
	"title": " Applications to biology and medical sciences",
	"parentcode": "62Pxx",
	"level": 3
}, {
	"code": "62P12",
	"title": " Applications to environmental and related topics",
	"parentcode": "62Pxx",
	"level": 3
}, {
	"code": "62P15",
	"title": " Applications to psychology",
	"parentcode": "62Pxx",
	"level": 3
}, {
	"code": "62P20",
	"title": " Applications to economics [See also 91Bxx]",
	"parentcode": "62Pxx",
	"level": 3
}, {
	"code": "62P25",
	"title": " Applications to social sciences",
	"parentcode": "62Pxx",
	"level": 3
}, {
	"code": "62P30",
	"title": " Applications in engineering and industry",
	"parentcode": "62Pxx",
	"level": 3
}, {
	"code": "62P35",
	"title": " Applications to physics",
	"parentcode": "62Pxx",
	"level": 3
}, {
	"code": "62P99",
	"title": " None of the above, but in this section",
	"parentcode": "62Pxx",
	"level": 3
}, {
	"code": "62Qxx",
	"title": " Statistical tables",
	"parentcode": "62-XX",
	"level": 2
}, {
	"code": "62Q05",
	"title": " Statistical tables",
	"parentcode": "62Qxx",
	"level": 3
}, {
	"code": "62Q99",
	"title": " None of the above, but in this section",
	"parentcode": "62Qxx",
	"level": 3
}, {
	"code": "65-XX",
	"title": " Numerical analysis",
	"parentcode": null,
	"level": 1
}, {
	"code": "65-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65-05",
	"title": " Experimental papers",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65Axx",
	"title": " Tables",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65A05",
	"title": " Tables",
	"parentcode": "65Axx",
	"level": 3
}, {
	"code": "65A99",
	"title": " None of the above, but in this section",
	"parentcode": "65Axx",
	"level": 3
}, {
	"code": "65Bxx",
	"title": " Acceleration of convergence",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65B05",
	"title": " Extrapolation to the limit, deferred corrections",
	"parentcode": "65Bxx",
	"level": 3
}, {
	"code": "65B10",
	"title": " Summation of series",
	"parentcode": "65Bxx",
	"level": 3
}, {
	"code": "65B15",
	"title": " Euler-Maclaurin formula",
	"parentcode": "65Bxx",
	"level": 3
}, {
	"code": "65B99",
	"title": " None of the above, but in this section",
	"parentcode": "65Bxx",
	"level": 3
}, {
	"code": "65Cxx",
	"title": " Probabilistic methods, simulation and stochastic differential equations {For theoretical aspects, see 68U20 and 60H35}",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65C05",
	"title": " Monte Carlo methods",
	"parentcode": "65Cxx",
	"level": 3
}, {
	"code": "65C10",
	"title": " Random number generation",
	"parentcode": "65Cxx",
	"level": 3
}, {
	"code": "65C20",
	"title": " Models, numerical methods [See also 68U20]",
	"parentcode": "65Cxx",
	"level": 3
}, {
	"code": "65C30",
	"title": " Stochastic differential and integral equations",
	"parentcode": "65Cxx",
	"level": 3
}, {
	"code": "65C35",
	"title": " Stochastic particle methods [See also 82C80]",
	"parentcode": "65Cxx",
	"level": 3
}, {
	"code": "65C40",
	"title": " Computational Markov chains",
	"parentcode": "65Cxx",
	"level": 3
}, {
	"code": "65C50",
	"title": " Other computational problems in probability",
	"parentcode": "65Cxx",
	"level": 3
}, {
	"code": "65C60",
	"title": " Computational problems in statistics",
	"parentcode": "65Cxx",
	"level": 3
}, {
	"code": "65C99",
	"title": " None of the above, but in this section",
	"parentcode": "65Cxx",
	"level": 3
}, {
	"code": "65Dxx",
	"title": " Numerical approximation and computational geometry (primarily algorithms) {For theory, see 41-XX and 68Uxx}",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65D05",
	"title": " Interpolation",
	"parentcode": "65Dxx",
	"level": 3
}, {
	"code": "65D07",
	"title": " Splines",
	"parentcode": "65Dxx",
	"level": 3
}, {
	"code": "65D10",
	"title": " Smoothing, curve fitting",
	"parentcode": "65Dxx",
	"level": 3
}, {
	"code": "65D15",
	"title": " Algorithms for functional approximation",
	"parentcode": "65Dxx",
	"level": 3
}, {
	"code": "65D17",
	"title": " Computer aided design (modeling of curves and surfaces) [See also 68U07]",
	"parentcode": "65Dxx",
	"level": 3
}, {
	"code": "65D18",
	"title": " Computer graphics, image analysis, and computational geometry [See also 51N05, 68U05]",
	"parentcode": "65Dxx",
	"level": 3
}, {
	"code": "65D19",
	"title": " Computational issues in computer and robotic vision",
	"parentcode": "65Dxx",
	"level": 3
}, {
	"code": "65D20",
	"title": " Computation of special functions, construction of tables [See also 33F05]",
	"parentcode": "65Dxx",
	"level": 3
}, {
	"code": "65D25",
	"title": " Numerical differentiation",
	"parentcode": "65Dxx",
	"level": 3
}, {
	"code": "65D30",
	"title": " Numerical integration",
	"parentcode": "65Dxx",
	"level": 3
}, {
	"code": "65D32",
	"title": " Quadrature and cubature formulas",
	"parentcode": "65Dxx",
	"level": 3
}, {
	"code": "65D99",
	"title": " None of the above, but in this section",
	"parentcode": "65Dxx",
	"level": 3
}, {
	"code": "65Exx",
	"title": " Numerical methods in complex analysis (potential theory, etc.) {For numerical methods in conformal mapping, see also 30C30}",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65E05",
	"title": " Numerical methods in complex analysis (potential theory, etc.)  {For numerical methods in conformal mapping, see also 30C30}",
	"parentcode": "65Exx",
	"level": 3
}, {
	"code": "65E99",
	"title": " None of the above, but in this section",
	"parentcode": "65Exx",
	"level": 3
}, {
	"code": "65Fxx",
	"title": " Numerical linear algebra",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65F05",
	"title": " Direct methods for linear systems and matrix inversion",
	"parentcode": "65Fxx",
	"level": 3
}, {
	"code": "65F08",
	"title": " Preconditioners for iterative methods",
	"parentcode": "65Fxx",
	"level": 3
}, {
	"code": "65F10",
	"title": " Iterative methods for linear systems [See also 65N22]",
	"parentcode": "65Fxx",
	"level": 3
}, {
	"code": "65F15",
	"title": " Eigenvalues, eigenvectors",
	"parentcode": "65Fxx",
	"level": 3
}, {
	"code": "65F18",
	"title": " Inverse eigenvalue problems",
	"parentcode": "65Fxx",
	"level": 3
}, {
	"code": "65F20",
	"title": " Overdetermined systems, pseudoinverses",
	"parentcode": "65Fxx",
	"level": 3
}, {
	"code": "65F22",
	"title": " Ill-posedness, regularization",
	"parentcode": "65Fxx",
	"level": 3
}, {
	"code": "65F25",
	"title": " Orthogonalization",
	"parentcode": "65Fxx",
	"level": 3
}, {
	"code": "65F30",
	"title": " Other matrix algorithms",
	"parentcode": "65Fxx",
	"level": 3
}, {
	"code": "65F35",
	"title": " Matrix norms, conditioning, scaling [See also 15A12, 15A60]",
	"parentcode": "65Fxx",
	"level": 3
}, {
	"code": "65F40",
	"title": " Determinants",
	"parentcode": "65Fxx",
	"level": 3
}, {
	"code": "65F50",
	"title": " Sparse matrices",
	"parentcode": "65Fxx",
	"level": 3
}, {
	"code": "65F60",
	"title": " Matrix exponential and similar matrix functions",
	"parentcode": "65Fxx",
	"level": 3
}, {
	"code": "65F99",
	"title": " None of the above, but in this section",
	"parentcode": "65Fxx",
	"level": 3
}, {
	"code": "65Gxx",
	"title": " Error analysis and interval analysis",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65G20",
	"title": " Algorithms with automatic result verification",
	"parentcode": "65Gxx",
	"level": 3
}, {
	"code": "65G30",
	"title": " Interval and finite arithmetic",
	"parentcode": "65Gxx",
	"level": 3
}, {
	"code": "65G40",
	"title": " General methods in interval analysis",
	"parentcode": "65Gxx",
	"level": 3
}, {
	"code": "65G50",
	"title": " Roundoff error",
	"parentcode": "65Gxx",
	"level": 3
}, {
	"code": "65G99",
	"title": " None of the above, but in this section",
	"parentcode": "65Gxx",
	"level": 3
}, {
	"code": "65Hxx",
	"title": " Nonlinear algebraic or transcendental equations",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65H04",
	"title": " Roots of polynomial equations",
	"parentcode": "65Hxx",
	"level": 3
}, {
	"code": "65H05",
	"title": " Single equations",
	"parentcode": "65Hxx",
	"level": 3
}, {
	"code": "65H10",
	"title": " Systems of equations",
	"parentcode": "65Hxx",
	"level": 3
}, {
	"code": "65H17",
	"title": " Eigenvalues, eigenvectors [See also 47Hxx, 47Jxx, 58C40, 58E07, 90C30]",
	"parentcode": "65Hxx",
	"level": 3
}, {
	"code": "65H20",
	"title": " Global methods, including homotopy approaches [See also 58C30, 90C30]",
	"parentcode": "65Hxx",
	"level": 3
}, {
	"code": "65H99",
	"title": " None of the above, but in this section",
	"parentcode": "65Hxx",
	"level": 3
}, {
	"code": "65Jxx",
	"title": " Numerical analysis in abstract spaces",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65J05",
	"title": " General theory",
	"parentcode": "65Jxx",
	"level": 3
}, {
	"code": "65J08",
	"title": " Abstract evolution equations",
	"parentcode": "65Jxx",
	"level": 3
}, {
	"code": "65J10",
	"title": " Equations with linear operators (do not use 65Fxx)",
	"parentcode": "65Jxx",
	"level": 3
}, {
	"code": "65J15",
	"title": " Equations with nonlinear operators (do not use 65Hxx)",
	"parentcode": "65Jxx",
	"level": 3
}, {
	"code": "65J20",
	"title": " Improperly posed problems; regularization",
	"parentcode": "65Jxx",
	"level": 3
}, {
	"code": "65J22",
	"title": " Inverse problems",
	"parentcode": "65Jxx",
	"level": 3
}, {
	"code": "65J99",
	"title": " None of the above, but in this section",
	"parentcode": "65Jxx",
	"level": 3
}, {
	"code": "65Kxx",
	"title": " Mathematical programming, optimization and variational techniques",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65K05",
	"title": " Mathematical programming methods  [See also 90Cxx]",
	"parentcode": "65Kxx",
	"level": 3
}, {
	"code": "65K10",
	"title": " Optimization and variational techniques [See also 49Mxx, 93B40]",
	"parentcode": "65Kxx",
	"level": 3
}, {
	"code": "65K15",
	"title": " Numerical methods for variational inequalities and related problems",
	"parentcode": "65Kxx",
	"level": 3
}, {
	"code": "65K99",
	"title": " None of the above, but in this section",
	"parentcode": "65Kxx",
	"level": 3
}, {
	"code": "65Lxx",
	"title": " Ordinary differential equations",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65L03",
	"title": " Functional-differential equations",
	"parentcode": "65Lxx",
	"level": 3
}, {
	"code": "65L04",
	"title": " Stiff equations",
	"parentcode": "65Lxx",
	"level": 3
}, {
	"code": "65L05",
	"title": " Initial value problems",
	"parentcode": "65Lxx",
	"level": 3
}, {
	"code": "65L06",
	"title": " Multistep, Runge-Kutta and extrapolation methods",
	"parentcode": "65Lxx",
	"level": 3
}, {
	"code": "65L07",
	"title": " Numerical investigation of stability of solutions",
	"parentcode": "65Lxx",
	"level": 3
}, {
	"code": "65L08",
	"title": " Improperly posed problems",
	"parentcode": "65Lxx",
	"level": 3
}, {
	"code": "65L09",
	"title": " Inverse problems",
	"parentcode": "65Lxx",
	"level": 3
}, {
	"code": "65L10",
	"title": " Boundary value problems",
	"parentcode": "65Lxx",
	"level": 3
}, {
	"code": "65L11",
	"title": " Singularly perturbed problems",
	"parentcode": "65Lxx",
	"level": 3
}, {
	"code": "65L12",
	"title": " Finite difference methods",
	"parentcode": "65Lxx",
	"level": 3
}, {
	"code": "65L15",
	"title": " Eigenvalue problems",
	"parentcode": "65Lxx",
	"level": 3
}, {
	"code": "65L20",
	"title": " Stability and convergence of numerical methods",
	"parentcode": "65Lxx",
	"level": 3
}, {
	"code": "65L50",
	"title": " Mesh generation and refinement",
	"parentcode": "65Lxx",
	"level": 3
}, {
	"code": "65L60",
	"title": " Finite elements, Rayleigh-Ritz, Galerkin and collocation methods",
	"parentcode": "65Lxx",
	"level": 3
}, {
	"code": "65L70",
	"title": " Error bounds",
	"parentcode": "65Lxx",
	"level": 3
}, {
	"code": "65L80",
	"title": " Methods for differential-algebraic equations",
	"parentcode": "65Lxx",
	"level": 3
}, {
	"code": "65L99",
	"title": " None of the above, but in this section",
	"parentcode": "65Lxx",
	"level": 3
}, {
	"code": "65Mxx",
	"title": " Partial differential equations, initial value and time-dependent initial-boundary value problems",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65M06",
	"title": " Finite difference methods",
	"parentcode": "65Mxx",
	"level": 3
}, {
	"code": "65M08",
	"title": " Finite volume methods",
	"parentcode": "65Mxx",
	"level": 3
}, {
	"code": "65M12",
	"title": " Stability and convergence of numerical methods",
	"parentcode": "65Mxx",
	"level": 3
}, {
	"code": "65M15",
	"title": " Error bounds",
	"parentcode": "65Mxx",
	"level": 3
}, {
	"code": "65M20",
	"title": " Method of lines",
	"parentcode": "65Mxx",
	"level": 3
}, {
	"code": "65M22",
	"title": " Solution of discretized equations [See also 65Fxx, 65Hxx]",
	"parentcode": "65Mxx",
	"level": 3
}, {
	"code": "65M25",
	"title": " Method of characteristics",
	"parentcode": "65Mxx",
	"level": 3
}, {
	"code": "65M30",
	"title": " Improperly posed problems",
	"parentcode": "65Mxx",
	"level": 3
}, {
	"code": "65M32",
	"title": " Inverse problems",
	"parentcode": "65Mxx",
	"level": 3
}, {
	"code": "65M38",
	"title": " Boundary element methods",
	"parentcode": "65Mxx",
	"level": 3
}, {
	"code": "65M50",
	"title": " Mesh generation and refinement",
	"parentcode": "65Mxx",
	"level": 3
}, {
	"code": "65M55",
	"title": " Multigrid methods; domain decomposition",
	"parentcode": "65Mxx",
	"level": 3
}, {
	"code": "65M60",
	"title": " Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods",
	"parentcode": "65Mxx",
	"level": 3
}, {
	"code": "65M70",
	"title": " Spectral, collocation and related methods",
	"parentcode": "65Mxx",
	"level": 3
}, {
	"code": "65M75",
	"title": " Probabilistic methods, particle methods, etc.",
	"parentcode": "65Mxx",
	"level": 3
}, {
	"code": "65M80",
	"title": " Fundamental solutions, Green's function methods, etc.",
	"parentcode": "65Mxx",
	"level": 3
}, {
	"code": "65M85",
	"title": " Fictitious domain methods",
	"parentcode": "65Mxx",
	"level": 3
}, {
	"code": "65M99",
	"title": " None of the above, but in this section",
	"parentcode": "65Mxx",
	"level": 3
}, {
	"code": "65Nxx",
	"title": " Partial differential equations, boundary value problems",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65N06",
	"title": " Finite difference methods",
	"parentcode": "65Nxx",
	"level": 3
}, {
	"code": "65N08",
	"title": " Finite volume methods",
	"parentcode": "65Nxx",
	"level": 3
}, {
	"code": "65N12",
	"title": " Stability and convergence of numerical methods",
	"parentcode": "65Nxx",
	"level": 3
}, {
	"code": "65N15",
	"title": " Error bounds",
	"parentcode": "65Nxx",
	"level": 3
}, {
	"code": "65N20",
	"title": " Ill-posed problems",
	"parentcode": "65Nxx",
	"level": 3
}, {
	"code": "65N21",
	"title": " Inverse problems",
	"parentcode": "65Nxx",
	"level": 3
}, {
	"code": "65N22",
	"title": " Solution of discretized equations [See also 65Fxx, 65Hxx]",
	"parentcode": "65Nxx",
	"level": 3
}, {
	"code": "65N25",
	"title": " Eigenvalue problems",
	"parentcode": "65Nxx",
	"level": 3
}, {
	"code": "65N30",
	"title": " Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods",
	"parentcode": "65Nxx",
	"level": 3
}, {
	"code": "65N35",
	"title": " Spectral, collocation and related methods",
	"parentcode": "65Nxx",
	"level": 3
}, {
	"code": "65N38",
	"title": " Boundary element methods",
	"parentcode": "65Nxx",
	"level": 3
}, {
	"code": "65N40",
	"title": " Method of lines",
	"parentcode": "65Nxx",
	"level": 3
}, {
	"code": "65N45",
	"title": " Method of contraction of the boundary",
	"parentcode": "65Nxx",
	"level": 3
}, {
	"code": "65N50",
	"title": " Mesh generation and refinement",
	"parentcode": "65Nxx",
	"level": 3
}, {
	"code": "65N55",
	"title": " Multigrid methods; domain decomposition",
	"parentcode": "65Nxx",
	"level": 3
}, {
	"code": "65N75",
	"title": " Probabilistic methods, particle methods, etc.",
	"parentcode": "65Nxx",
	"level": 3
}, {
	"code": "65N80",
	"title": " Fundamental solutions, Green's function methods, etc.",
	"parentcode": "65Nxx",
	"level": 3
}, {
	"code": "65N85",
	"title": " Fictitious domain methods",
	"parentcode": "65Nxx",
	"level": 3
}, {
	"code": "65N99",
	"title": " None of the above, but in this section",
	"parentcode": "65Nxx",
	"level": 3
}, {
	"code": "65Pxx",
	"title": " Numerical problems in dynamical systems [See also 37Mxx]",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65P10",
	"title": " Hamiltonian systems including symplectic integrators",
	"parentcode": "65Pxx",
	"level": 3
}, {
	"code": "65P20",
	"title": " Numerical chaos",
	"parentcode": "65Pxx",
	"level": 3
}, {
	"code": "65P30",
	"title": " Bifurcation problems",
	"parentcode": "65Pxx",
	"level": 3
}, {
	"code": "65P40",
	"title": " Nonlinear stabilities",
	"parentcode": "65Pxx",
	"level": 3
}, {
	"code": "65P99",
	"title": " None of the above, but in this section",
	"parentcode": "65Pxx",
	"level": 3
}, {
	"code": "65Qxx",
	"title": " Difference and functional equations, recurrence relations",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65Q10",
	"title": " Difference equations",
	"parentcode": "65Qxx",
	"level": 3
}, {
	"code": "65Q20",
	"title": " Functional equations",
	"parentcode": "65Qxx",
	"level": 3
}, {
	"code": "65Q30",
	"title": " Recurrence relations",
	"parentcode": "65Qxx",
	"level": 3
}, {
	"code": "65Q99",
	"title": " None of the above, but in this section",
	"parentcode": "65Qxx",
	"level": 3
}, {
	"code": "65Rxx",
	"title": " Integral equations, integral transforms",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65R10",
	"title": " Integral transforms",
	"parentcode": "65Rxx",
	"level": 3
}, {
	"code": "65R20",
	"title": " Integral equations",
	"parentcode": "65Rxx",
	"level": 3
}, {
	"code": "65R30",
	"title": " Improperly posed problems",
	"parentcode": "65Rxx",
	"level": 3
}, {
	"code": "65R32",
	"title": " Inverse problems",
	"parentcode": "65Rxx",
	"level": 3
}, {
	"code": "65R99",
	"title": " None of the above, but in this section",
	"parentcode": "65Rxx",
	"level": 3
}, {
	"code": "65Sxx",
	"title": " Graphical methods",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65S05",
	"title": " Graphical methods",
	"parentcode": "65Sxx",
	"level": 3
}, {
	"code": "65S99",
	"title": " None of the above, but in this section",
	"parentcode": "65Sxx",
	"level": 3
}, {
	"code": "65Txx",
	"title": " Numerical methods in Fourier analysis",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65T40",
	"title": " Trigonometric approximation and interpolation",
	"parentcode": "65Txx",
	"level": 3
}, {
	"code": "65T50",
	"title": " Discrete and fast Fourier transforms",
	"parentcode": "65Txx",
	"level": 3
}, {
	"code": "65T60",
	"title": " Wavelets",
	"parentcode": "65Txx",
	"level": 3
}, {
	"code": "65T99",
	"title": " None of the above, but in this section",
	"parentcode": "65Txx",
	"level": 3
}, {
	"code": "65Yxx",
	"title": " Computer aspects of numerical algorithms",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65Y04",
	"title": " Algorithms for computer arithmetic, etc. [See also 68M07]",
	"parentcode": "65Yxx",
	"level": 3
}, {
	"code": "65Y05",
	"title": " Parallel computation",
	"parentcode": "65Yxx",
	"level": 3
}, {
	"code": "65Y10",
	"title": " Algorithms for specific classes of architectures",
	"parentcode": "65Yxx",
	"level": 3
}, {
	"code": "65Y15",
	"title": " Packaged methods",
	"parentcode": "65Yxx",
	"level": 3
}, {
	"code": "65Y20",
	"title": " Complexity and performance of numerical algorithms [See also 68Q25]",
	"parentcode": "65Yxx",
	"level": 3
}, {
	"code": "65Y99",
	"title": " None of the above, but in this section",
	"parentcode": "65Yxx",
	"level": 3
}, {
	"code": "65Zxx",
	"title": " Applications to physics",
	"parentcode": "65-XX",
	"level": 2
}, {
	"code": "65Z05",
	"title": " Applications to physics",
	"parentcode": "65Zxx",
	"level": 3
}, {
	"code": "65Z99",
	"title": " None of the above, but in this section",
	"parentcode": "65Zxx",
	"level": 3
}, {
	"code": "68-XX",
	"title": " Computer science {For papers involving machine computations and programs in a specific mathematical area, see Section –04 in that area}",
	"parentcode": null,
	"level": 1
}, {
	"code": "68-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "68-XX",
	"level": 2
}, {
	"code": "68-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "68-XX",
	"level": 2
}, {
	"code": "68-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "68-XX",
	"level": 2
}, {
	"code": "68-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "68-XX",
	"level": 2
}, {
	"code": "68-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "68-XX",
	"level": 2
}, {
	"code": "68-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "68-XX",
	"level": 2
}, {
	"code": "68Mxx",
	"title": " Computer system organization",
	"parentcode": "68-XX",
	"level": 2
}, {
	"code": "68M01",
	"title": " General",
	"parentcode": "68Mxx",
	"level": 3
}, {
	"code": "68M07",
	"title": " Mathematical problems of computer architecture",
	"parentcode": "68Mxx",
	"level": 3
