My math homework from my undergraduate years at UW Madison as a math major. Math courses I've taken include:
- The first installment to the calc 3 + linear algebra sequence of the math major
- Introduces proofs for the first time
- Topic include: vector spaces, linear transformations, eigen decomposition, total derivatives, etc.
- The second installment to the calc 3 + linear algebra sequence of the math major
- Topics include: multiple integrals, line/surface integrals, green and stokes theorem, gauss divergence theorem
- Some ODE techniques are taught at the end
- Computational-based introduction to probability theory
- Topics include: conditional probability, CLT, LLN, statisitical significance, etc.
- MATH531 is a more rigorous alternative
- Historical runthrough of mathematical breakthroughs
- Is a humanities class with a heavy emphasis on geometry
- Topics include: the timeline of mathematics from pythagoras to projective geometry
- Semi-rigorous introduction to combinatorics
- Topics include: counting, pigeonhole principle, recursion, sequences, a bit of group theory at the end
- Rigorous overhaul of continuity and real numbers
- Defineds the entirety of calculus with topology
- Topic includes: real number properties, topologies, compactness, differentiation, integration
- It's calculus but on steroids
- Rigorous overhaul of mathematical structures
- Group and rings model symmetry and modular arithmetics respectively
- Topics include: group theory (homomorphism theorems, quotient groups, group characterizations) and ring theory (different kinds of domains, CRT, polynomial rings)
- Machine/data assisted computational introduction to SDEs
- Programming heavy, python or R recommended
- Topics include: Solving ODEs, markov chains, Ito's integral, Euler-maruyama method, kalman filtering, linear regression of SDE parameters
- Semi-rigorous introduction to markov chains
- Topics include: markov chains and their properties (i.e. limit properties, continuity, martingales)