}, {
	"code": "68M10",
	"title": " Network design and communication [See also 68R10, 90B18]",
	"parentcode": "68Mxx",
	"level": 3
}, {
	"code": "68M11",
	"title": " Internet topics [See also 68U35]",
	"parentcode": "68Mxx",
	"level": 3
}, {
	"code": "68M12",
	"title": " Network protocols",
	"parentcode": "68Mxx",
	"level": 3
}, {
	"code": "68M14",
	"title": " Distributed systems",
	"parentcode": "68Mxx",
	"level": 3
}, {
	"code": "68M15",
	"title": " Reliability, testing and fault tolerance [See also 94C12]",
	"parentcode": "68Mxx",
	"level": 3
}, {
	"code": "68M20",
	"title": " Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]",
	"parentcode": "68Mxx",
	"level": 3
}, {
	"code": "68M99",
	"title": " None of the above, but in this section",
	"parentcode": "68Mxx",
	"level": 3
}, {
	"code": "68Nxx",
	"title": " Software",
	"parentcode": "68-XX",
	"level": 2
}, {
	"code": "68N01",
	"title": " General",
	"parentcode": "68Nxx",
	"level": 3
}, {
	"code": "68N15",
	"title": " Programming languages",
	"parentcode": "68Nxx",
	"level": 3
}, {
	"code": "68N17",
	"title": " Logic programming",
	"parentcode": "68Nxx",
	"level": 3
}, {
	"code": "68N18",
	"title": " Functional programming and lambda calculus [See also 03B40]",
	"parentcode": "68Nxx",
	"level": 3
}, {
	"code": "68N19",
	"title": " Other programming techniques (object-oriented, sequential, concurrent, automatic, etc.)",
	"parentcode": "68Nxx",
	"level": 3
}, {
	"code": "68N20",
	"title": " Compilers and interpreters",
	"parentcode": "68Nxx",
	"level": 3
}, {
	"code": "68N25",
	"title": " Operating systems",
	"parentcode": "68Nxx",
	"level": 3
}, {
	"code": "68N30",
	"title": " Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)",
	"parentcode": "68Nxx",
	"level": 3
}, {
	"code": "68N99",
	"title": " None of the above, but in this section",
	"parentcode": "68Nxx",
	"level": 3
}, {
	"code": "68Pxx",
	"title": " Theory of data",
	"parentcode": "68-XX",
	"level": 2
}, {
	"code": "68P01",
	"title": " General",
	"parentcode": "68Pxx",
	"level": 3
}, {
	"code": "68P05",
	"title": " Data structures",
	"parentcode": "68Pxx",
	"level": 3
}, {
	"code": "68P10",
	"title": " Searching and sorting",
	"parentcode": "68Pxx",
	"level": 3
}, {
	"code": "68P15",
	"title": " Database theory",
	"parentcode": "68Pxx",
	"level": 3
}, {
	"code": "68P20",
	"title": " Information storage and retrieval",
	"parentcode": "68Pxx",
	"level": 3
}, {
	"code": "68P25",
	"title": " Data encryption [See also 94A60, 81P94]",
	"parentcode": "68Pxx",
	"level": 3
}, {
	"code": "68P30",
	"title": " Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) [See also 94Axx]",
	"parentcode": "68Pxx",
	"level": 3
}, {
	"code": "68P99",
	"title": " None of the above, but in this section",
	"parentcode": "68Pxx",
	"level": 3
}, {
	"code": "68Qxx",
	"title": " Theory of computing",
	"parentcode": "68-XX",
	"level": 2
}, {
	"code": "68Q01",
	"title": " General",
	"parentcode": "68Qxx",
	"level": 3
}, {
	"code": "68Q05",
	"title": " Models of computation (Turing machines, etc.) [See also 03D10,  68Q12, 81P68]",
	"parentcode": "68Qxx",
	"level": 3
}, {
	"code": "68Q10",
	"title": " Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) [See also 68Q85]",
	"parentcode": "68Qxx",
	"level": 3
}, {
	"code": "68Q12",
	"title": " Quantum algorithms and complexity [See also  68Q05,  81P68]",
	"parentcode": "68Qxx",
	"level": 3
}, {
	"code": "68Q15",
	"title": " Complexity classes (hierarchies, relations among complexity classes, etc.) [See also 03D15, 68Q17, 68Q19]",
	"parentcode": "68Qxx",
	"level": 3
}, {
	"code": "68Q17",
	"title": " Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) [See also 68Q15]",
	"parentcode": "68Qxx",
	"level": 3
}, {
	"code": "68Q19",
	"title": " Descriptive complexity and finite models [See also 03C13]",
	"parentcode": "68Qxx",
	"level": 3
}, {
	"code": "68Q25",
	"title": " Analysis of algorithms and problem complexity [See also 68W40]",
	"parentcode": "68Qxx",
	"level": 3
}, {
	"code": "68Q30",
	"title": " Algorithmic information theory (Kolmogorov complexity, etc.) [See also 03D32]",
	"parentcode": "68Qxx",
	"level": 3
}, {
	"code": "68Q32",
	"title": " Computational learning theory [See also 68T05]",
	"parentcode": "68Qxx",
	"level": 3
}, {
	"code": "68Q42",
	"title": " Grammars and rewriting systems",
	"parentcode": "68Qxx",
	"level": 3
}, {
	"code": "68Q45",
	"title": " Formal languages and automata [See also 03D05, 68Q70, 94A45]",
	"parentcode": "68Qxx",
	"level": 3
}, {
	"code": "68Q55",
	"title": " Semantics [See also 03B70, 06B35, 18C50]",
	"parentcode": "68Qxx",
	"level": 3
}, {
	"code": "68Q60",
	"title": " Specification and verification (program logics, model checking, etc.) [See also 03B70]",
	"parentcode": "68Qxx",
	"level": 3
}, {
	"code": "68Q65",
	"title": " Abstract data types; algebraic specification [See also 18C50]",
	"parentcode": "68Qxx",
	"level": 3
}, {
	"code": "68Q70",
	"title": " Algebraic theory of languages and automata [See also 18B20, 20M35]",
	"parentcode": "68Qxx",
	"level": 3
}, {
	"code": "68Q80",
	"title": " Cellular automata [See also 37B15]",
	"parentcode": "68Qxx",
	"level": 3
}, {
	"code": "68Q85",
	"title": " Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)",
	"parentcode": "68Qxx",
	"level": 3
}, {
	"code": "68Q87",
	"title": " Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) [See also 68W20, 68W40]",
	"parentcode": "68Qxx",
	"level": 3
}, {
	"code": "68Q99",
	"title": " None of the above, but in this section",
	"parentcode": "68Qxx",
	"level": 3
}, {
	"code": "68Rxx",
	"title": " Discrete mathematics in relation to computer science",
	"parentcode": "68-XX",
	"level": 2
}, {
	"code": "68R01",
	"title": " General",
	"parentcode": "68Rxx",
	"level": 3
}, {
	"code": "68R05",
	"title": " Combinatorics",
	"parentcode": "68Rxx",
	"level": 3
}, {
	"code": "68R10",
	"title": " Graph theory (including graph drawing) [See also 05Cxx, 90B10, 90B35, 90C35]",
	"parentcode": "68Rxx",
	"level": 3
}, {
	"code": "68R15",
	"title": " Combinatorics on words",
	"parentcode": "68Rxx",
	"level": 3
}, {
	"code": "68R99",
	"title": " None of the above, but in this section",
	"parentcode": "68Rxx",
	"level": 3
}, {
	"code": "68Txx",
	"title": " Artificial intelligence",
	"parentcode": "68-XX",
	"level": 2
}, {
	"code": "68T01",
	"title": " General",
	"parentcode": "68Txx",
	"level": 3
}, {
	"code": "68T05",
	"title": " Learning and adaptive systems [See also 68Q32, 91E40]",
	"parentcode": "68Txx",
	"level": 3
}, {
	"code": "68T10",
	"title": " Pattern recognition, speech recognition {For cluster analysis, see 62H30}",
	"parentcode": "68Txx",
	"level": 3
}, {
	"code": "68T15",
	"title": " Theorem proving (deduction, resolution, etc.) [See also 03B35]",
	"parentcode": "68Txx",
	"level": 3
}, {
	"code": "68T20",
	"title": " Problem solving (heuristics, search strategies, etc.)",
	"parentcode": "68Txx",
	"level": 3
}, {
	"code": "68T27",
	"title": " Logic in artificial intelligence",
	"parentcode": "68Txx",
	"level": 3
}, {
	"code": "68T30",
	"title": " Knowledge representation",
	"parentcode": "68Txx",
	"level": 3
}, {
	"code": "68T35",
	"title": " Languages and software systems (knowledge-based systems, expert systems, etc.)",
	"parentcode": "68Txx",
	"level": 3
}, {
	"code": "68T37",
	"title": " Reasoning under uncertainty",
	"parentcode": "68Txx",
	"level": 3
}, {
	"code": "68T40",
	"title": " Robotics [See also 93C85]",
	"parentcode": "68Txx",
	"level": 3
}, {
	"code": "68T42",
	"title": " Agent technology",
	"parentcode": "68Txx",
	"level": 3
}, {
	"code": "68T45",
	"title": " Machine vision and scene understanding",
	"parentcode": "68Txx",
	"level": 3
}, {
	"code": "68T50",
	"title": " Natural language processing [See also 03B65]",
	"parentcode": "68Txx",
	"level": 3
}, {
	"code": "68T99",
	"title": " None of the above, but in this section",
	"parentcode": "68Txx",
	"level": 3
}, {
	"code": "68Uxx",
	"title": " Computing methodologies and applications",
	"parentcode": "68-XX",
	"level": 2
}, {
	"code": "68U01",
	"title": " General",
	"parentcode": "68Uxx",
	"level": 3
}, {
	"code": "68U05",
	"title": " Computer graphics; computational geometry [See also 65D18]",
	"parentcode": "68Uxx",
	"level": 3
}, {
	"code": "68U07",
	"title": " Computer-aided design [See also 65D17]",
	"parentcode": "68Uxx",
	"level": 3
}, {
	"code": "68U10",
	"title": " Image processing",
	"parentcode": "68Uxx",
	"level": 3
}, {
	"code": "68U15",
	"title": " Text processing; mathematical typography",
	"parentcode": "68Uxx",
	"level": 3
}, {
	"code": "68U20",
	"title": " Simulation [See also 65Cxx]",
	"parentcode": "68Uxx",
	"level": 3
}, {
	"code": "68U35",
	"title": " Information systems (hypertext navigation, interfaces, decision support, etc.) [See also 68M11]",
	"parentcode": "68Uxx",
	"level": 3
}, {
	"code": "68U99",
	"title": " None of the above, but in this section",
	"parentcode": "68Uxx",
	"level": 3
}, {
	"code": "68Wxx",
	"title": " Algorithms {For numerical algorithms, see 65-XX; for combinatorics and graph theory, see  05C85,  68Rxx}",
	"parentcode": "68-XX",
	"level": 2
}, {
	"code": "68W01",
	"title": " General",
	"parentcode": "68Wxx",
	"level": 3
}, {
	"code": "68W05",
	"title": " Nonnumerical algorithms",
	"parentcode": "68Wxx",
	"level": 3
}, {
	"code": "68W10",
	"title": " Parallel algorithms",
	"parentcode": "68Wxx",
	"level": 3
}, {
	"code": "68W15",
	"title": " Distributed algorithms",
	"parentcode": "68Wxx",
	"level": 3
}, {
	"code": "68W20",
	"title": " Randomized algorithms",
	"parentcode": "68Wxx",
	"level": 3
}, {
	"code": "68W25",
	"title": " Approximation algorithms",
	"parentcode": "68Wxx",
	"level": 3
}, {
	"code": "68W27",
	"title": " Online algorithms",
	"parentcode": "68Wxx",
	"level": 3
}, {
	"code": "68W30",
	"title": " Symbolic computation and algebraic computation [See also 11Yxx, 12Y05, 13Pxx, 14Qxx, 16Z05, 17-08, 33F10]",
	"parentcode": "68Wxx",
	"level": 3
}, {
	"code": "68W32",
	"title": " Algorithms on strings",
	"parentcode": "68Wxx",
	"level": 3
}, {
	"code": "68W35",
	"title": " VLSI algorithms",
	"parentcode": "68Wxx",
	"level": 3
}, {
	"code": "68W40",
	"title": " Analysis of algorithms [See also 68Q25]",
	"parentcode": "68Wxx",
	"level": 3
}, {
	"code": "68W99",
	"title": " None of the above, but in this section",
	"parentcode": "68Wxx",
	"level": 3
}, {
	"code": "70-XX",
	"title": " Mechanics of particles and systems {For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX}",
	"parentcode": null,
	"level": 1
}, {
	"code": "70-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70-05",
	"title": " Experimental work",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70-08",
	"title": " Computational methods",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70Axx",
	"title": " Axiomatics, foundations",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70A05",
	"title": " Axiomatics, foundations",
	"parentcode": "70Axx",
	"level": 3
}, {
	"code": "70A99",
	"title": " None of the above, but in this section",
	"parentcode": "70Axx",
	"level": 3
}, {
	"code": "70Bxx",
	"title": " Kinematics [See also 53A17]",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70B05",
	"title": " Kinematics of a particle",
	"parentcode": "70Bxx",
	"level": 3
}, {
	"code": "70B10",
	"title": " Kinematics of a rigid body",
	"parentcode": "70Bxx",
	"level": 3
}, {
	"code": "70B15",
	"title": " Mechanisms, robots [See also 68T40, 70Q05, 93C85]",
	"parentcode": "70Bxx",
	"level": 3
}, {
	"code": "70B99",
	"title": " None of the above, but in this section",
	"parentcode": "70Bxx",
	"level": 3
}, {
	"code": "70Cxx",
	"title": " Statics",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70C20",
	"title": " Statics",
	"parentcode": "70Cxx",
	"level": 3
}, {
	"code": "70C99",
	"title": " None of the above, but in this section",
	"parentcode": "70Cxx",
	"level": 3
}, {
	"code": "70Exx",
	"title": " Dynamics of a rigid body and of multibody systems",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70E05",
	"title": " Motion of the gyroscope",
	"parentcode": "70Exx",
	"level": 3
}, {
	"code": "70E15",
	"title": " Free motion of a rigid body [See also 70M20]",
	"parentcode": "70Exx",
	"level": 3
}, {
	"code": "70E17",
	"title": " Motion of a rigid body with a fixed point",
	"parentcode": "70Exx",
	"level": 3
}, {
	"code": "70E18",
	"title": " Motion of a rigid body in contact with a solid surface [See also 70F25]",
	"parentcode": "70Exx",
	"level": 3
}, {
	"code": "70E20",
	"title": " Perturbation methods for rigid body dynamics",
	"parentcode": "70Exx",
	"level": 3
}, {
	"code": "70E40",
	"title": " Integrable cases of motion",
	"parentcode": "70Exx",
	"level": 3
}, {
	"code": "70E45",
	"title": " Higher-dimensional generalizations",
	"parentcode": "70Exx",
	"level": 3
}, {
	"code": "70E50",
	"title": " Stability problems",
	"parentcode": "70Exx",
	"level": 3
}, {
	"code": "70E55",
	"title": " Dynamics of multibody systems",
	"parentcode": "70Exx",
	"level": 3
}, {
	"code": "70E60",
	"title": " Robot dynamics and control [See also 68T40, 70Q05, 93C85]",
	"parentcode": "70Exx",
	"level": 3
}, {
	"code": "70E99",
	"title": " None of the above, but in this section",
	"parentcode": "70Exx",
	"level": 3
}, {
	"code": "70Fxx",
	"title": " Dynamics of a system of particles, including celestial mechanics",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70F05",
	"title": " Two-body problems",
	"parentcode": "70Fxx",
	"level": 3
}, {
	"code": "70F07",
	"title": " Three-body problems",
	"parentcode": "70Fxx",
	"level": 3
}, {
	"code": "70F10",
	"title": " $n$-body problems",
	"parentcode": "70Fxx",
	"level": 3
}, {
	"code": "70F15",
	"title": " Celestial mechanics",
	"parentcode": "70Fxx",
	"level": 3
}, {
	"code": "70F16",
	"title": " Collisions in celestial mechanics, regularization",
	"parentcode": "70Fxx",
	"level": 3
}, {
	"code": "70F17",
	"title": " Inverse problems",
	"parentcode": "70Fxx",
	"level": 3
}, {
	"code": "70F20",
	"title": " Holonomic systems",
	"parentcode": "70Fxx",
	"level": 3
}, {
	"code": "70F25",
	"title": " Nonholonomic systems",
	"parentcode": "70Fxx",
	"level": 3
}, {
	"code": "70F35",
	"title": " Collision of rigid or pseudo-rigid bodies",
	"parentcode": "70Fxx",
	"level": 3
}, {
	"code": "70F40",
	"title": " Problems with friction",
	"parentcode": "70Fxx",
	"level": 3
}, {
	"code": "70F45",
	"title": " Infinite particle systems",
	"parentcode": "70Fxx",
	"level": 3
}, {
	"code": "70F99",
	"title": " None of the above, but in this section",
	"parentcode": "70Fxx",
	"level": 3
}, {
	"code": "70Gxx",
	"title": " General models, approaches, and methods [See also 37-XX]",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70G10",
	"title": " Generalized coordinates; event, impulse-energy, configuration, state, or phase space",
	"parentcode": "70Gxx",
	"level": 3
}, {
	"code": "70G40",
	"title": " Topological and differential-topological methods",
	"parentcode": "70Gxx",
	"level": 3
}, {
	"code": "70G45",
	"title": " Differential-geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) [See also 53Cxx, 53Dxx, 58Axx]",
	"parentcode": "70Gxx",
	"level": 3
}, {
	"code": "70G55",
	"title": " Algebraic geometry methods",
	"parentcode": "70Gxx",
	"level": 3
}, {
	"code": "70G60",
	"title": " Dynamical systems methods",
	"parentcode": "70Gxx",
	"level": 3
}, {
	"code": "70G65",
	"title": " Symmetries, Lie-group and Lie-algebra methods",
	"parentcode": "70Gxx",
	"level": 3
}, {
	"code": "70G70",
	"title": " Functional-analytic methods",
	"parentcode": "70Gxx",
	"level": 3
}, {
	"code": "70G75",
	"title": " Variational methods",
	"parentcode": "70Gxx",
	"level": 3
}, {
	"code": "70G99",
	"title": " None of the above, but in this section",
	"parentcode": "70Gxx",
	"level": 3
}, {
	"code": "70Hxx",
	"title": " Hamiltonian and Lagrangian mechanics [See also 37Jxx]",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70H03",
	"title": " Lagrange's equations",
	"parentcode": "70Hxx",
	"level": 3
}, {
	"code": "70H05",
	"title": " Hamilton's equations",
	"parentcode": "70Hxx",
	"level": 3
}, {
	"code": "70H06",
	"title": " Completely integrable systems and methods of integration",
	"parentcode": "70Hxx",
	"level": 3
}, {
	"code": "70H07",
	"title": " Nonintegrable systems",
	"parentcode": "70Hxx",
	"level": 3
}, {
	"code": "70H08",
	"title": " Nearly integrable Hamiltonian systems, KAM theory",
	"parentcode": "70Hxx",
	"level": 3
}, {
	"code": "70H09",
	"title": " Perturbation theories",
	"parentcode": "70Hxx",
	"level": 3
}, {
	"code": "70H11",
	"title": " Adiabatic invariants",
	"parentcode": "70Hxx",
	"level": 3
}, {
	"code": "70H12",
	"title": " Periodic and almost periodic solutions",
	"parentcode": "70Hxx",
	"level": 3
}, {
	"code": "70H14",
	"title": " Stability problems",
	"parentcode": "70Hxx",
	"level": 3
}, {
	"code": "70H15",
	"title": " Canonical and symplectic transformations",
	"parentcode": "70Hxx",
	"level": 3
}, {
	"code": "70H20",
	"title": " Hamilton-Jacobi equations",
	"parentcode": "70Hxx",
	"level": 3
}, {
	"code": "70H25",
	"title": " Hamilton's principle",
	"parentcode": "70Hxx",
	"level": 3
}, {
	"code": "70H30",
	"title": " Other variational principles",
	"parentcode": "70Hxx",
	"level": 3
}, {
	"code": "70H33",
	"title": " Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction",
	"parentcode": "70Hxx",
	"level": 3
}, {
	"code": "70H40",
	"title": " Relativistic dynamics",
	"parentcode": "70Hxx",
	"level": 3
}, {
	"code": "70H45",
	"title": " Constrained dynamics, Dirac's theory of constraints [See also 70F20, 70F25, 70Gxx]",
	"parentcode": "70Hxx",
	"level": 3
}, {
	"code": "70H50",
	"title": " Higher-order theories",
	"parentcode": "70Hxx",
	"level": 3
}, {
	"code": "70H99",
	"title": " None of the above, but in this section",
	"parentcode": "70Hxx",
	"level": 3
}, {
	"code": "70Jxx",
	"title": " Linear vibration theory",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70J10",
	"title": " Modal analysis",
	"parentcode": "70Jxx",
	"level": 3
}, {
	"code": "70J25",
	"title": " Stability",
	"parentcode": "70Jxx",
	"level": 3
}, {
	"code": "70J30",
	"title": " Free motions",
	"parentcode": "70Jxx",
	"level": 3
}, {
	"code": "70J35",
	"title": " Forced motions",
	"parentcode": "70Jxx",
	"level": 3
}, {
	"code": "70J40",
	"title": " Parametric resonances",
	"parentcode": "70Jxx",
	"level": 3
}, {
	"code": "70J50",
	"title": " Systems arising from the discretization of structural vibration problems",
	"parentcode": "70Jxx",
	"level": 3
}, {
	"code": "70J99",
	"title": " None of the above, but in this section",
	"parentcode": "70Jxx",
	"level": 3
}, {
	"code": "70Kxx",
	"title": " Nonlinear dynamics [See also 34Cxx, 37-XX]",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70K05",
	"title": " Phase plane analysis, limit cycles",
	"parentcode": "70Kxx",
	"level": 3
}, {
	"code": "70K20",
	"title": " Stability",
	"parentcode": "70Kxx",
	"level": 3
}, {
	"code": "70K25",
	"title": " Free motions",
	"parentcode": "70Kxx",
	"level": 3
}, {
	"code": "70K28",
	"title": " Parametric resonances",
	"parentcode": "70Kxx",
	"level": 3
}, {
	"code": "70K30",
	"title": " Nonlinear resonances",
	"parentcode": "70Kxx",
	"level": 3
}, {
	"code": "70K40",
	"title": " Forced motions",
	"parentcode": "70Kxx",
	"level": 3
}, {
	"code": "70K42",
	"title": " Equilibria and periodic trajectories",
	"parentcode": "70Kxx",
	"level": 3
}, {
	"code": "70K43",
	"title": " Quasi-periodic motions and invariant tori",
	"parentcode": "70Kxx",
	"level": 3
}, {
	"code": "70K44",
	"title": " Homoclinic and heteroclinic trajectories",
	"parentcode": "70Kxx",
	"level": 3
}, {
	"code": "70K45",
	"title": " Normal forms",
	"parentcode": "70Kxx",
	"level": 3
}, {
	"code": "70K50",
	"title": " Bifurcations and instability",
	"parentcode": "70Kxx",
	"level": 3
}, {
	"code": "70K55",
	"title": " Transition to stochasticity (chaotic behavior) [See also 37D45]",
	"parentcode": "70Kxx",
	"level": 3
}, {
	"code": "70K60",
	"title": " General perturbation schemes",
	"parentcode": "70Kxx",
	"level": 3
}, {
	"code": "70K65",
	"title": " Averaging of perturbations",
	"parentcode": "70Kxx",
	"level": 3
}, {
	"code": "70K70",
	"title": " Systems with slow and fast motions",
	"parentcode": "70Kxx",
	"level": 3
}, {
	"code": "70K75",
	"title": " Nonlinear modes",
	"parentcode": "70Kxx",
	"level": 3
}, {
	"code": "70K99",
	"title": " None of the above, but in this section",
	"parentcode": "70Kxx",
	"level": 3
}, {
	"code": "70Lxx",
	"title": " Random vibrations [See also 74H50]",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70L05",
	"title": " Random vibrations [See also 74H50]",
	"parentcode": "70Lxx",
	"level": 3
}, {
	"code": "70L99",
	"title": " None of the above, but in this section",
	"parentcode": "70Lxx",
	"level": 3
}, {
	"code": "70Mxx",
	"title": " Orbital mechanics",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70M20",
	"title": " Orbital mechanics",
	"parentcode": "70Mxx",
	"level": 3
}, {
	"code": "70M99",
	"title": " None of the above, but in this section",
	"parentcode": "70Mxx",
	"level": 3
}, {
	"code": "70Pxx",
	"title": " Variable mass, rockets",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70P05",
	"title": " Variable mass, rockets",
	"parentcode": "70Pxx",
	"level": 3
}, {
	"code": "70P99",
	"title": " None of the above, but in this section",
	"parentcode": "70Pxx",
	"level": 3
}, {
	"code": "70Qxx",
	"title": " Control of mechanical systems [See also 60Gxx, 60Jxx]",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70Q05",
	"title": " Control of mechanical systems",
	"parentcode": "70Qxx",
	"level": 3
}, {
	"code": "70Q99",
	"title": " None of the above, but in this section",
	"parentcode": "70Qxx",
	"level": 3
}, {
	"code": "70Sxx",
	"title": " Classical field theories [See also 37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX]",
	"parentcode": "70-XX",
	"level": 2
}, {
	"code": "70S05",
	"title": " Lagrangian formalism and Hamiltonian formalism",
	"parentcode": "70Sxx",
	"level": 3
}, {
	"code": "70S10",
	"title": " Symmetries and conservation laws",
	"parentcode": "70Sxx",
	"level": 3
}, {
	"code": "70S15",
	"title": " Yang-Mills and other gauge theories",
	"parentcode": "70Sxx",
	"level": 3
}, {
	"code": "70S20",
	"title": " More general nonquantum field theories",
	"parentcode": "70Sxx",
	"level": 3
}, {
	"code": "70S99",
	"title": " None of the above, but in this section",
	"parentcode": "70Sxx",
	"level": 3
}, {
	"code": "74-XX",
	"title": " Mechanics of deformable solids",
	"parentcode": null,
	"level": 1
}, {
	"code": "74-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74-05",
	"title": " Experimental work",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74Axx",
	"title": " Generalities, axiomatics, foundations of continuum mechanics of solids",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74A05",
	"title": " Kinematics of deformation",
	"parentcode": "74Axx",
	"level": 3
}, {
	"code": "74A10",
	"title": " Stress",
	"parentcode": "74Axx",
	"level": 3
}, {
	"code": "74A15",
	"title": " Thermodynamics",
	"parentcode": "74Axx",
	"level": 3
}, {
	"code": "74A20",
	"title": " Theory of constitutive functions",
	"parentcode": "74Axx",
	"level": 3
}, {
	"code": "74A25",
	"title": " Molecular, statistical, and kinetic theories",
	"parentcode": "74Axx",
	"level": 3
}, {
	"code": "74A30",
	"title": " Nonsimple materials",
	"parentcode": "74Axx",
	"level": 3
}, {
	"code": "74A35",
	"title": " Polar materials",
	"parentcode": "74Axx",
	"level": 3
}, {
	"code": "74A40",
	"title": " Random materials and composite materials",
	"parentcode": "74Axx",
	"level": 3
}, {
	"code": "74A45",
	"title": " Theories of fracture and damage",
	"parentcode": "74Axx",
	"level": 3
}, {
	"code": "74A50",
	"title": " Structured surfaces and interfaces, coexistent phases",
	"parentcode": "74Axx",
	"level": 3
}, {
	"code": "74A55",
	"title": " Theories of friction (tribology)",
	"parentcode": "74Axx",
	"level": 3
}, {
	"code": "74A60",
	"title": " Micromechanical theories",
	"parentcode": "74Axx",
	"level": 3
}, {
	"code": "74A65",
	"title": " Reactive materials",
	"parentcode": "74Axx",
	"level": 3
}, {
	"code": "74A99",
	"title": " None of the above, but in this section",
	"parentcode": "74Axx",
	"level": 3
}, {
	"code": "74Bxx",
	"title": " Elastic materials",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74B05",
	"title": " Classical linear elasticity",
	"parentcode": "74Bxx",
	"level": 3
}, {
	"code": "74B10",
	"title": " Linear elasticity with initial stresses",
	"parentcode": "74Bxx",
	"level": 3
}, {
	"code": "74B15",
	"title": " Equations linearized about a deformed state (small deformations superposed on large)",
	"parentcode": "74Bxx",
	"level": 3
}, {
	"code": "74B20",
	"title": " Nonlinear elasticity",
	"parentcode": "74Bxx",
	"level": 3
}, {
	"code": "74B99",
	"title": " None of the above, but in this section",
	"parentcode": "74Bxx",
	"level": 3
}, {
	"code": "74Cxx",
	"title": " Plastic materials, materials of stress-rate and internal-variable type",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74C05",
	"title": " Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials)",
	"parentcode": "74Cxx",
	"level": 3
}, {
	"code": "74C10",
	"title": " Small-strain, rate-dependent theories (including theories of viscoplasticity)",
	"parentcode": "74Cxx",
	"level": 3
}, {
	"code": "74C15",
	"title": " Large-strain, rate-independent theories (including nonlinear plasticity)",
	"parentcode": "74Cxx",
	"level": 3
}, {
	"code": "74C20",
	"title": " Large-strain, rate-dependent theories",
	"parentcode": "74Cxx",
	"level": 3
}, {
	"code": "74C99",
	"title": " None of the above, but in this section",
	"parentcode": "74Cxx",
	"level": 3
}, {
	"code": "74Dxx",
	"title": " Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74D05",
	"title": " Linear constitutive equations",
	"parentcode": "74Dxx",
	"level": 3
}, {
	"code": "74D10",
	"title": " Nonlinear constitutive equations",
	"parentcode": "74Dxx",
	"level": 3
}, {
	"code": "74D99",
	"title": " None of the above, but in this section",
	"parentcode": "74Dxx",
	"level": 3
}, {
	"code": "74Exx",
	"title": " Material properties given special treatment",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74E05",
	"title": " Inhomogeneity",
	"parentcode": "74Exx",
	"level": 3
}, {
	"code": "74E10",
	"title": " Anisotropy",
	"parentcode": "74Exx",
	"level": 3
}, {
	"code": "74E15",
	"title": " Crystalline structure",
	"parentcode": "74Exx",
	"level": 3
}, {
	"code": "74E20",
	"title": " Granularity",
	"parentcode": "74Exx",
	"level": 3
}, {
	"code": "74E25",
	"title": " Texture",
	"parentcode": "74Exx",
	"level": 3
}, {
	"code": "74E30",
	"title": " Composite and mixture properties",
	"parentcode": "74Exx",
	"level": 3
}, {
	"code": "74E35",
	"title": " Random structure",
	"parentcode": "74Exx",
	"level": 3
}, {
	"code": "74E40",
	"title": " Chemical structure",
	"parentcode": "74Exx",
	"level": 3
}, {
	"code": "74E99",
	"title": " None of the above, but in this section",
	"parentcode": "74Exx",
	"level": 3
}, {
	"code": "74Fxx",
	"title": " Coupling of solid mechanics with other effects",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74F05",
	"title": " Thermal effects",
	"parentcode": "74Fxx",
	"level": 3
}, {
	"code": "74F10",
	"title": " Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)",
	"parentcode": "74Fxx",
	"level": 3
}, {
	"code": "74F15",
	"title": " Electromagnetic effects",
	"parentcode": "74Fxx",
	"level": 3
}, {
	"code": "74F20",
	"title": " Mixture effects",
	"parentcode": "74Fxx",
	"level": 3
}, {
	"code": "74F25",
	"title": " Chemical and reactive effects",
	"parentcode": "74Fxx",
	"level": 3
}, {
	"code": "74F99",
	"title": " None of the above, but in this section",
	"parentcode": "74Fxx",
	"level": 3
}, {
	"code": "74Gxx",
	"title": " Equilibrium (steady-state) problems",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74G05",
	"title": " Explicit solutions",
	"parentcode": "74Gxx",
	"level": 3
}, {
	"code": "74G10",
	"title": " Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)",
	"parentcode": "74Gxx",
	"level": 3
}, {
	"code": "74G15",
	"title": " Numerical approximation of solutions",
	"parentcode": "74Gxx",
	"level": 3
}, {
	"code": "74G20",
	"title": " Local existence of solutions (near a given solution)",
	"parentcode": "74Gxx",
	"level": 3
}, {
	"code": "74G25",
	"title": " Global existence of solutions",
	"parentcode": "74Gxx",
	"level": 3
}, {
	"code": "74G30",
	"title": " Uniqueness of solutions",
	"parentcode": "74Gxx",
	"level": 3
}, {
	"code": "74G35",
	"title": " Multiplicity of solutions",
	"parentcode": "74Gxx",
	"level": 3
}, {
	"code": "74G40",
	"title": " Regularity of solutions",
	"parentcode": "74Gxx",
	"level": 3
}, {
	"code": "74G45",
	"title": " Bounds for solutions",
	"parentcode": "74Gxx",
	"level": 3
}, {
	"code": "74G50",
	"title": " Saint-Venant's principle",
	"parentcode": "74Gxx",
	"level": 3
}, {
	"code": "74G55",
	"title": " Qualitative behavior of solutions",
	"parentcode": "74Gxx",
	"level": 3
}, {
	"code": "74G60",
	"title": " Bifurcation and buckling",
	"parentcode": "74Gxx",
	"level": 3
}, {
	"code": "74G65",
	"title": " Energy minimization",
	"parentcode": "74Gxx",
	"level": 3
}, {
	"code": "74G70",
	"title": " Stress concentrations, singularities",
	"parentcode": "74Gxx",
	"level": 3
}, {
	"code": "74G75",
	"title": " Inverse problems",
	"parentcode": "74Gxx",
	"level": 3
}, {
	"code": "74G99",
	"title": " None of the above, but in this section",
	"parentcode": "74Gxx",
	"level": 3
}, {
	"code": "74Hxx",
	"title": " Dynamical problems",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74H05",
	"title": " Explicit solutions",
	"parentcode": "74Hxx",
	"level": 3
}, {
	"code": "74H10",
	"title": " Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)",
	"parentcode": "74Hxx",
	"level": 3
}, {
	"code": "74H15",
	"title": " Numerical approximation of solutions",
	"parentcode": "74Hxx",
	"level": 3
}, {
	"code": "74H20",
	"title": " Existence of solutions",
	"parentcode": "74Hxx",
	"level": 3
}, {
	"code": "74H25",
	"title": " Uniqueness of solutions",
	"parentcode": "74Hxx",
	"level": 3
}, {
	"code": "74H30",
	"title": " Regularity of solutions",
	"parentcode": "74Hxx",
	"level": 3
}, {
	"code": "74H35",
	"title": " Singularities, blowup, stress concentrations",
	"parentcode": "74Hxx",
	"level": 3
}, {
	"code": "74H40",
	"title": " Long-time behavior of solutions",
	"parentcode": "74Hxx",
	"level": 3
}, {
	"code": "74H45",
	"title": " Vibrations",
	"parentcode": "74Hxx",
	"level": 3
}, {
	"code": "74H50",
	"title": " Random vibrations",
	"parentcode": "74Hxx",
	"level": 3
}, {
	"code": "74H55",
	"title": " Stability",
	"parentcode": "74Hxx",
	"level": 3
}, {
	"code": "74H60",
	"title": " Dynamical bifurcation",
	"parentcode": "74Hxx",
	"level": 3
}, {
	"code": "74H65",
	"title": " Chaotic behavior",
	"parentcode": "74Hxx",
	"level": 3
}, {
	"code": "74H99",
	"title": " None of the above, but in this section",
	"parentcode": "74Hxx",
	"level": 3
}, {
	"code": "74Jxx",
	"title": " Waves",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74J05",
	"title": " Linear waves",
	"parentcode": "74Jxx",
	"level": 3
}, {
	"code": "74J10",
	"title": " Bulk waves",
	"parentcode": "74Jxx",
	"level": 3
}, {
	"code": "74J15",
	"title": " Surface waves",
	"parentcode": "74Jxx",
	"level": 3
}, {
	"code": "74J20",
	"title": " Wave scattering",
	"parentcode": "74Jxx",
	"level": 3
}, {
	"code": "74J25",
	"title": " Inverse problems",
	"parentcode": "74Jxx",
	"level": 3
}, {
	"code": "74J30",
	"title": " Nonlinear waves",
	"parentcode": "74Jxx",
	"level": 3
}, {
	"code": "74J35",
	"title": " Solitary waves",
	"parentcode": "74Jxx",
	"level": 3
}, {
	"code": "74J40",
	"title": " Shocks and related discontinuities",
	"parentcode": "74Jxx",
	"level": 3
}, {
	"code": "74J99",
	"title": " None of the above, but in this section",
	"parentcode": "74Jxx",
	"level": 3
}, {
	"code": "74Kxx",
	"title": " Thin bodies, structures",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74K05",
	"title": " Strings",
	"parentcode": "74Kxx",
	"level": 3
}, {
	"code": "74K10",
	"title": " Rods (beams, columns, shafts, arches, rings, etc.)",
	"parentcode": "74Kxx",
	"level": 3
}, {
	"code": "74K15",
	"title": " Membranes",
	"parentcode": "74Kxx",
	"level": 3
}, {
	"code": "74K20",
	"title": " Plates",
	"parentcode": "74Kxx",
	"level": 3
}, {
	"code": "74K25",
	"title": " Shells",
	"parentcode": "74Kxx",
	"level": 3
}, {
	"code": "74K30",
	"title": " Junctions",
	"parentcode": "74Kxx",
	"level": 3
}, {
	"code": "74K35",
	"title": " Thin films",
	"parentcode": "74Kxx",
	"level": 3
}, {
	"code": "74K99",
	"title": " None of the above, but in this section",
	"parentcode": "74Kxx",
	"level": 3
}, {
	"code": "74Lxx",
	"title": " Special subfields of solid mechanics",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74L05",
	"title": " Geophysical solid mechanics [See also 86-XX]",
	"parentcode": "74Lxx",
	"level": 3
}, {
	"code": "74L10",
	"title": " Soil and rock mechanics",
	"parentcode": "74Lxx",
	"level": 3
}, {
	"code": "74L15",
	"title": " Biomechanical solid mechanics [See also 92C10]",
	"parentcode": "74Lxx",
	"level": 3
}, {
	"code": "74L99",
	"title": " None of the above, but in this section",
	"parentcode": "74Lxx",
	"level": 3
}, {
	"code": "74Mxx",
	"title": " Special kinds of problems",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74M05",
	"title": " Control, switches and devices (“smart materials”) [See also 93Cxx]",
	"parentcode": "74Mxx",
	"level": 3
}, {
	"code": "74M10",
	"title": " Friction",
	"parentcode": "74Mxx",
	"level": 3
}, {
	"code": "74M15",
	"title": " Contact",
	"parentcode": "74Mxx",
	"level": 3
}, {
	"code": "74M20",
	"title": " Impact",
	"parentcode": "74Mxx",
	"level": 3
}, {
	"code": "74M25",
	"title": " Micromechanics",
	"parentcode": "74Mxx",
	"level": 3
}, {
	"code": "74M99",
	"title": " None of the above, but in this section",
	"parentcode": "74Mxx",
	"level": 3
}, {
	"code": "74Nxx",
	"title": " Phase transformations in solids [See also 74A50, 80Axx, 82B26, 82C26]",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74N05",
	"title": " Crystals",
	"parentcode": "74Nxx",
	"level": 3
}, {
	"code": "74N10",
	"title": " Displacive transformations",
	"parentcode": "74Nxx",
	"level": 3
}, {
	"code": "74N15",
	"title": " Analysis of microstructure",
	"parentcode": "74Nxx",
	"level": 3
}, {
	"code": "74N20",
	"title": " Dynamics of phase boundaries",
	"parentcode": "74Nxx",
	"level": 3
}, {
	"code": "74N25",
	"title": " Transformations involving diffusion",
	"parentcode": "74Nxx",
	"level": 3
}, {
	"code": "74N30",
	"title": " Problems involving hysteresis",
	"parentcode": "74Nxx",
	"level": 3
}, {
	"code": "74N99",
	"title": " None of the above, but in this section",
	"parentcode": "74Nxx",
	"level": 3
}, {
	"code": "74Pxx",
	"title": " Optimization [See also 49Qxx]",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74P05",
	"title": " Compliance or weight optimization",
	"parentcode": "74Pxx",
	"level": 3
}, {
	"code": "74P10",
	"title": " Optimization of other properties",
	"parentcode": "74Pxx",
	"level": 3
}, {
	"code": "74P15",
	"title": " Topological methods",
	"parentcode": "74Pxx",
	"level": 3
}, {
	"code": "74P20",
	"title": " Geometrical methods",
	"parentcode": "74Pxx",
	"level": 3
}, {
	"code": "74P99",
	"title": " None of the above, but in this section",
	"parentcode": "74Pxx",
	"level": 3
}, {
	"code": "74Qxx",
	"title": " Homogenization, determination of effective properties",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74Q05",
	"title": " Homogenization in equilibrium problems",
	"parentcode": "74Qxx",
	"level": 3
}, {
	"code": "74Q10",
	"title": " Homogenization and oscillations in dynamical problems",
	"parentcode": "74Qxx",
	"level": 3
}, {
	"code": "74Q15",
	"title": " Effective constitutive equations",
	"parentcode": "74Qxx",
	"level": 3
}, {
	"code": "74Q20",
	"title": " Bounds on effective properties",
	"parentcode": "74Qxx",
	"level": 3
}, {
	"code": "74Q99",
	"title": " None of the above, but in this section",
	"parentcode": "74Qxx",
	"level": 3
}, {
	"code": "74Rxx",
	"title": " Fracture and damage",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74R05",
	"title": " Brittle damage",
	"parentcode": "74Rxx",
	"level": 3
}, {
	"code": "74R10",
	"title": " Brittle fracture",
	"parentcode": "74Rxx",
	"level": 3
}, {
	"code": "74R15",
	"title": " High-velocity fracture",
	"parentcode": "74Rxx",
	"level": 3
}, {
	"code": "74R20",
	"title": " Anelastic fracture and damage",
	"parentcode": "74Rxx",
	"level": 3
}, {
	"code": "74R99",
	"title": " None of the above, but in this section",
	"parentcode": "74Rxx",
	"level": 3
}, {
	"code": "74Sxx",
	"title": " Numerical methods [See also 65-XX, 74G15, 74H15]",
	"parentcode": "74-XX",
	"level": 2
}, {
	"code": "74S05",
	"title": " Finite element methods",
	"parentcode": "74Sxx",
	"level": 3
}, {
	"code": "74S10",
	"title": " Finite volume methods",
	"parentcode": "74Sxx",
	"level": 3
}, {
	"code": "74S15",
	"title": " Boundary element methods",
	"parentcode": "74Sxx",
	"level": 3
}, {
	"code": "74S20",
	"title": " Finite difference methods",
	"parentcode": "74Sxx",
	"level": 3
}, {
	"code": "74S25",
	"title": " Spectral and related methods",
	"parentcode": "74Sxx",
	"level": 3
}, {
	"code": "74S30",
	"title": " Other numerical methods",
	"parentcode": "74Sxx",
	"level": 3
}, {
	"code": "74S60",
	"title": " Stochastic methods",
	"parentcode": "74Sxx",
	"level": 3
}, {
	"code": "74S70",
	"title": " Complex variable methods",
	"parentcode": "74Sxx",
	"level": 3
}, {
	"code": "74S99",
	"title": " None of the above, but in this section",
	"parentcode": "74Sxx",
	"level": 3
}, {
	"code": "76-XX",
	"title": " Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX}",
	"parentcode": null,
	"level": 1
}, {
	"code": "76-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76-05",
	"title": " Experimental work",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76Axx",
	"title": " Foundations, constitutive equations, rheology",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76A02",
	"title": " Foundations of fluid mechanics",
	"parentcode": "76Axx",
	"level": 3
}, {
	"code": "76A05",
	"title": " Non-Newtonian fluids",
	"parentcode": "76Axx",
	"level": 3
}, {
	"code": "76A10",
	"title": " Viscoelastic fluids",
	"parentcode": "76Axx",
	"level": 3
}, {
	"code": "76A15",
	"title": " Liquid crystals [See also 82D30]",
	"parentcode": "76Axx",
	"level": 3
}, {
	"code": "76A20",
	"title": " Thin fluid films",
	"parentcode": "76Axx",
	"level": 3
}, {
	"code": "76A25",
	"title": " Superfluids (classical aspects)",
	"parentcode": "76Axx",
	"level": 3
}, {
	"code": "76A99",
	"title": " None of the above, but in this section",
	"parentcode": "76Axx",
	"level": 3
}, {
	"code": "76Bxx",
	"title": " Incompressible inviscid fluids",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76B03",
	"title": " Existence, uniqueness, and regularity theory [See also 35Q35]",
	"parentcode": "76Bxx",
	"level": 3
}, {
	"code": "76B07",
	"title": " Free-surface potential flows",
	"parentcode": "76Bxx",
	"level": 3
}, {
	"code": "76B10",
	"title": " Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing",
	"parentcode": "76Bxx",
	"level": 3
}, {
	"code": "76B15",
	"title": " Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30]",
	"parentcode": "76Bxx",
	"level": 3
}, {
	"code": "76B20",
	"title": " Ship waves",
	"parentcode": "76Bxx",
	"level": 3
}, {
	"code": "76B25",
	"title": " Solitary waves [See also 35C11]",
	"parentcode": "76Bxx",
	"level": 3
}, {
	"code": "76B45",
	"title": " Capillarity (surface tension) [See also 76D45]",
	"parentcode": "76Bxx",
	"level": 3
}, {
	"code": "76B47",
	"title": " Vortex flows",
	"parentcode": "76Bxx",
	"level": 3
}, {
	"code": "76B55",
	"title": " Internal waves",
	"parentcode": "76Bxx",
	"level": 3
}, {
	"code": "76B60",
	"title": " Atmospheric waves [See also 86A10]",
	"parentcode": "76Bxx",
	"level": 3
}, {
	"code": "76B65",
	"title": " Rossby waves [See also 86A05, 86A10]",
	"parentcode": "76Bxx",
	"level": 3
}, {
	"code": "76B70",
	"title": " Stratification effects in inviscid fluids",
	"parentcode": "76Bxx",
	"level": 3
}, {
	"code": "76B75",
	"title": " Flow control and optimization [See also 49Q10, 93C20, 93C95]",
	"parentcode": "76Bxx",
	"level": 3
}, {
	"code": "76B99",
	"title": " None of the above, but in this section",
	"parentcode": "76Bxx",
	"level": 3
}, {
	"code": "76Dxx",
	"title": " Incompressible viscous fluids",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76D03",
	"title": " Existence, uniqueness, and regularity theory [See also 35Q30]",
	"parentcode": "76Dxx",
	"level": 3
}, {
	"code": "76D05",
	"title": " Navier-Stokes equations [See also 35Q30]",
	"parentcode": "76Dxx",
	"level": 3
}, {
	"code": "76D06",
	"title": " Statistical solutions of Navier-Stokes and related equations [See also 60H30, 76M35]",
	"parentcode": "76Dxx",
	"level": 3
}, {
	"code": "76D07",
	"title": " Stokes and related (Oseen, etc.) flows",
	"parentcode": "76Dxx",
	"level": 3
}, {
	"code": "76D08",
	"title": " Lubrication theory",
	"parentcode": "76Dxx",
	"level": 3
}, {
	"code": "76D09",
	"title": " Viscous-inviscid interaction",
	"parentcode": "76Dxx",
	"level": 3
}, {
	"code": "76D10",
	"title": " Boundary-layer theory, separation and reattachment, higher-order effects",
	"parentcode": "76Dxx",
	"level": 3
}, {
	"code": "76D17",
	"title": " Viscous vortex flows",
	"parentcode": "76Dxx",
	"level": 3
}, {
	"code": "76D25",
	"title": " Wakes and jets",
	"parentcode": "76Dxx",
	"level": 3
}, {
	"code": "76D27",
	"title": " Other free-boundary flows; Hele-Shaw flows",
	"parentcode": "76Dxx",
	"level": 3
}, {
	"code": "76D33",
	"title": " Waves",
	"parentcode": "76Dxx",
	"level": 3
}, {
	"code": "76D45",
	"title": " Capillarity (surface tension) [See also 76B45]",
	"parentcode": "76Dxx",
	"level": 3
}, {
	"code": "76D50",
	"title": " Stratification effects in viscous fluids",
	"parentcode": "76Dxx",
	"level": 3
}, {
	"code": "76D55",
	"title": " Flow control and optimization [See also 49Q10, 93C20, 93C95]",
	"parentcode": "76Dxx",
	"level": 3
}, {
	"code": "76D99",
	"title": " None of the above, but in this section",
	"parentcode": "76Dxx",
	"level": 3
}, {
	"code": "76Exx",
	"title": " Hydrodynamic stability",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76E05",
	"title": " Parallel shear flows",
	"parentcode": "76Exx",
	"level": 3
}, {
	"code": "76E06",
	"title": " Convection",
	"parentcode": "76Exx",
	"level": 3
}, {
	"code": "76E07",
	"title": " Rotation",
	"parentcode": "76Exx",
	"level": 3
}, {
	"code": "76E09",
	"title": " Stability and instability of nonparallel flows",
	"parentcode": "76Exx",
	"level": 3
}, {
	"code": "76E15",
	"title": " Absolute and convective instability and stability",
	"parentcode": "76Exx",
	"level": 3
}, {
	"code": "76E17",
	"title": " Interfacial stability and instability",
	"parentcode": "76Exx",
	"level": 3
}, {
	"code": "76E19",
	"title": " Compressibility effects",
	"parentcode": "76Exx",
	"level": 3
}, {
	"code": "76E20",
	"title": " Stability and instability of geophysical and astrophysical flows",
	"parentcode": "76Exx",
	"level": 3
}, {
	"code": "76E25",
	"title": " Stability and instability of magnetohydrodynamic and electrohydrodynamic flows",
	"parentcode": "76Exx",
	"level": 3
}, {
	"code": "76E30",
	"title": " Nonlinear effects",
	"parentcode": "76Exx",
	"level": 3
}, {
	"code": "76E99",
	"title": " None of the above, but in this section",
	"parentcode": "76Exx",
	"level": 3
}, {
	"code": "76Fxx",
	"title": " Turbulence [See also 37-XX, 60Gxx, 60Jxx]",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76F02",
	"title": " Fundamentals",
	"parentcode": "76Fxx",
	"level": 3
}, {
	"code": "76F05",
	"title": " Isotropic turbulence; homogeneous turbulence",
	"parentcode": "76Fxx",
	"level": 3
}, {
	"code": "76F06",
	"title": " Transition to turbulence",
	"parentcode": "76Fxx",
	"level": 3
}, {
	"code": "76F10",
	"title": " Shear flows",
	"parentcode": "76Fxx",
	"level": 3
}, {
	"code": "76F20",
	"title": " Dynamical systems approach to turbulence [See also 37-XX]",
	"parentcode": "76Fxx",
	"level": 3
}, {
	"code": "76F25",
	"title": " Turbulent transport, mixing",
	"parentcode": "76Fxx",
	"level": 3
}, {
	"code": "76F30",
	"title": " Renormalization and other field-theoretical methods [See also 81T99]",
	"parentcode": "76Fxx",
	"level": 3
}, {
	"code": "76F35",
	"title": " Convective turbulence [See also 76E15, 76Rxx]",
	"parentcode": "76Fxx",
	"level": 3
}, {
	"code": "76F40",
	"title": " Turbulent boundary layers",
	"parentcode": "76Fxx",
	"level": 3
}, {
	"code": "76F45",
	"title": " Stratification effects",
	"parentcode": "76Fxx",
	"level": 3
}, {
	"code": "76F50",
	"title": " Compressibility effects",
	"parentcode": "76Fxx",
	"level": 3
}, {
	"code": "76F55",
	"title": " Statistical turbulence modeling [See also 76M35]",
	"parentcode": "76Fxx",
	"level": 3
}, {
	"code": "76F60",
	"title": " $k$-$\\varepsilon$ modeling",
	"parentcode": "76Fxx",
	"level": 3
}, {
	"code": "76F65",
	"title": " Direct numerical and large eddy simulation of turbulence",
	"parentcode": "76Fxx",
	"level": 3
}, {
	"code": "76F70",
	"title": " Control of turbulent flows",
	"parentcode": "76Fxx",
	"level": 3
}, {
	"code": "76F99",
	"title": " None of the above, but in this section",
	"parentcode": "76Fxx",
	"level": 3
}, {
	"code": "76Gxx",
	"title": " General aerodynamics and subsonic flows",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76G25",
	"title": " General aerodynamics and subsonic flows",
	"parentcode": "76Gxx",
	"level": 3
}, {
	"code": "76G99",
	"title": " None of the above, but in this section",
	"parentcode": "76Gxx",
	"level": 3
}, {
	"code": "76Hxx",
	"title": " Transonic flows",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76H05",
	"title": " Transonic flows",
	"parentcode": "76Hxx",
	"level": 3
}, {
	"code": "76H99",
	"title": " None of the above, but in this section",
	"parentcode": "76Hxx",
	"level": 3
}, {
	"code": "76Jxx",
	"title": " Supersonic flows",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76J20",
	"title": " Supersonic flows",
	"parentcode": "76Jxx",
	"level": 3
}, {
	"code": "76J99",
	"title": " None of the above, but in this section",
	"parentcode": "76Jxx",
	"level": 3
}, {
	"code": "76Kxx",
	"title": " Hypersonic flows",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76K05",
	"title": " Hypersonic flows",
	"parentcode": "76Kxx",
	"level": 3
}, {
	"code": "76K99",
	"title": " None of the above, but in this section",
	"parentcode": "76Kxx",
	"level": 3
}, {
	"code": "76Lxx",
	"title": " Shock waves and blast waves [See also 35L67]",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76L05",
	"title": " Shock waves and blast waves [See also 35L67]",
	"parentcode": "76Lxx",
	"level": 3
}, {
	"code": "76L99",
	"title": " None of the above, but in this section",
	"parentcode": "76Lxx",
	"level": 3
}, {
	"code": "76Mxx",
	"title": " Basic methods in fluid mechanics [See also 65-XX]",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76M10",
	"title": " Finite element methods",
	"parentcode": "76Mxx",
	"level": 3
}, {
	"code": "76M12",
	"title": " Finite volume methods",
	"parentcode": "76Mxx",
	"level": 3
}, {
	"code": "76M15",
	"title": " Boundary element methods",
	"parentcode": "76Mxx",
	"level": 3
}, {
	"code": "76M20",
	"title": " Finite difference methods",
	"parentcode": "76Mxx",
	"level": 3
}, {
	"code": "76M22",
	"title": " Spectral methods",
	"parentcode": "76Mxx",
	"level": 3
}, {
	"code": "76M23",
	"title": " Vortex methods",
	"parentcode": "76Mxx",
	"level": 3
}, {
	"code": "76M25",
	"title": " Other numerical methods",
	"parentcode": "76Mxx",
	"level": 3
}, {
	"code": "76M27",
	"title": " Visualization algorithms",
	"parentcode": "76Mxx",
	"level": 3
}, {
	"code": "76M28",
	"title": " Particle methods and lattice-gas methods",
	"parentcode": "76Mxx",
	"level": 3
}, {
	"code": "76M30",
	"title": " Variational methods",
	"parentcode": "76Mxx",
	"level": 3
}, {
	"code": "76M35",
	"title": " Stochastic analysis",
	"parentcode": "76Mxx",
	"level": 3
}, {
	"code": "76M40",
	"title": " Complex-variables methods",
	"parentcode": "76Mxx",
	"level": 3
}, {
	"code": "76M45",
	"title": " Asymptotic methods, singular perturbations",
	"parentcode": "76Mxx",
	"level": 3
}, {
	"code": "76M50",
	"title": " Homogenization",
	"parentcode": "76Mxx",
	"level": 3
}, {
	"code": "76M55",
	"title": " Dimensional analysis and similarity",
	"parentcode": "76Mxx",
	"level": 3
}, {
	"code": "76M60",
	"title": " Symmetry analysis, Lie group and algebra methods",
	"parentcode": "76Mxx",
	"level": 3
}, {
	"code": "76M99",
	"title": " None of the above, but in this section",
	"parentcode": "76Mxx",
	"level": 3
}, {
	"code": "76Nxx",
	"title": " Compressible fluids and gas dynamics, general",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76N10",
	"title": " Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30]",
	"parentcode": "76Nxx",
	"level": 3
}, {
	"code": "76N15",
	"title": " Gas dynamics, general",
	"parentcode": "76Nxx",
	"level": 3
}, {
	"code": "76N17",
	"title": " Viscous-inviscid interaction",
	"parentcode": "76Nxx",
	"level": 3
}, {
	"code": "76N20",
	"title": " Boundary-layer theory",
	"parentcode": "76Nxx",
	"level": 3
}, {
	"code": "76N25",
	"title": " Flow control and optimization",
	"parentcode": "76Nxx",
	"level": 3
}, {
	"code": "76N99",
	"title": " None of the above, but in this section",
	"parentcode": "76Nxx",
	"level": 3
}, {
	"code": "76Pxx",
	"title": " Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05]",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76P05",
	"title": " Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05]",
	"parentcode": "76Pxx",
	"level": 3
}, {
	"code": "76P99",
	"title": " None of the above, but in this section",
	"parentcode": "76Pxx",
	"level": 3
}, {
	"code": "76Qxx",
	"title": " Hydro- and aero-acoustics",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76Q05",
	"title": " Hydro- and aero-acoustics",
	"parentcode": "76Qxx",
	"level": 3
}, {
	"code": "76Q99",
	"title": " None of the above, but in this section",
	"parentcode": "76Qxx",
	"level": 3
}, {
	"code": "76Rxx",
	"title": " Diffusion and convection",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76R05",
	"title": " Forced convection",
	"parentcode": "76Rxx",
	"level": 3
}, {
	"code": "76R10",
	"title": " Free convection",
	"parentcode": "76Rxx",
	"level": 3
}, {
	"code": "76R50",
	"title": " Diffusion [See also 60J60]",
	"parentcode": "76Rxx",
	"level": 3
}, {
	"code": "76R99",
	"title": " None of the above, but in this section",
	"parentcode": "76Rxx",
	"level": 3
}, {
	"code": "76Sxx",
	"title": " Flows in porous media; filtration; seepage",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76S05",
	"title": " Flows in porous media; filtration; seepage",
	"parentcode": "76Sxx",
	"level": 3
}, {
	"code": "76S99",
	"title": " None of the above, but in this section",
	"parentcode": "76Sxx",
	"level": 3
}, {
	"code": "76Txx",
	"title": " Two-phase and multiphase flows",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76T10",
	"title": " Liquid-gas two-phase flows, bubbly flows",
	"parentcode": "76Txx",
	"level": 3
}, {
	"code": "76T15",
	"title": " Dusty-gas two-phase flows",
	"parentcode": "76Txx",
	"level": 3
}, {
	"code": "76T20",
	"title": " Suspensions",
	"parentcode": "76Txx",
	"level": 3
}, {
	"code": "76T25",
	"title": " Granular flows [See also 74C99, 74E20]",
	"parentcode": "76Txx",
	"level": 3
}, {
	"code": "76T30",
	"title": " Three or more component flows",
	"parentcode": "76Txx",
	"level": 3
}, {
	"code": "76T99",
	"title": " None of the above, but in this section",
	"parentcode": "76Txx",
	"level": 3
}, {
	"code": "76Uxx",
	"title": " Rotating fluids",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76U05",
	"title": " Rotating fluids",
	"parentcode": "76Uxx",
	"level": 3
}, {
	"code": "76U99",
	"title": " None of the above, but in this section",
	"parentcode": "76Uxx",
	"level": 3
}, {
	"code": "76Vxx",
	"title": " Reaction effects in flows [See also 80A32]",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76V05",
	"title": " Reaction effects in flows [See also 80A32]",
	"parentcode": "76Vxx",
	"level": 3
}, {
	"code": "76V99",
	"title": " None of the above, but in this section",
	"parentcode": "76Vxx",
	"level": 3
}, {
	"code": "76Wxx",
	"title": " Magnetohydrodynamics and electrohydrodynamics",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76W05",
	"title": " Magnetohydrodynamics and electrohydrodynamics",
	"parentcode": "76Wxx",
	"level": 3
}, {
	"code": "76W99",
	"title": " None of the above, but in this section",
	"parentcode": "76Wxx",
	"level": 3
}, {
	"code": "76Xxx",
	"title": " Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10]",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76X05",
	"title": " Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10]",
	"parentcode": "76Xxx",
	"level": 3
}, {
	"code": "76X99",
	"title": " None of the above, but in this section",
	"parentcode": "76Xxx",
	"level": 3
}, {
	"code": "76Yxx",
	"title": " Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30]",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76Y05",
	"title": " Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30]",
	"parentcode": "76Yxx",
	"level": 3
}, {
	"code": "76Y99",
	"title": " None of the above, but in this section",
	"parentcode": "76Yxx",
	"level": 3
}, {
	"code": "76Zxx",
	"title": " Biological fluid mechanics [See also 74F10, 74L15, 92Cxx]",
	"parentcode": "76-XX",
	"level": 2
}, {
	"code": "76Z05",
	"title": " Physiological flows [See also 92C35]",
	"parentcode": "76Zxx",
	"level": 3
}, {
	"code": "76Z10",
	"title": " Biopropulsion in water and in air",
	"parentcode": "76Zxx",
	"level": 3
}, {
	"code": "76Z99",
	"title": " None of the above, but in this section",
	"parentcode": "76Zxx",
	"level": 3
}, {
	"code": "78-XX",
	"title": " Optics, electromagnetic theory {For quantum optics, see 81V80}",
	"parentcode": null,
	"level": 1
}, {
	"code": "78-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "78-XX",
	"level": 2
}, {
	"code": "78-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "78-XX",
	"level": 2
}, {
	"code": "78-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "78-XX",
	"level": 2
}, {
	"code": "78-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "78-XX",
	"level": 2
}, {
	"code": "78-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "78-XX",
	"level": 2
}, {
	"code": "78-05",
	"title": " Experimental work",
	"parentcode": "78-XX",
	"level": 2
}, {
	"code": "78-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "78-XX",
	"level": 2
}, {
	"code": "78Axx",
	"title": " General",
	"parentcode": "78-XX",
	"level": 2
}, {
	"code": "78A02",
	"title": " Foundations",
	"parentcode": "78Axx",
	"level": 3
}, {
	"code": "78A05",
	"title": " Geometric optics",
	"parentcode": "78Axx",
	"level": 3
}, {
	"code": "78A10",
	"title": " Physical optics",
	"parentcode": "78Axx",
	"level": 3
}, {
	"code": "78A15",
	"title": " Electron optics",
	"parentcode": "78Axx",
	"level": 3
}, {
	"code": "78A20",
	"title": " Space charge waves",
	"parentcode": "78Axx",
	"level": 3
}, {
	"code": "78A25",
	"title": " Electromagnetic theory, general",
	"parentcode": "78Axx",
	"level": 3
}, {
	"code": "78A30",
	"title": " Electro- and magnetostatics",
	"parentcode": "78Axx",
	"level": 3
}, {
	"code": "78A35",
	"title": " Motion of charged particles",
	"parentcode": "78Axx",
	"level": 3
}, {
	"code": "78A37",
	"title": " Ion traps",
	"parentcode": "78Axx",
	"level": 3
}, {
	"code": "78A40",
	"title": " Waves and radiation",
	"parentcode": "78Axx",
	"level": 3
}, {
	"code": "78A45",
	"title": " Diffraction, scattering [See also 34E20 for WKB methods]",
	"parentcode": "78Axx",
	"level": 3
}, {
	"code": "78A46",
	"title": " Inverse scattering problems",
	"parentcode": "78Axx",
	"level": 3
}, {
	"code": "78A48",
	"title": " Composite media; random media",
	"parentcode": "78Axx",
	"level": 3
}, {
	"code": "78A50",
	"title": " Antennas, wave-guides",
	"parentcode": "78Axx",
	"level": 3
}, {
	"code": "78A55",
	"title": " Technical applications",
	"parentcode": "78Axx",
	"level": 3
}, {
	"code": "78A57",
	"title": " Electrochemistry",
	"parentcode": "78Axx",
	"level": 3
}, {
	"code": "78A60",
	"title": " Lasers, masers, optical bistability, nonlinear optics [See also 81V80]",
	"parentcode": "78Axx",
	"level": 3
}, {
	"code": "78A70",
	"title": " Biological applications [See also 91D30, 92C30]",
	"parentcode": "78Axx",
	"level": 3
}, {
	"code": "78A97",
	"title": " Mathematically heuristic optics and electromagnetic theory (must also be assigned at least one other classification number in this section)",
	"parentcode": "78Axx",
	"level": 3
}, {
	"code": "78A99",
	"title": " Miscellaneous topics",
	"parentcode": "78Axx",
	"level": 3
}, {
	"code": "78Mxx",
	"title": " Basic methods",
	"parentcode": "78-XX",
	"level": 2
}, {
	"code": "78M05",
	"title": " Method of moments",
	"parentcode": "78Mxx",
	"level": 3
}, {
	"code": "78M10",
	"title": " Finite element methods",
	"parentcode": "78Mxx",
	"level": 3
}, {
	"code": "78M12",
	"title": " Finite volume methods, finite integration techniques",
	"parentcode": "78Mxx",
	"level": 3
}, {
	"code": "78M15",
	"title": " Boundary element methods",
	"parentcode": "78Mxx",
	"level": 3
}, {
	"code": "78M16",
	"title": " Multipole methods",
	"parentcode": "78Mxx",
	"level": 3
}, {
	"code": "78M20",
	"title": " Finite difference methods",
	"parentcode": "78Mxx",
	"level": 3
}, {
	"code": "78M22",
	"title": " Spectral methods",
	"parentcode": "78Mxx",
	"level": 3
}, {
	"code": "78M25",
	"title": " Other numerical methods",
	"parentcode": "78Mxx",
	"level": 3
}, {
	"code": "78M30",
	"title": " Variational methods",
	"parentcode": "78Mxx",
	"level": 3
}, {
	"code": "78M31",
	"title": " Monte Carlo methods",
	"parentcode": "78Mxx",
	"level": 3
}, {
	"code": "78M32",
	"title": " Neural and heuristic methods",
	"parentcode": "78Mxx",
	"level": 3
}, {
	"code": "78M34",
	"title": " Model reduction",
	"parentcode": "78Mxx",
	"level": 3
}, {
	"code": "78M35",
	"title": " Asymptotic analysis",
	"parentcode": "78Mxx",
	"level": 3
}, {
	"code": "78M40",
	"title": " Homogenization",
	"parentcode": "78Mxx",
	"level": 3
}, {
	"code": "78M50",
	"title": " Optimization",
	"parentcode": "78Mxx",
	"level": 3
}, {
	"code": "78M99",
	"title": " None of the above, but in this section",
	"parentcode": "78Mxx",
	"level": 3
}, {
	"code": "80-XX",
	"title": " Classical thermodynamics, heat transfer {For thermodynamics of solids, see 74A15}",
	"parentcode": null,
	"level": 1
}, {
	"code": "80-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "80-XX",
	"level": 2
}, {
	"code": "80-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "80-XX",
	"level": 2
}, {
	"code": "80-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "80-XX",
	"level": 2
}, {
	"code": "80-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "80-XX",
	"level": 2
}, {
	"code": "80-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "80-XX",
	"level": 2
}, {
	"code": "80-05",
	"title": " Experimental work",
	"parentcode": "80-XX",
	"level": 2
}, {
	"code": "80-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "80-XX",
	"level": 2
}, {
	"code": "80Axx",
	"title": " Thermodynamics and heat transfer",
	"parentcode": "80-XX",
	"level": 2
}, {
	"code": "80A05",
	"title": " Foundations",
	"parentcode": "80Axx",
	"level": 3
}, {
	"code": "80A10",
	"title": " Classical thermodynamics, including relativistic",
	"parentcode": "80Axx",
	"level": 3
}, {
	"code": "80A17",
	"title": " Thermodynamics of continua [See also 74A15]",
	"parentcode": "80Axx",
	"level": 3
}, {
	"code": "80A20",
	"title": " Heat and mass transfer, heat flow",
	"parentcode": "80Axx",
	"level": 3
}, {
	"code": "80A22",
	"title": " Stefan problems, phase changes, etc. [See also 74Nxx]",
	"parentcode": "80Axx",
	"level": 3
}, {
	"code": "80A23",
	"title": " Inverse problems",
	"parentcode": "80Axx",
	"level": 3
}, {
	"code": "80A25",
	"title": " Combustion",
	"parentcode": "80Axx",
	"level": 3
}, {
	"code": "80A30",
	"title": " Chemical kinetics [See also 76V05, 92C45, 92E20]",
	"parentcode": "80Axx",
	"level": 3
}, {
	"code": "80A32",
	"title": " Chemically reacting flows [See also 92C45, 92E20]",
	"parentcode": "80Axx",
	"level": 3
}, {
	"code": "80A50",
	"title": " Chemistry (general) [See mainly 92Exx]",
	"parentcode": "80Axx",
	"level": 3
}, {
	"code": "80A99",
	"title": " None of the above, but in this section",
	"parentcode": "80Axx",
	"level": 3
}, {
	"code": "80Mxx",
	"title": " Basic methods",
	"parentcode": "80-XX",
	"level": 2
}, {
	"code": "80M10",
	"title": " Finite element methods",
	"parentcode": "80Mxx",
	"level": 3
}, {
	"code": "80M12",
	"title": " Finite volume methods",
	"parentcode": "80Mxx",
	"level": 3
}, {
	"code": "80M15",
	"title": " Boundary element methods",
	"parentcode": "80Mxx",
	"level": 3
}, {
	"code": "80M20",
	"title": " Finite difference methods",
	"parentcode": "80Mxx",
	"level": 3
}, {
	"code": "80M22",
	"title": " Spectral methods",
	"parentcode": "80Mxx",
	"level": 3
}, {
	"code": "80M25",
	"title": " Other numerical methods",
	"parentcode": "80Mxx",
	"level": 3
}, {
	"code": "80M30",
	"title": " Variational methods",
	"parentcode": "80Mxx",
	"level": 3
}, {
	"code": "80M31",
	"title": " Monte Carlo methods",
	"parentcode": "80Mxx",
	"level": 3
}, {
	"code": "80M35",
	"title": " Asymptotic analysis",
	"parentcode": "80Mxx",
	"level": 3
}, {
	"code": "80M40",
	"title": " Homogenization",
	"parentcode": "80Mxx",
	"level": 3
}, {
	"code": "80M50",
	"title": " Optimization",
	"parentcode": "80Mxx",
	"level": 3
}, {
	"code": "80M99",
	"title": " None of the above, but in this section",
	"parentcode": "80Mxx",
	"level": 3
}, {
	"code": "81-XX",
	"title": " Quantum theory",
	"parentcode": null,
	"level": 1
}, {
	"code": "81-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "81-XX",
	"level": 2
}, {
	"code": "81-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "81-XX",
	"level": 2
}, {
	"code": "81-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "81-XX",
	"level": 2
}, {
	"code": "81-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "81-XX",
	"level": 2
}, {
	"code": "81-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "81-XX",
	"level": 2
}, {
	"code": "81-05",
	"title": " Experimental papers",
	"parentcode": "81-XX",
	"level": 2
}, {
	"code": "81-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "81-XX",
	"level": 2
}, {
	"code": "81-08",
	"title": " Computational methods",
	"parentcode": "81-XX",
	"level": 2
}, {
	"code": "81Pxx",
	"title": " Axiomatics, foundations, philosophy",
	"parentcode": "81-XX",
	"level": 2
}, {
	"code": "81P05",
	"title": " General and philosophical",
	"parentcode": "81Pxx",
	"level": 3
}, {
	"code": "81P10",
	"title": " Logical foundations of quantum mechanics; quantum logic [See also 03G12, 06C15]",
	"parentcode": "81Pxx",
	"level": 3
}, {
	"code": "81P13",
	"title": " Contextuality",
	"parentcode": "81Pxx",
	"level": 3
}, {
	"code": "81P15",
	"title": " Quantum measurement theory",
	"parentcode": "81Pxx",
	"level": 3
}, {
	"code": "81P16",
	"title": " Quantum state spaces, operational and probabilistic concepts",
	"parentcode": "81Pxx",
	"level": 3
}, {
	"code": "81P20",
	"title": " Stochastic mechanics (including stochastic electrodynamics)",
	"parentcode": "81Pxx",
	"level": 3
}, {
	"code": "81P40",
	"title": " Quantum coherence, entanglement, quantum correlations",
	"parentcode": "81Pxx",
	"level": 3
}, {
	"code": "81P45",
	"title": " Quantum information, communication, networks [See also 94A15, 94A17]",
	"parentcode": "81Pxx",
	"level": 3
}, {
	"code": "81P50",
	"title": " Quantum state estimation, approximate cloning",
	"parentcode": "81Pxx",
	"level": 3
}, {
	"code": "81P68",
	"title": " Quantum computation  [See also 68Q05, 68Q12]",
	"parentcode": "81Pxx",
	"level": 3
}, {
	"code": "81P70",
	"title": " Quantum coding (general)",
	"parentcode": "81Pxx",
	"level": 3
}, {
	"code": "81P94",
	"title": " Quantum cryptography [See also 94A60]",
	"parentcode": "81Pxx",
	"level": 3
}, {
	"code": "81P99",
	"title": " None of the above, but in this section",
	"parentcode": "81Pxx",
	"level": 3
}, {
	"code": "81Qxx",
	"title": " General mathematical topics and methods in quantum theory",
	"parentcode": "81-XX",
	"level": 2
}, {
	"code": "81Q05",
	"title": " Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics",
	"parentcode": "81Qxx",
	"level": 3
}, {
	"code": "81Q10",
	"title": " Selfadjoint operator theory in quantum theory, including spectral analysis",
	"parentcode": "81Qxx",
	"level": 3
}, {
	"code": "81Q12",
	"title": " Non-selfadjoint operator theory in quantum theory",
	"parentcode": "81Qxx",
	"level": 3
}, {
	"code": "81Q15",
	"title": " Perturbation theories for operators and differential equations",
	"parentcode": "81Qxx",
	"level": 3
}, {
	"code": "81Q20",
	"title": " Semiclassical techniques, including WKB and Maslov methods",
	"parentcode": "81Qxx",
	"level": 3
}, {
	"code": "81Q30",
	"title": " Feynman integrals and graphs; applications of algebraic topology and algebraic geometry [See also 14D05, 32S40]",
	"parentcode": "81Qxx",
	"level": 3
}, {
	"code": "81Q35",
	"title": " Quantum mechanics on special spaces",
	"parentcode": "81Qxx",
	"level": 3
}, {
	"code": "81Q37",
	"title": " Quantum dots, waveguides, ratchets, etc.",
	"parentcode": "81Qxx",
	"level": 3
}, {
	"code": "81Q40",
	"title": " Bethe-Salpeter and other integral equations",
	"parentcode": "81Qxx",
	"level": 3
}, {
	"code": "81Q50",
	"title": " Quantum chaos [See also 37Dxx]",
	"parentcode": "81Qxx",
	"level": 3
}, {
	"code": "81Q60",
	"title": " Supersymmetry and quantum mechanics",
	"parentcode": "81Qxx",
	"level": 3
}, {
	"code": "81Q65",
	"title": " Alternative quantum mechanics",
	"parentcode": "81Qxx",
	"level": 3
}, {
	"code": "81Q70",
	"title": " Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.",
	"parentcode": "81Qxx",
	"level": 3
}, {
	"code": "81Q80",
	"title": " Special quantum systems, such as solvable systems",
	"parentcode": "81Qxx",
	"level": 3
}, {
	"code": "81Q93",
	"title": " Quantum control",
	"parentcode": "81Qxx",
	"level": 3
}, {
	"code": "81Q99",
	"title": " None of the above, but in this section",
	"parentcode": "81Qxx",
	"level": 3
}, {
	"code": "81Rxx",
	"title": " Groups and algebras in quantum theory",
	"parentcode": "81-XX",
	"level": 2
}, {
	"code": "81R05",
	"title": " Finite-dimensional groups and algebras motivated by physics and their representations [See also 20C35, 22E70]",
	"parentcode": "81Rxx",
	"level": 3
}, {
	"code": "81R10",
	"title": " Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $W$-algebras and other current algebras and their representations [See also 17B65, 17B67, 22E65, 22E67, 22E70]",
	"parentcode": "81Rxx",
	"level": 3
}, {
	"code": "81R12",
	"title": " Relations with integrable systems [See also 17Bxx, 37J35]",
	"parentcode": "81Rxx",
	"level": 3
}, {
	"code": "81R15",
	"title": " Operator algebra methods [See also 46Lxx, 81T05]",
	"parentcode": "81Rxx",
	"level": 3
}, {
	"code": "81R20",
	"title": " Covariant wave equations",
	"parentcode": "81Rxx",
	"level": 3
}, {
	"code": "81R25",
	"title": " Spinor and twistor methods [See also 32L25]",
	"parentcode": "81Rxx",
	"level": 3
}, {
	"code": "81R30",
	"title": " Coherent states [See also 22E45]; squeezed states [See also 81V80]",
	"parentcode": "81Rxx",
	"level": 3
}, {
	"code": "81R40",
	"title": " Symmetry breaking",
	"parentcode": "81Rxx",
	"level": 3
}, {
	"code": "81R50",
	"title": " Quantum groups and related algebraic methods [See also 16T20, 17B37]",
	"parentcode": "81Rxx",
	"level": 3
}, {
	"code": "81R60",
	"title": " Noncommutative geometry",
	"parentcode": "81Rxx",
	"level": 3
}, {
	"code": "81R99",
	"title": " None of the above, but in this section",
	"parentcode": "81Rxx",
	"level": 3
}, {
	"code": "81Sxx",
	"title": " General quantum mechanics and problems of quantization",
	"parentcode": "81-XX",
	"level": 2
}, {
	"code": "81S05",
	"title": " Canonical quantization, commutation relations and statistics",
	"parentcode": "81Sxx",
	"level": 3
}, {
	"code": "81S10",
	"title": " Geometry and quantization, symplectic methods [See also 53D50]",
	"parentcode": "81Sxx",
	"level": 3
}, {
	"code": "81S20",
	"title": " Stochastic quantization",
	"parentcode": "81Sxx",
	"level": 3
}, {
	"code": "81S22",
	"title": " Open systems, reduced dynamics, master equations, decoherence [See also 82C31]",
	"parentcode": "81Sxx",
	"level": 3
}, {
	"code": "81S25",
	"title": " Quantum stochastic calculus",
	"parentcode": "81Sxx",
	"level": 3
}, {
	"code": "81S30",
	"title": " Phase-space methods including Wigner distributions, etc.",
	"parentcode": "81Sxx",
	"level": 3
}, {
	"code": "81S40",
	"title": " Path integrals [See also 58D30]",
	"parentcode": "81Sxx",
	"level": 3
}, {
	"code": "81S99",
	"title": " None of the above, but in this section",
	"parentcode": "81Sxx",
	"level": 3
}, {
	"code": "81Txx",
	"title": " Quantum field theory; related classical field theories [See also 70Sxx]",
	"parentcode": "81-XX",
	"level": 2
}, {
	"code": "81T05",
	"title": " Axiomatic quantum field theory; operator algebras",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T08",
	"title": " Constructive quantum field theory",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T10",
	"title": " Model quantum field theories",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T13",
	"title": " Yang-Mills and other gauge theories [See also 53C07, 58E15]",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T15",
	"title": " Perturbative methods of renormalization",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T16",
	"title": " Nonperturbative methods of renormalization",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T17",
	"title": " Renormalization group methods",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T18",
	"title": " Feynman diagrams",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T20",
	"title": " Quantum field theory on curved space backgrounds",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T25",
	"title": " Quantum field theory on lattices",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T27",
	"title": " Continuum limits",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T28",
	"title": " Thermal quantum field theory [See also 82B30]",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T30",
	"title": " String and superstring theories; other extended objects (e.g., branes) [See also 83E30]",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T40",
	"title": " Two-dimensional field theories, conformal field theories, etc.",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T45",
	"title": " Topological field theories [See also 57R56, 58Dxx]",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T50",
	"title": " Anomalies",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T55",
	"title": " Casimir effect",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T60",
	"title": " Supersymmetric field theories",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T70",
	"title": " Quantization in field theory; cohomological methods [See also 58D29]",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T75",
	"title": " Noncommutative geometry methods [See also 46L85, 46L87, 58B34]",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T80",
	"title": " Simulation and numerical modeling",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81T99",
	"title": " None of the above, but in this section",
	"parentcode": "81Txx",
	"level": 3
}, {
	"code": "81Uxx",
	"title": " Scattering theory [See also 34A55, 34L25, 34L40, 35P25, 47A40]",
	"parentcode": "81-XX",
	"level": 2
}, {
	"code": "81U05",
	"title": " $2$-body potential scattering theory [See also 34E20 for WKB methods]",
	"parentcode": "81Uxx",
	"level": 3
}, {
	"code": "81U10",
	"title": " $n$-body potential scattering theory",
	"parentcode": "81Uxx",
	"level": 3
}, {
	"code": "81U15",
	"title": " Exactly and quasi-solvable systems",
	"parentcode": "81Uxx",
	"level": 3
}, {
	"code": "81U20",
	"title": " $S$-matrix theory, etc.",
	"parentcode": "81Uxx",
	"level": 3
}, {
	"code": "81U30",
	"title": " Dispersion theory, dispersion relations",
	"parentcode": "81Uxx",
	"level": 3
}, {
	"code": "81U35",
	"title": " Inelastic and multichannel scattering",
	"parentcode": "81Uxx",
	"level": 3
}, {
	"code": "81U40",
	"title": " Inverse scattering problems",
	"parentcode": "81Uxx",
	"level": 3
}, {
	"code": "81U99",
	"title": " None of the above, but in this section",
	"parentcode": "81Uxx",
	"level": 3
}, {
	"code": "81Vxx",
	"title": " Applications to specific physical systems",
	"parentcode": "81-XX",
	"level": 2
}, {
	"code": "81V05",
	"title": " Strong interaction, including quantum chromodynamics",
	"parentcode": "81Vxx",
	"level": 3
}, {
	"code": "81V10",
	"title": " Electromagnetic interaction; quantum electrodynamics",
	"parentcode": "81Vxx",
	"level": 3
}, {
	"code": "81V15",
	"title": " Weak interaction",
	"parentcode": "81Vxx",
	"level": 3
}, {
	"code": "81V17",
	"title": " Gravitational interaction [See also 83Cxx and 83Exx]",
	"parentcode": "81Vxx",
	"level": 3
}, {
	"code": "81V19",
	"title": " Other fundamental interactions",
	"parentcode": "81Vxx",
	"level": 3
}, {
	"code": "81V22",
	"title": " Unified theories",
	"parentcode": "81Vxx",
	"level": 3
}, {
	"code": "81V25",
	"title": " Other elementary particle theory",
	"parentcode": "81Vxx",
	"level": 3
}, {
	"code": "81V35",
	"title": " Nuclear physics",
	"parentcode": "81Vxx",
	"level": 3
}, {
	"code": "81V45",
	"title": " Atomic physics",
	"parentcode": "81Vxx",
	"level": 3
}, {
	"code": "81V55",
	"title": " Molecular physics [See also 92E10]",
	"parentcode": "81Vxx",
	"level": 3
}, {
	"code": "81V65",
	"title": " Quantum dots [See also 82D20]",
	"parentcode": "81Vxx",
	"level": 3
}, {
	"code": "81V70",
	"title": " Many-body theory; quantum Hall effect",
	"parentcode": "81Vxx",
	"level": 3
}, {
	"code": "81V80",
	"title": " Quantum optics",
	"parentcode": "81Vxx",
	"level": 3
}, {
	"code": "81V99",
	"title": " None of the above, but in this section",
	"parentcode": "81Vxx",
	"level": 3
}, {
	"code": "82-XX",
	"title": " Statistical mechanics, structure of matter",
	"parentcode": null,
	"level": 1
}, {
	"code": "82-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "82-XX",
	"level": 2
}, {
	"code": "82-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "82-XX",
	"level": 2
}, {
	"code": "82-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "82-XX",
	"level": 2
}, {
	"code": "82-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "82-XX",
	"level": 2
}, {
	"code": "82-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "82-XX",
	"level": 2
}, {
	"code": "82-05",
	"title": " Experimental papers",
	"parentcode": "82-XX",
	"level": 2
}, {
	"code": "82-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "82-XX",
	"level": 2
}, {
	"code": "82-08",
	"title": " Computational methods",
	"parentcode": "82-XX",
	"level": 2
}, {
	"code": "82Bxx",
	"title": " Equilibrium statistical mechanics",
	"parentcode": "82-XX",
	"level": 2
}, {
	"code": "82B03",
	"title": " Foundations",
	"parentcode": "82Bxx",
	"level": 3
}, {
	"code": "82B05",
	"title": " Classical equilibrium statistical mechanics (general)",
	"parentcode": "82Bxx",
	"level": 3
}, {
	"code": "82B10",
	"title": " Quantum equilibrium statistical mechanics (general)",
	"parentcode": "82Bxx",
	"level": 3
}, {
	"code": "82B20",
	"title": " Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs",
	"parentcode": "82Bxx",
	"level": 3
}, {
	"code": "82B21",
	"title": " Continuum models (systems of particles, etc.)",
	"parentcode": "82Bxx",
	"level": 3
}, {
	"code": "82B23",
	"title": " Exactly solvable models; Bethe ansatz",
	"parentcode": "82Bxx",
	"level": 3
}, {
	"code": "82B24",
	"title": " Interface problems; diffusion-limited aggregation",
	"parentcode": "82Bxx",
	"level": 3
}, {
	"code": "82B26",
	"title": " Phase transitions (general)",
	"parentcode": "82Bxx",
	"level": 3
}, {
	"code": "82B27",
	"title": " Critical phenomena",
	"parentcode": "82Bxx",
	"level": 3
}, {
	"code": "82B28",
	"title": " Renormalization group methods [See also 81T17]",
	"parentcode": "82Bxx",
	"level": 3
}, {
	"code": "82B30",
	"title": " Statistical thermodynamics [See also 80-XX]",
	"parentcode": "82Bxx",
	"level": 3
}, {
	"code": "82B31",
	"title": " Stochastic methods",
	"parentcode": "82Bxx",
	"level": 3
}, {
	"code": "82B35",
	"title": " Irreversible thermodynamics, including Onsager-Machlup theory [See also 92E20]",
	"parentcode": "82Bxx",
	"level": 3
}, {
	"code": "82B40",
	"title": " Kinetic theory of gases",
	"parentcode": "82Bxx",
	"level": 3
}, {
	"code": "82B41",
	"title": " Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]",
	"parentcode": "82Bxx",
	"level": 3
}, {
	"code": "82B43",
	"title": " Percolation [See also 60K35]",
	"parentcode": "82Bxx",
	"level": 3
}, {
	"code": "82B44",
	"title": " Disordered systems (random Ising models, random Schrödinger operators, etc.)",
	"parentcode": "82Bxx",
	"level": 3
}, {
	"code": "82B80",
	"title": " Numerical methods (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80]",
	"parentcode": "82Bxx",
	"level": 3
}, {
	"code": "82B99",
	"title": " None of the above, but in this section",
	"parentcode": "82Bxx",
	"level": 3
}, {
	"code": "82Cxx",
	"title": " Time-dependent statistical mechanics (dynamic and nonequilibrium)",
	"parentcode": "82-XX",
	"level": 2
}, {
	"code": "82C03",
	"title": " Foundations",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82C05",
	"title": " Classical dynamic and nonequilibrium statistical mechanics (general)",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82C10",
	"title": " Quantum dynamics and nonequilibrium statistical mechanics (general)",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82C20",
	"title": " Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82C21",
	"title": " Dynamic continuum models (systems of particles, etc.)",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82C22",
	"title": " Interacting particle systems [See also 60K35]",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82C23",
	"title": " Exactly solvable dynamic models [See also 37K60]",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82C24",
	"title": " Interface problems; diffusion-limited aggregation",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82C26",
	"title": " Dynamic and nonequilibrium phase transitions (general)",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82C27",
	"title": " Dynamic critical phenomena",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82C28",
	"title": " Dynamic renormalization group methods [See also 81T17]",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82C31",
	"title": " Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82C32",
	"title": " Neural nets [See also 68T05, 91E40, 92B20]",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82C35",
	"title": " Irreversible thermodynamics, including Onsager-Machlup theory",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82C40",
	"title": " Kinetic theory of gases",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82C41",
	"title": " Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50]",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82C43",
	"title": " Time-dependent percolation [See also 60K35]",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82C44",
	"title": " Dynamics of disordered systems (random Ising systems, etc.)",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82C70",
	"title": " Transport processes",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82C80",
	"title": " Numerical methods (Monte Carlo, series resummation, etc.)",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82C99",
	"title": " None of the above, but in this section",
	"parentcode": "82Cxx",
	"level": 3
}, {
	"code": "82Dxx",
	"title": " Applications to specific types of physical systems",
	"parentcode": "82-XX",
	"level": 2
}, {
	"code": "82D05",
	"title": " Gases",
	"parentcode": "82Dxx",
	"level": 3
}, {
	"code": "82D10",
	"title": " Plasmas",
	"parentcode": "82Dxx",
	"level": 3
}, {
	"code": "82D15",
	"title": " Liquids",
	"parentcode": "82Dxx",
	"level": 3
}, {
	"code": "82D20",
	"title": " Solids",
	"parentcode": "82Dxx",
	"level": 3
}, {
	"code": "82D25",
	"title": " Crystals {For crystallographic group theory, see 20H15}",
	"parentcode": "82Dxx",
	"level": 3
}, {
	"code": "82D30",
	"title": " Random media, disordered materials (including liquid crystals and spin glasses)",
	"parentcode": "82Dxx",
	"level": 3
}, {
	"code": "82D35",
	"title": " Metals",
	"parentcode": "82Dxx",
	"level": 3
}, {
	"code": "82D37",
	"title": " Semiconductors",
	"parentcode": "82Dxx",
	"level": 3
}, {
	"code": "82D40",
	"title": " Magnetic materials",
	"parentcode": "82Dxx",
	"level": 3
}, {
	"code": "82D45",
	"title": " Ferroelectrics",
	"parentcode": "82Dxx",
	"level": 3
}, {
	"code": "82D50",
	"title": " Superfluids",
	"parentcode": "82Dxx",
	"level": 3
}, {
	"code": "82D55",
	"title": " Superconductors",
	"parentcode": "82Dxx",
	"level": 3
}, {
	"code": "82D60",
	"title": " Polymers",
	"parentcode": "82Dxx",
	"level": 3
}, {
	"code": "82D75",
	"title": " Nuclear reactor theory; neutron transport",
	"parentcode": "82Dxx",
	"level": 3
}, {
	"code": "82D77",
	"title": " Quantum wave guides, quantum wires [See also 78A50]",
	"parentcode": "82Dxx",
	"level": 3
}, {
	"code": "82D80",
	"title": " Nanostructures and nanoparticles",
	"parentcode": "82Dxx",
	"level": 3
}, {
	"code": "82D99",
	"title": " None of the above, but in this section",
	"parentcode": "82Dxx",
	"level": 3
}, {
	"code": "83-XX",
	"title": " Relativity and gravitational theory",
	"parentcode": null,
	"level": 1
}, {
	"code": "83-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "83-XX",
	"level": 2
}, {
	"code": "83-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "83-XX",
	"level": 2
}, {
	"code": "83-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "83-XX",
	"level": 2
}, {
	"code": "83-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "83-XX",
	"level": 2
}, {
	"code": "83-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "83-XX",
	"level": 2
}, {
	"code": "83-05",
	"title": " Experimental work",
	"parentcode": "83-XX",
	"level": 2
}, {
	"code": "83-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "83-XX",
	"level": 2
}, {
	"code": "83-08",
	"title": " Computational methods",
	"parentcode": "83-XX",
	"level": 2
}, {
	"code": "83Axx",
	"title": " Special relativity",
	"parentcode": "83-XX",
	"level": 2
}, {
	"code": "83A05",
	"title": " Special relativity",
	"parentcode": "83Axx",
	"level": 3
}, {
	"code": "83A99",
	"title": " None of the above, but in this section",
	"parentcode": "83Axx",
	"level": 3
}, {
	"code": "83Bxx",
	"title": " Observational and experimental questions",
	"parentcode": "83-XX",
	"level": 2
}, {
	"code": "83B05",
	"title": " Observational and experimental questions",
	"parentcode": "83Bxx",
	"level": 3
}, {
	"code": "83B99",
	"title": " None of the above, but in this section",
	"parentcode": "83Bxx",
	"level": 3
}, {
	"code": "83Cxx",
	"title": " General relativity",
	"parentcode": "83-XX",
	"level": 2
}, {
	"code": "83C05",
	"title": " Einstein's equations (general structure, canonical formalism, Cauchy problems)",
	"parentcode": "83Cxx",
	"level": 3
}, {
	"code": "83C10",
	"title": " Equations of motion",
	"parentcode": "83Cxx",
	"level": 3
}, {
	"code": "83C15",
	"title": " Exact solutions",
	"parentcode": "83Cxx",
	"level": 3
}, {
	"code": "83C20",
	"title": " Classes of solutions; algebraically special solutions, metrics with symmetries",
	"parentcode": "83Cxx",
	"level": 3
}, {
	"code": "83C22",
	"title": " Einstein-Maxwell equations",
	"parentcode": "83Cxx",
	"level": 3
}, {
	"code": "83C25",
	"title": " Approximation procedures, weak fields",
	"parentcode": "83Cxx",
	"level": 3
}, {
	"code": "83C27",
	"title": " Lattice gravity, Regge calculus and other discrete methods",
	"parentcode": "83Cxx",
	"level": 3
}, {
	"code": "83C30",
	"title": " Asymptotic procedures (radiation, news functions, $\\scr H$-spaces, etc.)",
	"parentcode": "83Cxx",
	"level": 3
}, {
	"code": "83C35",
	"title": " Gravitational waves",
	"parentcode": "83Cxx",
	"level": 3
}, {
	"code": "83C40",
	"title": " Gravitational energy and conservation laws; groups of motions",
	"parentcode": "83Cxx",
	"level": 3
}, {
	"code": "83C45",
	"title": " Quantization of the gravitational field",
	"parentcode": "83Cxx",
	"level": 3
}, {
	"code": "83C47",
	"title": " Methods of quantum field theory [See also 81T20]",
	"parentcode": "83Cxx",
	"level": 3
}, {
	"code": "83C50",
	"title": " Electromagnetic fields",
	"parentcode": "83Cxx",
	"level": 3
}, {
	"code": "83C55",
	"title": " Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)",
	"parentcode": "83Cxx",
	"level": 3
}, {
	"code": "83C57",
	"title": " Black holes",
	"parentcode": "83Cxx",
	"level": 3
}, {
	"code": "83C60",
	"title": " Spinor and twistor methods; Newman-Penrose formalism",
	"parentcode": "83Cxx",
	"level": 3
}, {
	"code": "83C65",
	"title": " Methods of noncommutative geometry [See also 58B34]",
	"parentcode": "83Cxx",
	"level": 3
}, {
	"code": "83C75",
	"title": " Space-time singularities, cosmic censorship, etc.",
	"parentcode": "83Cxx",
	"level": 3
}, {
	"code": "83C80",
	"title": " Analogues in lower dimensions",
	"parentcode": "83Cxx",
	"level": 3
}, {
	"code": "83C99",
	"title": " None of the above, but in this section",
	"parentcode": "83Cxx",
	"level": 3
}, {
	"code": "83Dxx",
	"title": " Relativistic gravitational theories other than Einstein's, including asymmetric field theories",
	"parentcode": "83-XX",
	"level": 2
}, {
	"code": "83D05",
	"title": " Relativistic gravitational theories other than Einstein's, including asymmetric field theories",
	"parentcode": "83Dxx",
	"level": 3
}, {
	"code": "83D99",
	"title": " None of the above, but in this section",
	"parentcode": "83Dxx",
	"level": 3
}, {
	"code": "83Exx",
	"title": " Unified, higher-dimensional and super field theories",
	"parentcode": "83-XX",
	"level": 2
}, {
	"code": "83E05",
	"title": " Geometrodynamics",
	"parentcode": "83Exx",
	"level": 3
}, {
	"code": "83E15",
	"title": " Kaluza-Klein and other higher-dimensional theories",
	"parentcode": "83Exx",
	"level": 3
}, {
	"code": "83E30",
	"title": " String and superstring theories [See also 81T30]",
	"parentcode": "83Exx",
	"level": 3
}, {
	"code": "83E50",
	"title": " Supergravity",
	"parentcode": "83Exx",
	"level": 3
}, {
	"code": "83E99",
	"title": " None of the above, but in this section",
	"parentcode": "83Exx",
	"level": 3
}, {
	"code": "83Fxx",
	"title": " Cosmology",
	"parentcode": "83-XX",
	"level": 2
}, {
	"code": "83F05",
	"title": " Cosmology",
	"parentcode": "83Fxx",
	"level": 3
}, {
	"code": "83F99",
	"title": " None of the above, but in this section",
	"parentcode": "83Fxx",
	"level": 3
}, {
	"code": "85-XX",
	"title": " Astronomy and astrophysics {For celestial mechanics, see 70F15}",
	"parentcode": null,
	"level": 1
}, {
	"code": "85-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "85-XX",
	"level": 2
}, {
	"code": "85-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "85-XX",
	"level": 2
}, {
	"code": "85-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "85-XX",
	"level": 2
}, {
	"code": "85-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "85-XX",
	"level": 2
}, {
	"code": "85-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "85-XX",
	"level": 2
}, {
	"code": "85-05",
	"title": " Experimental work",
	"parentcode": "85-XX",
	"level": 2
}, {
	"code": "85-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "85-XX",
	"level": 2
}, {
	"code": "85-08",
	"title": " Computational methods",
	"parentcode": "85-XX",
	"level": 2
}, {
	"code": "85Axx",
	"title": " Astronomy and astrophysics {For celestial mechanics, see 70F15}",
	"parentcode": "85-XX",
	"level": 2
}, {
	"code": "85A04",
	"title": " General",
	"parentcode": "85Axx",
	"level": 3
}, {
	"code": "85A05",
	"title": " Galactic and stellar dynamics",
	"parentcode": "85Axx",
	"level": 3
}, {
	"code": "85A15",
	"title": " Galactic and stellar structure",
	"parentcode": "85Axx",
	"level": 3
}, {
	"code": "85A20",
	"title": " Planetary atmospheres",
	"parentcode": "85Axx",
	"level": 3
}, {
	"code": "85A25",
	"title": " Radiative transfer",
	"parentcode": "85Axx",
	"level": 3
}, {
	"code": "85A30",
	"title": " Hydrodynamic and hydromagnetic problems [See also 76Y05]",
	"parentcode": "85Axx",
	"level": 3
}, {
	"code": "85A35",
	"title": " Statistical astronomy",
	"parentcode": "85Axx",
	"level": 3
}, {
	"code": "85A40",
	"title": " Cosmology {For relativistic cosmology, see 83F05}",
	"parentcode": "85Axx",
	"level": 3
}, {
	"code": "85A99",
	"title": " Miscellaneous topics",
	"parentcode": "85Axx",
	"level": 3
}, {
	"code": "86-XX",
	"title": " Geophysics [See also 76U05, 76V05]",
	"parentcode": null,
	"level": 1
}, {
	"code": "86-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "86-XX",
	"level": 2
}, {
	"code": "86-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "86-XX",
	"level": 2
}, {
	"code": "86-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "86-XX",
	"level": 2
}, {
	"code": "86-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "86-XX",
	"level": 2
}, {
	"code": "86-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "86-XX",
	"level": 2
}, {
	"code": "86-05",
	"title": " Experimental work",
	"parentcode": "86-XX",
	"level": 2
}, {
	"code": "86-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "86-XX",
	"level": 2
}, {
	"code": "86-08",
	"title": " Computational methods",
	"parentcode": "86-XX",
	"level": 2
}, {
	"code": "86Axx",
	"title": " Geophysics [See also 76U05, 76V05]",
	"parentcode": "86-XX",
	"level": 2
}, {
	"code": "86A04",
	"title": " General",
	"parentcode": "86Axx",
	"level": 3
}, {
	"code": "86A05",
	"title": " Hydrology, hydrography, oceanography [See also 76Bxx, 76E20, 76Q05, 76Rxx, 76U05]",
	"parentcode": "86Axx",
	"level": 3
}, {
	"code": "86A10",
	"title": " Meteorology and atmospheric physics [See also 76Bxx, 76E20, 76N15, 76Q05, 76Rxx, 76U05]",
	"parentcode": "86Axx",
	"level": 3
}, {
	"code": "86A15",
	"title": " Seismology",
	"parentcode": "86Axx",
	"level": 3
}, {
	"code": "86A17",
	"title": " Global dynamics, earthquake problems",
	"parentcode": "86Axx",
	"level": 3
}, {
	"code": "86A20",
	"title": " Potentials, prospecting",
	"parentcode": "86Axx",
	"level": 3
}, {
	"code": "86A22",
	"title": " Inverse problems [See also 35R30]",
	"parentcode": "86Axx",
	"level": 3
}, {
	"code": "86A25",
	"title": " Geo-electricity and geomagnetism [See also 76W05, 78A25]",
	"parentcode": "86Axx",
	"level": 3
}, {
	"code": "86A30",
	"title": " Geodesy, mapping problems",
	"parentcode": "86Axx",
	"level": 3
}, {
	"code": "86A32",
	"title": " Geostatistics",
	"parentcode": "86Axx",
	"level": 3
}, {
	"code": "86A40",
	"title": " Glaciology",
	"parentcode": "86Axx",
	"level": 3
}, {
	"code": "86A60",
	"title": " Geological problems",
	"parentcode": "86Axx",
	"level": 3
}, {
	"code": "86A99",
	"title": " Miscellaneous topics",
	"parentcode": "86Axx",
	"level": 3
}, {
	"code": "90-XX",
	"title": " Operations research, mathematical programming",
	"parentcode": null,
	"level": 1
}, {
	"code": "90-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "90-XX",
	"level": 2
}, {
	"code": "90-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "90-XX",
	"level": 2
}, {
	"code": "90-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "90-XX",
	"level": 2
}, {
	"code": "90-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "90-XX",
	"level": 2
}, {
	"code": "90-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "90-XX",
	"level": 2
}, {
	"code": "90-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "90-XX",
	"level": 2
}, {
	"code": "90-08",
	"title": " Computational methods",
	"parentcode": "90-XX",
	"level": 2
}, {
	"code": "90Bxx",
	"title": " Operations research and management science",
	"parentcode": "90-XX",
	"level": 2
}, {
	"code": "90B05",
	"title": " Inventory, storage, reservoirs",
	"parentcode": "90Bxx",
	"level": 3
}, {
	"code": "90B06",
	"title": " Transportation, logistics",
	"parentcode": "90Bxx",
	"level": 3
}, {
	"code": "90B10",
	"title": " Network models, deterministic",
	"parentcode": "90Bxx",
	"level": 3
}, {
	"code": "90B15",
	"title": " Network models, stochastic",
	"parentcode": "90Bxx",
	"level": 3
}, {
	"code": "90B18",
	"title": " Communication networks [See also 68M10, 94A05]",
	"parentcode": "90Bxx",
	"level": 3
}, {
	"code": "90B20",
	"title": " Traffic problems",
	"parentcode": "90Bxx",
	"level": 3
}, {
	"code": "90B22",
	"title": " Queues and service [See also 60K25, 68M20]",
	"parentcode": "90Bxx",
	"level": 3
}, {
	"code": "90B25",
	"title": " Reliability, availability, maintenance, inspection [See also 60K10, 62N05]",
	"parentcode": "90Bxx",
	"level": 3
}, {
	"code": "90B30",
	"title": " Production models",
	"parentcode": "90Bxx",
	"level": 3
}, {
	"code": "90B35",
	"title": " Scheduling theory, deterministic [See also 68M20]",
	"parentcode": "90Bxx",
	"level": 3
}, {
	"code": "90B36",
	"title": " Scheduling theory, stochastic [See also 68M20]",
	"parentcode": "90Bxx",
	"level": 3
}, {
	"code": "90B40",
	"title": " Search theory",
	"parentcode": "90Bxx",
	"level": 3
}, {
	"code": "90B50",
	"title": " Management decision making, including multiple objectives [See also 90C29, 90C31, 91A35, 91B06]",
	"parentcode": "90Bxx",
	"level": 3
}, {
	"code": "90B60",
	"title": " Marketing, advertising [See also 91B60]",
	"parentcode": "90Bxx",
	"level": 3
}, {
	"code": "90B70",
	"title": " Theory of organizations, manpower planning [See also 91D35]",
	"parentcode": "90Bxx",
	"level": 3
}, {
	"code": "90B80",
	"title": " Discrete location and assignment [See also 90C10]",
	"parentcode": "90Bxx",
	"level": 3
}, {
	"code": "90B85",
	"title": " Continuous location",
	"parentcode": "90Bxx",
	"level": 3
}, {
	"code": "90B90",
	"title": " Case-oriented studies",
	"parentcode": "90Bxx",
	"level": 3
}, {
	"code": "90B99",
	"title": " None of the above, but in this section",
	"parentcode": "90Bxx",
	"level": 3
}, {
	"code": "90Cxx",
	"title": " Mathematical programming [See also 49Mxx, 65Kxx]",
	"parentcode": "90-XX",
	"level": 2
}, {
	"code": "90C05",
	"title": " Linear programming",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C06",
	"title": " Large-scale problems",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C08",
	"title": " Special problems of linear programming (transportation, multi-index, etc.)",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C09",
	"title": " Boolean programming",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C10",
	"title": " Integer programming",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C11",
	"title": " Mixed integer programming",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C15",
	"title": " Stochastic programming",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C20",
	"title": " Quadratic programming",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C22",
	"title": " Semidefinite programming",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C25",
	"title": " Convex programming",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C26",
	"title": " Nonconvex programming, global optimization",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C27",
	"title": " Combinatorial optimization",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C29",
	"title": " Multi-objective and goal programming",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C30",
	"title": " Nonlinear programming",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C31",
	"title": " Sensitivity, stability, parametric optimization",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C32",
	"title": " Fractional programming",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C33",
	"title": " Complementarity and equilibrium problems and variational inequalities (finite dimensions)",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C34",
	"title": " Semi-infinite programming",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C35",
	"title": " Programming involving graphs or networks [See also 90C27]",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C39",
	"title": " Dynamic programming [See also 49L20]",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C40",
	"title": " Markov and semi-Markov decision processes",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C46",
	"title": " Optimality conditions, duality [See also 49N15]",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C47",
	"title": " Minimax problems [See also 49K35]",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C48",
	"title": " Programming in abstract spaces",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C49",
	"title": " Extreme-point and pivoting methods",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C51",
	"title": " Interior-point methods",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C52",
	"title": " Methods of reduced gradient type",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C53",
	"title": " Methods of quasi-Newton type",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C55",
	"title": " Methods of successive quadratic programming type",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C56",
	"title": " Derivative-free methods  and methods using generalized derivatives [See also 49J52]",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C57",
	"title": " Polyhedral combinatorics, branch-and-bound, branch-and-cut",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C59",
	"title": " Approximation methods and heuristics",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C60",
	"title": " Abstract computational complexity for mathematical programming problems [See also 68Q25]",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C70",
	"title": " Fuzzy programming",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C90",
	"title": " Applications of mathematical programming",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "90C99",
	"title": " None of the above, but in this section",
	"parentcode": "90Cxx",
	"level": 3
}, {
	"code": "91-XX",
	"title": " Game theory, economics, social and behavioral sciences",
	"parentcode": null,
	"level": 1
}, {
	"code": "91-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "91-XX",
	"level": 2
}, {
	"code": "91-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "91-XX",
	"level": 2
}, {
	"code": "91-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "91-XX",
	"level": 2
}, {
	"code": "91-03",
	"title": " Historical (must also be assigned at least one classification number from section 01)",
	"parentcode": "91-XX",
	"level": 2
}, {
	"code": "91-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "91-XX",
	"level": 2
}, {
	"code": "91-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "91-XX",
	"level": 2
}, {
	"code": "91-08",
	"title": " Computational methods",
	"parentcode": "91-XX",
	"level": 2
}, {
	"code": "91Axx",
	"title": " Game theory",
	"parentcode": "91-XX",
	"level": 2
}, {
	"code": "91A05",
	"title": " 2-person games",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A06",
	"title": " $n$-person games, $n>2$",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A10",
	"title": " Noncooperative games",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A12",
	"title": " Cooperative games",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A13",
	"title": " Games with infinitely many players",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A15",
	"title": " Stochastic games",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A18",
	"title": " Games in extensive form",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A20",
	"title": " Multistage and repeated games",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A22",
	"title": " Evolutionary games",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A23",
	"title": " Differential games [See also 49N70]",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A24",
	"title": " Positional games (pursuit and evasion, etc.) [See also 49N75]",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A25",
	"title": " Dynamic games",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A26",
	"title": " Rationality, learning",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A28",
	"title": " Signaling, communication",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A30",
	"title": " Utility theory for games [See also 91B16]",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A35",
	"title": " Decision theory for games [See also 62Cxx, 91B06, 90B50]",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A40",
	"title": " Game-theoretic models",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A43",
	"title": " Games involving graphs [See also 05C57]",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A44",
	"title": " Games involving topology or set theory",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A46",
	"title": " Combinatorial games",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A50",
	"title": " Discrete-time games",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A55",
	"title": " Games of timing",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A60",
	"title": " Probabilistic games; gambling [See also 60G40]",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A65",
	"title": " Hierarchical games",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A70",
	"title": " Spaces of games",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A80",
	"title": " Applications of game theory",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A90",
	"title": " Experimental studies",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91A99",
	"title": " None of the above, but in this section",
	"parentcode": "91Axx",
	"level": 3
}, {
	"code": "91Bxx",
	"title": " Mathematical economics {For econometrics, see 62P20}",
	"parentcode": "91-XX",
	"level": 2
}, {
	"code": "91B02",
	"title": " Fundamental topics (basic mathematics, methodology; applicable to economics in general)",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B06",
	"title": " Decision theory [See also 62Cxx, 90B50, 91A35]",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B08",
	"title": " Individual preferences",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B10",
	"title": " Group preferences",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B12",
	"title": " Voting theory",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B14",
	"title": " Social choice",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B15",
	"title": " Welfare economics",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B16",
	"title": " Utility theory",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B18",
	"title": " Public goods",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B24",
	"title": " Price theory and market structure",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B25",
	"title": " Asset pricing models",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B26",
	"title": " Market models (auctions, bargaining, bidding, selling, etc.)",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B30",
	"title": " Risk theory, insurance",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B32",
	"title": " Resource and cost allocation",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B38",
	"title": " Production theory, theory of the firm",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B40",
	"title": " Labor market, contracts",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B42",
	"title": " Consumer behavior, demand theory",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B44",
	"title": " Informational economics",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B50",
	"title": " General equilibrium theory",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B51",
	"title": " Dynamic stochastic general equilibrium theory",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B52",
	"title": " Special types of equilibria",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B54",
	"title": " Special types of economies",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B55",
	"title": " Economic dynamics",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B60",
	"title": " Trade models",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B62",
	"title": "  Growth models",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B64",
	"title": " Macro-economic models (monetary models, models of taxation)",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B66",
	"title": " Multisectoral models",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B68",
	"title": " Matching models",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B69",
	"title": " Heterogeneous agent models",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B70",
	"title": " Stochastic models",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B72",
	"title": " Spatial models",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B74",
	"title": " Models of real-world systems",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B76",
	"title": " Environmental economics (natural resource models, harvesting, pollution, etc.)",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B80",
	"title": " Applications of statistical and quantum mechanics to economics (econophysics)",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B82",
	"title": " Statistical methods; economic indices and measures",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B84",
	"title": " Economic time series analysis [See also 62M10]",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91B99",
	"title": " None of the above, but in this section",
	"parentcode": "91Bxx",
	"level": 3
}, {
	"code": "91Cxx",
	"title": " Social and behavioral sciences",
	"parentcode": "91-XX",
	"level": 2
}, {
	"code": "91C05",
	"title": " Measurement theory",
	"parentcode": "91Cxx",
	"level": 3
}, {
	"code": "91C15",
	"title": " One- and multidimensional scaling",
	"parentcode": "91Cxx",
	"level": 3
}, {
	"code": "91C20",
	"title": " Clustering [See also 62H30]",
	"parentcode": "91Cxx",
	"level": 3
}, {
	"code": "91C99",
	"title": " None of the above, but in this section",
	"parentcode": "91Cxx",
	"level": 3
}, {
	"code": "91Dxx",
	"title": " Mathematical sociology (including anthropology)",
	"parentcode": "91-XX",
	"level": 2
}, {
	"code": "91D10",
	"title": " Models of societies, social and urban evolution",
	"parentcode": "91Dxx",
	"level": 3
}, {
	"code": "91D20",
	"title": " Mathematical geography and demography",
	"parentcode": "91Dxx",
	"level": 3
}, {
	"code": "91D25",
	"title": " Spatial models [See also 91B72]",
	"parentcode": "91Dxx",
	"level": 3
}, {
	"code": "91D30",
	"title": " Social networks",
	"parentcode": "91Dxx",
	"level": 3
}, {
	"code": "91D35",
	"title": " Manpower systems [See also 91B40, 90B70]",
	"parentcode": "91Dxx",
	"level": 3
}, {
	"code": "91D99",
	"title": " None of the above, but in this section",
	"parentcode": "91Dxx",
	"level": 3
}, {
	"code": "91Exx",
	"title": " Mathematical psychology",
	"parentcode": "91-XX",
	"level": 2
}, {
	"code": "91E10",
	"title": " Cognitive psychology",
	"parentcode": "91Exx",
	"level": 3
}, {
	"code": "91E30",
	"title": " Psychophysics and psychophysiology; perception",
	"parentcode": "91Exx",
	"level": 3
}, {
	"code": "91E40",
	"title": " Memory and learning [See also 68T05]",
	"parentcode": "91Exx",
	"level": 3
}, {
	"code": "91E45",
	"title": " Measurement and performance",
	"parentcode": "91Exx",
	"level": 3
}, {
	"code": "91E99",
	"title": " None of the above, but in this section",
	"parentcode": "91Exx",
	"level": 3
}, {
	"code": "91Fxx",
	"title": " Other social and behavioral sciences (mathematical treatment)",
	"parentcode": "91-XX",
	"level": 2
}, {
	"code": "91F10",
	"title": " History, political science",
	"parentcode": "91Fxx",
	"level": 3
}, {
	"code": "91F20",
	"title": " Linguistics [See also 03B65, 68T50]",
	"parentcode": "91Fxx",
	"level": 3
}, {
	"code": "91F99",
	"title": " None of the above, but in this section",
	"parentcode": "91Fxx",
	"level": 3
}, {
	"code": "91Gxx",
	"title": " Mathematical finance",
	"parentcode": "91-XX",
	"level": 2
}, {
	"code": "91G10",
	"title": " Portfolio theory",
	"parentcode": "91Gxx",
	"level": 3
}, {
	"code": "91G20",
	"title": " Derivative securities",
	"parentcode": "91Gxx",
	"level": 3
}, {
	"code": "91G30",
	"title": " Interest rates (stochastic models)",
	"parentcode": "91Gxx",
	"level": 3
}, {
	"code": "91G40",
	"title": " Credit risk",
	"parentcode": "91Gxx",
	"level": 3
}, {
	"code": "91G50",
	"title": " Corporate finance",
	"parentcode": "91Gxx",
	"level": 3
}, {
	"code": "91G60",
	"title": " Numerical methods (including Monte Carlo methods)",
	"parentcode": "91Gxx",
	"level": 3
}, {
	"code": "91G70",
	"title": " Statistical methods, econometrics",
	"parentcode": "91Gxx",
	"level": 3
}, {
	"code": "91G80",
	"title": " Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)",
	"parentcode": "91Gxx",
	"level": 3
}, {
	"code": "91G99",
	"title": " None of the above, but in this section",
	"parentcode": "91Gxx",
	"level": 3
}, {
	"code": "92-XX",
	"title": " Biology and other natural sciences",
	"parentcode": null,
	"level": 1
}, {
	"code": "92-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "92-XX",
	"level": 2
}, {
	"code": "92-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "92-XX",
	"level": 2
}, {
	"code": "92-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "92-XX",
	"level": 2
}, {
	"code": "92-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "92-XX",
	"level": 2
}, {
	"code": "92-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "92-XX",
	"level": 2
}, {
	"code": "92-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "92-XX",
	"level": 2
}, {
	"code": "92-08",
	"title": " Computational methods",
	"parentcode": "92-XX",
	"level": 2
}, {
	"code": "92Bxx",
	"title": " Mathematical biology in general",
	"parentcode": "92-XX",
	"level": 2
}, {
	"code": "92B05",
	"title": " General biology and biomathematics",
	"parentcode": "92Bxx",
	"level": 3
}, {
	"code": "92B10",
	"title": " Taxonomy, cladistics, statistics",
	"parentcode": "92Bxx",
	"level": 3
}, {
	"code": "92B15",
	"title": " General biostatistics [See also 62P10]",
	"parentcode": "92Bxx",
	"level": 3
}, {
	"code": "92B20",
	"title": " Neural networks, artificial life and related topics [See also 68T05, 82C32, 94Cxx]",
	"parentcode": "92Bxx",
	"level": 3
}, {
	"code": "92B25",
	"title": " Biological rhythms and synchronization",
	"parentcode": "92Bxx",
	"level": 3
}, {
	"code": "92B99",
	"title": " None of the above, but in this section",
	"parentcode": "92Bxx",
	"level": 3
}, {
	"code": "92Cxx",
	"title": " Physiological, cellular and medical topics",
	"parentcode": "92-XX",
	"level": 2
}, {
	"code": "92C05",
	"title": " Biophysics",
	"parentcode": "92Cxx",
	"level": 3
}, {
	"code": "92C10",
	"title": " Biomechanics [See also 74L15]",
	"parentcode": "92Cxx",
	"level": 3
}, {
	"code": "92C15",
	"title": " Developmental biology, pattern formation",
	"parentcode": "92Cxx",
	"level": 3
}, {
	"code": "92C17",
	"title": " Cell movement (chemotaxis, etc.)",
	"parentcode": "92Cxx",
	"level": 3
}, {
	"code": "92C20",
	"title": " Neural biology",
	"parentcode": "92Cxx",
	"level": 3
}, {
	"code": "92C30",
	"title": " Physiology (general)",
	"parentcode": "92Cxx",
	"level": 3
}, {
	"code": "92C35",
	"title": " Physiological flow [See also 76Z05]",
	"parentcode": "92Cxx",
	"level": 3
}, {
	"code": "92C37",
	"title": " Cell biology",
	"parentcode": "92Cxx",
	"level": 3
}, {
	"code": "92C40",
	"title": " Biochemistry, molecular biology",
	"parentcode": "92Cxx",
	"level": 3
}, {
	"code": "92C42",
	"title": " Systems biology, networks",
	"parentcode": "92Cxx",
	"level": 3
}, {
	"code": "92C45",
	"title": " Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) [See also 80A30]",
	"parentcode": "92Cxx",
	"level": 3
}, {
	"code": "92C50",
	"title": " Medical applications (general)",
	"parentcode": "92Cxx",
	"level": 3
}, {
	"code": "92C55",
	"title": " Biomedical imaging and signal processing [See also 44A12, 65R10, 94A08, 94A12]",
	"parentcode": "92Cxx",
	"level": 3
}, {
	"code": "92C60",
	"title": " Medical epidemiology",
	"parentcode": "92Cxx",
	"level": 3
}, {
	"code": "92C80",
	"title": " Plant biology",
	"parentcode": "92Cxx",
	"level": 3
}, {
	"code": "92C99",
	"title": " None of the above, but in this section",
	"parentcode": "92Cxx",
	"level": 3
}, {
	"code": "92Dxx",
	"title": " Genetics and population dynamics",
	"parentcode": "92-XX",
	"level": 2
}, {
	"code": "92D10",
	"title": " Genetics {For genetic algebras, see 17D92}",
	"parentcode": "92Dxx",
	"level": 3
}, {
	"code": "92D15",
	"title": " Problems related to evolution",
	"parentcode": "92Dxx",
	"level": 3
}, {
	"code": "92D20",
	"title": " Protein sequences, DNA sequences",
	"parentcode": "92Dxx",
	"level": 3
}, {
	"code": "92D25",
	"title": " Population dynamics (general)",
	"parentcode": "92Dxx",
	"level": 3
}, {
	"code": "92D30",
	"title": " Epidemiology",
	"parentcode": "92Dxx",
	"level": 3
}, {
	"code": "92D40",
	"title": " Ecology",
	"parentcode": "92Dxx",
	"level": 3
}, {
	"code": "92D50",
	"title": " Animal behavior",
	"parentcode": "92Dxx",
	"level": 3
}, {
	"code": "92D99",
	"title": " None of the above, but in this section",
	"parentcode": "92Dxx",
	"level": 3
}, {
	"code": "92Exx",
	"title": " Chemistry {For biochemistry, see 92C40}",
	"parentcode": "92-XX",
	"level": 2
}, {
	"code": "92E10",
	"title": " Molecular structure (graph-theoretic methods, methods of differential topology, etc.)",
	"parentcode": "92Exx",
	"level": 3
}, {
	"code": "92E20",
	"title": " Classical flows, reactions, etc. [See also 80A30, 80A32]",
	"parentcode": "92Exx",
	"level": 3
}, {
	"code": "92E99",
	"title": " None of the above, but in this section",
	"parentcode": "92Exx",
	"level": 3
}, {
	"code": "92Fxx",
	"title": " Other natural sciences (should also be assigned at least one other classification number in this section)",
	"parentcode": "92-XX",
	"level": 2
}, {
	"code": "92F05",
	"title": " Other natural sciences (should also be assigned at least one other classification number in section 92)",
	"parentcode": "92Fxx",
	"level": 3
}, {
	"code": "92F99",
	"title": " None of the above, but in this section",
	"parentcode": "92Fxx",
	"level": 3
}, {
	"code": "93-XX",
	"title": " Systems theory; control {For optimal control, see 49-XX}",
	"parentcode": null,
	"level": 1
}, {
	"code": "93-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "93-XX",
	"level": 2
}, {
	"code": "93-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "93-XX",
	"level": 2
}, {
	"code": "93-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "93-XX",
	"level": 2
}, {
	"code": "93-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "93-XX",
	"level": 2
}, {
	"code": "93-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "93-XX",
	"level": 2
}, {
	"code": "93-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "93-XX",
	"level": 2
}, {
	"code": "93Axx",
	"title": " General",
	"parentcode": "93-XX",
	"level": 2
}, {
	"code": "93A05",
	"title": " Axiomatic system theory",
	"parentcode": "93Axx",
	"level": 3
}, {
	"code": "93A10",
	"title": " General systems",
	"parentcode": "93Axx",
	"level": 3
}, {
	"code": "93A13",
	"title": " Hierarchical systems",
	"parentcode": "93Axx",
	"level": 3
}, {
	"code": "93A14",
	"title": " Decentralized systems",
	"parentcode": "93Axx",
	"level": 3
}, {
	"code": "93A15",
	"title": " Large scale systems",
	"parentcode": "93Axx",
	"level": 3
}, {
	"code": "93A30",
	"title": " Mathematical modeling (models of systems, model-matching, etc.)",
	"parentcode": "93Axx",
	"level": 3
}, {
	"code": "93A99",
	"title": " None of the above, but in this section",
	"parentcode": "93Axx",
	"level": 3
}, {
	"code": "93Bxx",
	"title": " Controllability, observability, and system structure",
	"parentcode": "93-XX",
	"level": 2
}, {
	"code": "93B03",
	"title": " Attainable sets",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B05",
	"title": " Controllability",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B07",
	"title": " Observability",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B10",
	"title": " Canonical structure",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B11",
	"title": " System structure simplification",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B12",
	"title": " Variable structure systems",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B15",
	"title": " Realizations from input-output data",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B17",
	"title": " Transformations",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B18",
	"title": " Linearizations",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B20",
	"title": " Minimal systems representations",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B25",
	"title": " Algebraic methods",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B27",
	"title": " Geometric methods",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B28",
	"title": " Operator-theoretic methods [See also 47A48, 47A57, 47B35, 47N70]",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B30",
	"title": " System identification",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B35",
	"title": " Sensitivity (robustness)",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B36",
	"title": " $H^\\infty$-control",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B40",
	"title": " Computational methods",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B50",
	"title": " Synthesis problems",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B51",
	"title": " Design techniques (robust design, computer-aided design, etc.)",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B52",
	"title": " Feedback control",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B55",
	"title": " Pole and zero placement problems",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B60",
	"title": " Eigenvalue problems",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93B99",
	"title": " None of the above, but in this section",
	"parentcode": "93Bxx",
	"level": 3
}, {
	"code": "93Cxx",
	"title": " Control systems",
	"parentcode": "93-XX",
	"level": 2
}, {
	"code": "93C05",
	"title": " Linear systems",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C10",
	"title": " Nonlinear systems",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C15",
	"title": " Systems governed by ordinary differential equations [See also 34H05]",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C20",
	"title": " Systems governed by partial differential equations",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C23",
	"title": " Systems governed by functional-differential equations [See also 34K35]",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C25",
	"title": " Systems in abstract spaces",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C30",
	"title": " Systems governed by functional relations other than differential equations (such as hybrid and switching systems)",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C35",
	"title": " Multivariable systems",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C40",
	"title": " Adaptive control",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C41",
	"title": " Problems with incomplete information",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C42",
	"title": " Fuzzy control systems",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C55",
	"title": " Discrete-time systems",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C57",
	"title": " Sampled-data systems",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C62",
	"title": " Digital systems",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C65",
	"title": " Discrete event systems",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C70",
	"title": " Time-scale analysis and singular perturbations",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C73",
	"title": " Perturbations",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C80",
	"title": " Frequency-response methods",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C83",
	"title": " Control problems involving computers (process control, etc.)",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C85",
	"title": " Automated systems (robots, etc.) [See also 68T40, 70B15, 70Q05]",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C95",
	"title": " Applications",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93C99",
	"title": " None of the above, but in this section",
	"parentcode": "93Cxx",
	"level": 3
}, {
	"code": "93Dxx",
	"title": " Stability",
	"parentcode": "93-XX",
	"level": 2
}, {
	"code": "93D05",
	"title": " Lyapunov and other classical stabilities (Lagrange, Poisson, $L^p, l^p$, etc.)",
	"parentcode": "93Dxx",
	"level": 3
}, {
	"code": "93D09",
	"title": " Robust stability",
	"parentcode": "93Dxx",
	"level": 3
}, {
	"code": "93D10",
	"title": " Popov-type stability of feedback systems",
	"parentcode": "93Dxx",
	"level": 3
}, {
	"code": "93D15",
	"title": " Stabilization of systems by feedback",
	"parentcode": "93Dxx",
	"level": 3
}, {
	"code": "93D20",
	"title": " Asymptotic stability",
	"parentcode": "93Dxx",
	"level": 3
}, {
	"code": "93D21",
	"title": " Adaptive or robust stabilization",
	"parentcode": "93Dxx",
	"level": 3
}, {
	"code": "93D25",
	"title": " Input-output approaches",
	"parentcode": "93Dxx",
	"level": 3
}, {
	"code": "93D30",
	"title": " Scalar and vector Lyapunov functions",
	"parentcode": "93Dxx",
	"level": 3
}, {
	"code": "93D99",
	"title": " None of the above, but in this section",
	"parentcode": "93Dxx",
	"level": 3
}, {
	"code": "93Exx",
	"title": " Stochastic systems and control",
	"parentcode": "93-XX",
	"level": 2
}, {
	"code": "93E03",
	"title": " Stochastic systems, general",
	"parentcode": "93Exx",
	"level": 3
}, {
	"code": "93E10",
	"title": " Estimation and detection [See also 60G35]",
	"parentcode": "93Exx",
	"level": 3
}, {
	"code": "93E11",
	"title": " Filtering [See also 60G35]",
	"parentcode": "93Exx",
	"level": 3
}, {
	"code": "93E12",
	"title": " System identification",
	"parentcode": "93Exx",
	"level": 3
}, {
	"code": "93E14",
	"title": " Data smoothing",
	"parentcode": "93Exx",
	"level": 3
}, {
	"code": "93E15",
	"title": " Stochastic stability",
	"parentcode": "93Exx",
	"level": 3
}, {
	"code": "93E20",
	"title": " Optimal stochastic control",
	"parentcode": "93Exx",
	"level": 3
}, {
	"code": "93E24",
	"title": " Least squares and related methods",
	"parentcode": "93Exx",
	"level": 3
}, {
	"code": "93E25",
	"title": " Other computational methods",
	"parentcode": "93Exx",
	"level": 3
}, {
	"code": "93E35",
	"title": " Stochastic learning and adaptive control",
	"parentcode": "93Exx",
	"level": 3
}, {
	"code": "93E99",
	"title": " None of the above, but in this section",
	"parentcode": "93Exx",
	"level": 3
}, {
	"code": "94-XX",
	"title": " Information and communication, circuits",
	"parentcode": null,
	"level": 1
}, {
	"code": "94-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "94-XX",
	"level": 2
}, {
	"code": "94-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "94-XX",
	"level": 2
}, {
	"code": "94-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "94-XX",
	"level": 2
}, {
	"code": "94-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "94-XX",
	"level": 2
}, {
	"code": "94-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "94-XX",
	"level": 2
}, {
	"code": "94-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "94-XX",
	"level": 2
}, {
	"code": "94Axx",
	"title": " Communication, information",
	"parentcode": "94-XX",
	"level": 2
}, {
	"code": "94A05",
	"title": " Communication theory [See also 60G35, 90B18]",
	"parentcode": "94Axx",
	"level": 3
}, {
	"code": "94A08",
	"title": " Image processing (compression, reconstruction, etc.) [See also 68U10]",
	"parentcode": "94Axx",
	"level": 3
}, {
	"code": "94A11",
	"title": " Application of orthogonal and other special functions",
	"parentcode": "94Axx",
	"level": 3
}, {
	"code": "94A12",
	"title": " Signal theory (characterization, reconstruction, filtering, etc.)",
	"parentcode": "94Axx",
	"level": 3
}, {
	"code": "94A13",
	"title": " Detection theory",
	"parentcode": "94Axx",
	"level": 3
}, {
	"code": "94A14",
	"title": " Modulation and demodulation",
	"parentcode": "94Axx",
	"level": 3
}, {
	"code": "94A15",
	"title": " Information theory, general [See also 62B10, 81P45]",
	"parentcode": "94Axx",
	"level": 3
}, {
	"code": "94A17",
	"title": " Measures of information, entropy",
	"parentcode": "94Axx",
	"level": 3
}, {
	"code": "94A20",
	"title": " Sampling theory",
	"parentcode": "94Axx",
	"level": 3
}, {
	"code": "94A24",
	"title": " Coding theorems (Shannon theory)",
	"parentcode": "94Axx",
	"level": 3
}, {
	"code": "94A29",
	"title": " Source coding [See also 68P30]",
	"parentcode": "94Axx",
	"level": 3
}, {
	"code": "94A34",
	"title": " Rate-distortion theory",
	"parentcode": "94Axx",
	"level": 3
}, {
	"code": "94A40",
	"title": " Channel models (including quantum)",
	"parentcode": "94Axx",
	"level": 3
}, {
	"code": "94A45",
	"title": " Prefix, length-variable, comma-free codes [See also 20M35, 68Q45]",
	"parentcode": "94Axx",
	"level": 3
}, {
	"code": "94A50",
	"title": " Theory of questionnaires",
	"parentcode": "94Axx",
	"level": 3
}, {
	"code": "94A55",
	"title": " Shift register sequences and sequences over finite alphabets",
	"parentcode": "94Axx",
	"level": 3
}, {
	"code": "94A60",
	"title": " Cryptography [See also 11T71, 14G50, 68P25, 81P94]",
	"parentcode": "94Axx",
	"level": 3
}, {
	"code": "94A62",
	"title": " Authentication and secret sharing [See also 81P94]",
	"parentcode": "94Axx",
	"level": 3
}, {
	"code": "94A99",
	"title": " None of the above, but in this section",
	"parentcode": "94Axx",
	"level": 3
}, {
	"code": "94Bxx",
	"title": " Theory of error-correcting codes and error-detecting codes",
	"parentcode": "94-XX",
	"level": 2
}, {
	"code": "94B05",
	"title": " Linear codes, general",
	"parentcode": "94Bxx",
	"level": 3
}, {
	"code": "94B10",
	"title": " Convolutional codes",
	"parentcode": "94Bxx",
	"level": 3
}, {
	"code": "94B12",
	"title": " Combined modulation schemes (including trellis codes)",
	"parentcode": "94Bxx",
	"level": 3
}, {
	"code": "94B15",
	"title": " Cyclic codes",
	"parentcode": "94Bxx",
	"level": 3
}, {
	"code": "94B20",
	"title": " Burst-correcting codes",
	"parentcode": "94Bxx",
	"level": 3
}, {
	"code": "94B25",
	"title": " Combinatorial codes",
	"parentcode": "94Bxx",
	"level": 3
}, {
	"code": "94B27",
	"title": " Geometric methods (including applications of algebraic geometry) [See also 11T71, 14G50]",
	"parentcode": "94Bxx",
	"level": 3
}, {
	"code": "94B30",
	"title": " Majority codes",
	"parentcode": "94Bxx",
	"level": 3
}, {
	"code": "94B35",
	"title": " Decoding",
	"parentcode": "94Bxx",
	"level": 3
}, {
	"code": "94B40",
	"title": " Arithmetic codes [See also 11T71, 14G50]",
	"parentcode": "94Bxx",
	"level": 3
}, {
	"code": "94B50",
	"title": " Synchronization error-correcting codes",
	"parentcode": "94Bxx",
	"level": 3
}, {
	"code": "94B60",
	"title": " Other types of codes",
	"parentcode": "94Bxx",
	"level": 3
}, {
	"code": "94B65",
	"title": " Bounds on codes",
	"parentcode": "94Bxx",
	"level": 3
}, {
	"code": "94B70",
	"title": " Error probability",
	"parentcode": "94Bxx",
	"level": 3
}, {
	"code": "94B75",
	"title": " Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) [See also 11H31, 11H71]",
	"parentcode": "94Bxx",
	"level": 3
}, {
	"code": "94B99",
	"title": " None of the above, but in this section",
	"parentcode": "94Bxx",
	"level": 3
}, {
	"code": "94Cxx",
	"title": " Circuits, networks",
	"parentcode": "94-XX",
	"level": 2
}, {
	"code": "94C05",
	"title": " Analytic circuit theory",
	"parentcode": "94Cxx",
	"level": 3
}, {
	"code": "94C10",
	"title": " Switching theory, application of Boolean algebra; Boolean functions [See also 06E30]",
	"parentcode": "94Cxx",
	"level": 3
}, {
	"code": "94C12",
	"title": " Fault detection; testing",
	"parentcode": "94Cxx",
	"level": 3
}, {
	"code": "94C15",
	"title": " Applications of graph theory [See also 05Cxx, 68R10]",
	"parentcode": "94Cxx",
	"level": 3
}, {
	"code": "94C30",
	"title": " Applications of design theory [See also 05Bxx]",
	"parentcode": "94Cxx",
	"level": 3
}, {
	"code": "94C99",
	"title": " None of the above, but in this section",
	"parentcode": "94Cxx",
	"level": 3
}, {
	"code": "94Dxx",
	"title": " Fuzzy sets and logic (in connection with questions of Section 94) [See also 03B52, 03E72, 28E10]",
	"parentcode": "94-XX",
	"level": 2
}, {
	"code": "94D05",
	"title": " Fuzzy sets and logic (in connection with questions of Section 94) [See also 03B52, 03E72, 28E10]",
	"parentcode": "94Dxx",
	"level": 3
}, {
	"code": "94D99",
	"title": " None of the above, but in this section",
	"parentcode": "94Dxx",
	"level": 3
}, {
	"code": "97-XX",
	"title": " Mathematics education",
	"parentcode": null,
	"level": 1
}, {
	"code": "97-00",
	"title": " General reference works (handbooks, dictionaries, bibliographies, etc.)",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97-01",
	"title": " Instructional exposition (textbooks, tutorial papers, etc.)",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97-02",
	"title": " Research exposition (monographs, survey articles)",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97-03",
	"title": " Historical (must also be assigned at least one classification number from Section 01)",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97-04",
	"title": " Explicit machine computation and programs (not the theory of computation or programming)",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97-06",
	"title": " Proceedings, conferences, collections, etc.",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97Axx",
	"title": " General, mathematics and education",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97A10",
	"title": " Comprehensive works, reference books",
	"parentcode": "97Axx",
	"level": 3
}, {
	"code": "97A20",
	"title": " Recreational mathematics, games [See also 00A08]",
	"parentcode": "97Axx",
	"level": 3
}, {
	"code": "97A30",
	"title": " History of mathematics and mathematics education [See also 01-XX]",
	"parentcode": "97Axx",
	"level": 3
}, {
	"code": "97A40",
	"title": "  Mathematics and society",
	"parentcode": "97Axx",
	"level": 3
}, {
	"code": "97A50",
	"title": " Bibliographies [See also  01-00]",
	"parentcode": "97Axx",
	"level": 3
}, {
	"code": "97A70",
	"title": " Theses and postdoctoral theses",
	"parentcode": "97Axx",
	"level": 3
}, {
	"code": "97A80",
	"title": "  Popularization of mathematics",
	"parentcode": "97Axx",
	"level": 3
}, {
	"code": "97A99",
	"title": " None of the above, but in this section",
	"parentcode": "97Axx",
	"level": 3
}, {
	"code": "97Bxx",
	"title": " Educational policy and systems",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97B10",
	"title": " Educational research and planning",
	"parentcode": "97Bxx",
	"level": 3
}, {
	"code": "97B20",
	"title": " General education",
	"parentcode": "97Bxx",
	"level": 3
}, {
	"code": "97B30",
	"title": " Vocational education",
	"parentcode": "97Bxx",
	"level": 3
}, {
	"code": "97B40",
	"title": " Higher education",
	"parentcode": "97Bxx",
	"level": 3
}, {
	"code": "97B50",
	"title": " Teacher education {For research aspects, see 97C70}",
	"parentcode": "97Bxx",
	"level": 3
}, {
	"code": "97B60",
	"title": " Adult and further education",
	"parentcode": "97Bxx",
	"level": 3
}, {
	"code": "97B70",
	"title": " Syllabuses,  educational standards",
	"parentcode": "97Bxx",
	"level": 3
}, {
	"code": "97B99",
	"title": " None of the above, but in this section",
	"parentcode": "97Bxx",
	"level": 3
}, {
	"code": "97Cxx",
	"title": " Psychology of mathematics education, research in mathematics education",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97C10",
	"title": " Comprehensive works",
	"parentcode": "97Cxx",
	"level": 3
}, {
	"code": "97C20",
	"title": " Affective behavior",
	"parentcode": "97Cxx",
	"level": 3
}, {
	"code": "97C30",
	"title": "  Cognitive processes, learning theories",
	"parentcode": "97Cxx",
	"level": 3
}, {
	"code": "97C40",
	"title": " Intelligence and aptitudes",
	"parentcode": "97Cxx",
	"level": 3
}, {
	"code": "97C50",
	"title": "  Language and verbal communities",
	"parentcode": "97Cxx",
	"level": 3
}, {
	"code": "97C60",
	"title": " Sociological aspects of learning",
	"parentcode": "97Cxx",
	"level": 3
}, {
	"code": "97C70",
	"title": " Teaching-learning processes",
	"parentcode": "97Cxx",
	"level": 3
}, {
	"code": "97C99",
	"title": " None of the above, but in this section",
	"parentcode": "97Cxx",
	"level": 3
}, {
	"code": "97Dxx",
	"title": " Education and instruction in mathematics",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97D10",
	"title": " Comprehensive works, comparative studies",
	"parentcode": "97Dxx",
	"level": 3
}, {
	"code": "97D20",
	"title": " Philosophical and theoretical contributions (maths didactics)",
	"parentcode": "97Dxx",
	"level": 3
}, {
	"code": "97D30",
	"title": " Objectives and goals",
	"parentcode": "97Dxx",
	"level": 3
}, {
	"code": "97D40",
	"title": " Teaching methods and classroom techniques",
	"parentcode": "97Dxx",
	"level": 3
}, {
	"code": "97D50",
	"title": " Teaching problem solving and heuristic strategies {For research aspects, see 97Cxx}",
	"parentcode": "97Dxx",
	"level": 3
}, {
	"code": "97D60",
	"title": " Student assessment, achievement control and rating",
	"parentcode": "97Dxx",
	"level": 3
}, {
	"code": "97D70",
	"title": " Learning difficulties and student errors",
	"parentcode": "97Dxx",
	"level": 3
}, {
	"code": "97D80",
	"title": " Teaching units and draft lessons",
	"parentcode": "97Dxx",
	"level": 3
}, {
	"code": "97D99",
	"title": " None of the above, but in this section",
	"parentcode": "97Dxx",
	"level": 3
}, {
	"code": "97Exx",
	"title": " Foundations of mathematics",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97E10",
	"title": " Comprehensive works",
	"parentcode": "97Exx",
	"level": 3
}, {
	"code": "97E20",
	"title": " Philosophy and mathematics",
	"parentcode": "97Exx",
	"level": 3
}, {
	"code": "97E30",
	"title": " Logic",
	"parentcode": "97Exx",
	"level": 3
}, {
	"code": "97E40",
	"title": " Language of mathematics",
	"parentcode": "97Exx",
	"level": 3
}, {
	"code": "97E50",
	"title": " Reasoning and proving in the mathematics classroom",
	"parentcode": "97Exx",
	"level": 3
}, {
	"code": "97E60",
	"title": " Sets, relations, set theory",
	"parentcode": "97Exx",
	"level": 3
}, {
	"code": "97E99",
	"title": " None of the above, but in this section",
	"parentcode": "97Exx",
	"level": 3
}, {
	"code": "97Fxx",
	"title": " Arithmetic, number theory",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97F10",
	"title": " Comprehensive works",
	"parentcode": "97Fxx",
	"level": 3
}, {
	"code": "97F20",
	"title": " Pre-numerical stage, concept of numbers",
	"parentcode": "97Fxx",
	"level": 3
}, {
	"code": "97F30",
	"title": " Natural numbers",
	"parentcode": "97Fxx",
	"level": 3
}, {
	"code": "97F40",
	"title": " Integers, rational numbers",
	"parentcode": "97Fxx",
	"level": 3
}, {
	"code": "97F50",
	"title": " Real numbers, complex numbers",
	"parentcode": "97Fxx",
	"level": 3
}, {
	"code": "97F60",
	"title": " Number theory",
	"parentcode": "97Fxx",
	"level": 3
}, {
	"code": "97F70",
	"title": " Measures and units",
	"parentcode": "97Fxx",
	"level": 3
}, {
	"code": "97F80",
	"title": " Ratio and proportion, percentages",
	"parentcode": "97Fxx",
	"level": 3
}, {
	"code": "97F90",
	"title": " Real life mathematics, practical arithmetic",
	"parentcode": "97Fxx",
	"level": 3
}, {
	"code": "97F99",
	"title": " None of the above, but in this section",
	"parentcode": "97Fxx",
	"level": 3
}, {
	"code": "97Gxx",
	"title": " Geometry",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97G10",
	"title": " Comprehensive works",
	"parentcode": "97Gxx",
	"level": 3
}, {
	"code": "97G20",
	"title": " Informal geometry",
	"parentcode": "97Gxx",
	"level": 3
}, {
	"code": "97G30",
	"title": " Areas and volumes",
	"parentcode": "97Gxx",
	"level": 3
}, {
	"code": "97G40",
	"title": " Plane and solid geometry",
	"parentcode": "97Gxx",
	"level": 3
}, {
	"code": "97G50",
	"title": " Transformation geometry",
	"parentcode": "97Gxx",
	"level": 3
}, {
	"code": "97G60",
	"title": " Plane and spherical trigonometry",
	"parentcode": "97Gxx",
	"level": 3
}, {
	"code": "97G70",
	"title": " Analytic geometry. Vector algebra",
	"parentcode": "97Gxx",
	"level": 3
}, {
	"code": "97G80",
	"title": " Descriptive geometry",
	"parentcode": "97Gxx",
	"level": 3
}, {
	"code": "97G99",
	"title": " None of the above, but in this section",
	"parentcode": "97Gxx",
	"level": 3
}, {
	"code": "97Hxx",
	"title": " Algebra",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97H10",
	"title": " Comprehensive works",
	"parentcode": "97Hxx",
	"level": 3
}, {
	"code": "97H20",
	"title": " Elementary algebra",
	"parentcode": "97Hxx",
	"level": 3
}, {
	"code": "97H30",
	"title": " Equations and inequalities",
	"parentcode": "97Hxx",
	"level": 3
}, {
	"code": "97H40",
	"title": " Groups, rings, fields",
	"parentcode": "97Hxx",
	"level": 3
}, {
	"code": "97H50",
	"title": " Ordered algebraic structures",
	"parentcode": "97Hxx",
	"level": 3
}, {
	"code": "97H60",
	"title": " Linear algebra",
	"parentcode": "97Hxx",
	"level": 3
}, {
	"code": "97H99",
	"title": " None of the above, but in this section",
	"parentcode": "97Hxx",
	"level": 3
}, {
	"code": "97Ixx",
	"title": " Analysis",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97I10",
	"title": " Comprehensive works",
	"parentcode": "97Ixx",
	"level": 3
}, {
	"code": "97I20",
	"title": " Mappings and functions",
	"parentcode": "97Ixx",
	"level": 3
}, {
	"code": "97I30",
	"title": " Sequences and series",
	"parentcode": "97Ixx",
	"level": 3
}, {
	"code": "97I40",
	"title": " Differential calculus",
	"parentcode": "97Ixx",
	"level": 3
}, {
	"code": "97I50",
	"title": " Integral calculus",
	"parentcode": "97Ixx",
	"level": 3
}, {
	"code": "97I60",
	"title": " Functions of several variables",
	"parentcode": "97Ixx",
	"level": 3
}, {
	"code": "97I70",
	"title": " Functional equations",
	"parentcode": "97Ixx",
	"level": 3
}, {
	"code": "97I80",
	"title": " Complex analysis",
	"parentcode": "97Ixx",
	"level": 3
}, {
	"code": "97I99",
	"title": " None of the above, but in this section",
	"parentcode": "97Ixx",
	"level": 3
}, {
	"code": "97Kxx",
	"title": " Combinatorics, graph theory, probability theory, statistics",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97K10",
	"title": " Comprehensive works",
	"parentcode": "97Kxx",
	"level": 3
}, {
	"code": "97K20",
	"title": " Combinatorics",
	"parentcode": "97Kxx",
	"level": 3
}, {
	"code": "97K30",
	"title": " Graph theory",
	"parentcode": "97Kxx",
	"level": 3
}, {
	"code": "97K40",
	"title": " Descriptive statistics",
	"parentcode": "97Kxx",
	"level": 3
}, {
	"code": "97K50",
	"title": " Probability theory",
	"parentcode": "97Kxx",
	"level": 3
}, {
	"code": "97K60",
	"title": " Distributions and stochastic processes",
	"parentcode": "97Kxx",
	"level": 3
}, {
	"code": "97K70",
	"title": " Foundations and methodology of statistics",
	"parentcode": "97Kxx",
	"level": 3
}, {
	"code": "97K80",
	"title": " Applied statistics",
	"parentcode": "97Kxx",
	"level": 3
}, {
	"code": "97K99",
	"title": " None of the above, but in this section",
	"parentcode": "97Kxx",
	"level": 3
}, {
	"code": "97Mxx",
	"title": " Mathematical modeling, applications of mathematics",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97M10",
	"title": " Modeling and interdisciplinarity",
	"parentcode": "97Mxx",
	"level": 3
}, {
	"code": "97M20",
	"title": " Mathematics in vocational training and career education",
	"parentcode": "97Mxx",
	"level": 3
}, {
	"code": "97M30",
	"title": " Financial and insurance mathematics",
	"parentcode": "97Mxx",
	"level": 3
}, {
	"code": "97M40",
	"title": " Operations research, economics",
	"parentcode": "97Mxx",
	"level": 3
}, {
	"code": "97M50",
	"title": " Physics, astronomy, technology, engineering",
	"parentcode": "97Mxx",
	"level": 3
}, {
	"code": "97M60",
	"title": " Biology, chemistry, medicine",
	"parentcode": "97Mxx",
	"level": 3
}, {
	"code": "97M70",
	"title": " Behavioral and social sciences",
	"parentcode": "97Mxx",
	"level": 3
}, {
	"code": "97M80",
	"title": " Arts, music, language, architecture",
	"parentcode": "97Mxx",
	"level": 3
}, {
	"code": "97M99",
	"title": " None of the above, but in this section",
	"parentcode": "97Mxx",
	"level": 3
}, {
	"code": "97Nxx",
	"title": " Numerical mathematics",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97N10",
	"title": " Comprehensive works",
	"parentcode": "97Nxx",
	"level": 3
}, {
	"code": "97N20",
	"title": " Rounding, estimation, theory of errors",
	"parentcode": "97Nxx",
	"level": 3
}, {
	"code": "97N30",
	"title": " Numerical algebra",
	"parentcode": "97Nxx",
	"level": 3
}, {
	"code": "97N40",
	"title": " Numerical analysis",
	"parentcode": "97Nxx",
	"level": 3
}, {
	"code": "97N50",
	"title": " Interpolation and approximation",
	"parentcode": "97Nxx",
	"level": 3
}, {
	"code": "97N60",
	"title": " Mathematical programming",
	"parentcode": "97Nxx",
	"level": 3
}, {
	"code": "97N70",
	"title": " Discrete mathematics",
	"parentcode": "97Nxx",
	"level": 3
}, {
	"code": "97N80",
	"title": " Mathematical software, computer programs",
	"parentcode": "97Nxx",
	"level": 3
}, {
	"code": "97N99",
	"title": " None of the above, but in this section",
	"parentcode": "97Nxx",
	"level": 3
}, {
	"code": "97Pxx",
	"title": " Computer science",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97P10",
	"title": " Comprehensive works",
	"parentcode": "97Pxx",
	"level": 3
}, {
	"code": "97P20",
	"title": " Theory of computer science",
	"parentcode": "97Pxx",
	"level": 3
}, {
	"code": "97P30",
	"title": " System software",
	"parentcode": "97Pxx",
	"level": 3
}, {
	"code": "97P40",
	"title": " Programming languages",
	"parentcode": "97Pxx",
	"level": 3
}, {
	"code": "97P50",
	"title": " Programming techniques",
	"parentcode": "97Pxx",
	"level": 3
}, {
	"code": "97P60",
	"title": " Hardware",
	"parentcode": "97Pxx",
	"level": 3
}, {
	"code": "97P70",
	"title": " Computer science and society",
	"parentcode": "97Pxx",
	"level": 3
}, {
	"code": "97P99",
	"title": " None of the above, but in this section",
	"parentcode": "97Pxx",
	"level": 3
}, {
	"code": "97Qxx",
	"title": " Computer science education",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97Q10",
	"title": " Comprehensive works",
	"parentcode": "97Qxx",
	"level": 3
}, {
	"code": "97Q20",
	"title": " Affective aspects in teaching computer science",
	"parentcode": "97Qxx",
	"level": 3
}, {
	"code": "97Q30",
	"title": " Cognitive processes",
	"parentcode": "97Qxx",
	"level": 3
}, {
	"code": "97Q40",
	"title": " Sociological aspects",
	"parentcode": "97Qxx",
	"level": 3
}, {
	"code": "97Q50",
	"title": " Objectives",
	"parentcode": "97Qxx",
	"level": 3
}, {
	"code": "97Q60",
	"title": " Teaching methods and classroom techniques",
	"parentcode": "97Qxx",
	"level": 3
}, {
	"code": "97Q70",
	"title": " Student assessment",
	"parentcode": "97Qxx",
	"level": 3
}, {
	"code": "97Q80",
	"title": " Teaching units",
	"parentcode": "97Qxx",
	"level": 3
}, {
	"code": "97Q99",
	"title": " None of the above, but in this section",
	"parentcode": "97Qxx",
	"level": 3
}, {
	"code": "97Rxx",
	"title": " Computer science applications",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97R10",
	"title": " Comprehensive works, collections of programs",
	"parentcode": "97Rxx",
	"level": 3
}, {
	"code": "97R20",
	"title": " Applications in mathematics",
	"parentcode": "97Rxx",
	"level": 3
}, {
	"code": "97R30",
	"title": " Applications in sciences",
	"parentcode": "97Rxx",
	"level": 3
}, {
	"code": "97R40",
	"title": " Artificial intelligence",
	"parentcode": "97Rxx",
	"level": 3
}, {
	"code": "97R50",
	"title": " Data bases, information systems",
	"parentcode": "97Rxx",
	"level": 3
}, {
	"code": "97R60",
	"title": " Computer graphics",
	"parentcode": "97Rxx",
	"level": 3
}, {
	"code": "97R70",
	"title": " User programs, administrative applications",
	"parentcode": "97Rxx",
	"level": 3
}, {
	"code": "97R80",
	"title": " Recreational computing",
	"parentcode": "97Rxx",
	"level": 3
}, {
	"code": "97R99",
	"title": " None of the above, but in this section",
	"parentcode": "97Rxx",
	"level": 3
}, {
	"code": "97Uxx",
	"title": " Educational material and media, educational technology",
	"parentcode": "97-XX",
	"level": 2
}, {
	"code": "97U10",
	"title": " Comprehensive works",
	"parentcode": "97Uxx",
	"level": 3
}, {
	"code": "97U20",
	"title": " Textbooks. Textbook research",
	"parentcode": "97Uxx",
	"level": 3
}, {
	"code": "97U30",
	"title": " Teachers' manuals and planning aids",
	"parentcode": "97Uxx",
	"level": 3
}, {
	"code": "97U40",
	"title": " Problem books. Competitions. Examinations",
	"parentcode": "97Uxx",
	"level": 3
}, {
	"code": "97U50",
	"title": " Computer assisted instruction; e-learning",
	"parentcode": "97Uxx",
	"level": 3
}, {
	"code": "97U60",
	"title": " Manipulative materials",
	"parentcode": "97Uxx",
	"level": 3
}, {
	"code": "97U70",
	"title": " Technological tools, calculators",
	"parentcode": "97Uxx",
	"level": 3
}, {
	"code": "97U80",
	"title": " Audiovisual media",
	"parentcode": "97Uxx",
	"level": 3
}, {
	"code": "97U99",
	"title": " None of the above, but in this section",
	"parentcode": "97Uxx",
	"level": 3
}, {
	"code": ""
}]