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ELTE Final Exam
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ELTE Final Exam preparation

This repository contains the flashcards and other material used to prepare for the BSc. Computer Science final exam.

Anki flashcards

Exam Topics

  1. Sequences, series, funcions, limits and continuity
  • Convergence of sequences of real and complex numbers and vectors
  • Monotonic sequences
  • Notion and convergence of infinite numerical series
  • Positive series
  • The root and the ratio test
  • Alternating (Leibniz type) series
  • Power series
  • The Cauchy–Hadamard theorem
  • Limits and continuity of vector–vector functions
  • Properties of functions on a compact set: Theorems of Heine
  • Properties of functions on a compact set: Weierstrass
  • Continuity of the inverse function
  • The Bolzano theorem
  1. Differential and integral calculus and applications
  • Differentiation and integration of functions of one real variable
  • Rules of differentiation
  • Theorems of Rolle, Cauchyand Lagrange
  • Extrema, concavity, discussion of functions
  • The Riemannian integral
  • Integration by parts, integration with substitution
  • The fundamental theorem of calculus (The Newton–Leibniz formula)
  • Area, arc length, volume, surface
  • Differentiation of vector–vector functions
  • Jacobi matrix, gradient, partial derivative
  1. Systems of differential equations
  • The initial value problem
  • Linear systems of differential equations
  • Linear equations of higher-order
  1. Methods of interpolation
  • Lagrange interpolation
  • Hermite interpolation
  • Spline in-terpolation Extra: [ ] 3rd degree spline interpolation (cubic)
  1. Numerical solution of linear systems of equations
  • Gaussian elimination
  • Methods based on product decomposition
  • Iterative methods
  • Least-squares methods
  1. Sets, relations and enumeration problems
  • Basic operations on sets and their properties
  • Binary relations and their properties (transitivity, etc.)
  • Partial orderings and equivalence relations
  • Permutations, variations, combinations
  • Inclusion-exclusion principle
  • Pigeonhole principle
  • Binomial theorem
  1. Undirected and directed graphs
  • Basic concepts in graph theory: vertex, edge, degree, walk, trail, path, cycle, connectivity, component
  • Trees and their characterizations
  • Eulerian and Hamiltonian graphs
  • Labeling and coloring, Kruskal’s algorithms on minimal spanning trees
  1. Basics of linear algebra
  • Matrices
  • Determinants
  • Basis and dimension in vector spaces
  • Eigenvalues and eigenvectors of matrices, diagonalization
  • Orthogonal and orthonormal systems in Euclidean spaces
  1. Basics of probability and statistics
  • Discrete and continuous random variables
  • Law of large numbers
  • Central limit theorem
  • Statistical estimates
  • Classical statistical tests
  1. Artificial intelligence
  • Path-finding problems and their modelling with directed graph(state-space model, problem decomposition model)
  • Heuristic path-finding algorithms (their outcomes and computational cost): local searches, backtracking algorithms, graph searches (A, A∗, AC, Balgorithm)
  • Two-player games (game tree, existence of winning strategy, minimax algorithm, alpha-beta pruning)
  1. Programming theorems
  • Usage of programming theorems in programming
  • Summation, counting, maximum search, conditional maximum search (conditional maximum search is missing)
  • Sequential search
  • Binary search
  1. Software development models
  • Development stages of large scale systems (ambiguous)
  • The concept of object-oriented programming, type inheritance
  • Views of object-oriented modeling, UML tools (wtf is views?)
  • The notion of software design patterns
  1. Static and dynamic models
  • Static model (class diagram, object diagram)
  • Usecase diagrams
  1. Compilation and execution of programs
  • Compilers and interpreters, bytecode
  • Pre-processor, compiler, linker
  • Make
  • Compilation units, libraries
  • Syntactic and semantic rules
  • Static and dynamic type checking
  • Parallel programming
  1. Data, operators and control structures
  • Representation of numbers, basic data types
  • User defined types
  • Operators, expression evaluation
  • Statements, control structures,recursion, exception handling
  • Data abstraction
  • Class, inheritance, static and dy-namic binding, subtype polymorphism
  • Generics
  1. Program structure
  • Block, visibility, scope
  • Automatic, static and dynamic variables,garbage collection
  • Constructor, destructor
  • Cloning and comparing objects
  • Programmodules, namespaces
  • Subroutines, parameter passing
  • Overloading
  1. Compilers
  • Structure of compilers, the tasks of the components
  • Lexical analyzer and its functions, implementation
  • Classification and comparison of syntactic analyzers, overview of their creation and functioning
  • The notion and use of ATGs
  • Code generation in assembly for basic imperative constructs
  1. Logic
  • The syntax and semantics of propositional and predicate calculus
  • The notion of logical consequence
  • Basic methods for proving logical consequences in propositional calculus: truth tables, the method of semantic tableaux, and the resolution
  1. Theory of computation
  • The Church–Turing thesis
  • Variants of Turing machines (one tape – multi tape, deterministic – non-deterministic)
  • Recursive and recursively enumerable languages
  • Undecidable problems
  • Reducibility
  • The time complexity classes P and NP
  • Polinomial time reducibility
  • NP-complete problems
  • The space complexityclasses PSPACE and NPSPACE
  • Savitch’s theorem
  • PSPACE-complete problems
  1. Data structures
  • Representations and operations of basic data structures—array, stack, queue, priority queue, list, binary tree, graph
  1. Basic algorithms
  • Representations of search data structures (binary search tree, AVLtree, 2-3 tree, B tree, hashing with chaining and open addressing)
  • Sorting algorithms and their efficiency (bubble, insert, maximum selection, tournament, heap, quick and merge sort algorithms)
  • Sorting in linear time: bucket sorts, radix sorts
  1. Formal languages
  • Generative grammars, the Chomsky hierarchy
  • Basic properties and application of regular and context-free grammars and languages
  • Finite automata and pushdown automata
  1. Operating systems—parallel processes
  • The notion and implementation of process and thread
  • Interactive, batch and real-time processes, scheduling algorithms
  • Types of parallelism, race conditions, critical sections
  • Shared memory and messaging
  • Semafors and monitors
  • Deadlocks: description, avoidance, prevention, recognition
  1. Operating systems—storage handling
  • Hierarchy of storages
  • Memory handling: fixed and dynamic partitions, virtual memory
  • Paging and segmentation
  • Page re-placement algorithms, working set
  • Scheduling input and output, reducing serving time
  • Organizing disk storage, physical and logical formatting, partitions
  • Redundant arrays, array handling systems
  • File systems and their implementation
  • Block reservation strategies, registering free storage space, journaled file systems
  1. Computer networks
  • Physical layer, data link layer, MAC, network layer, transport layer—services, methods, protocols
  1. Distributed systems
  • Definition
  • Design goals
  • Distribution transparency
  • Typesof distributed systems
  • Architectures
  • Middleware
  • Processes
  • Threads
  • Virtualization
  • Clients-servers
  • Code migration
  • Types of communication (transient, persistent,message-oriented, RPC, multicasting, data dissemination)
  • Naming (flat, structured,attributed)
  • Coordination
  • Clock synchronization
  • Logical clocks
  • Vector clocks
  • Mutual exclusion
  • Election algorithms
  • Location systems
  • Consistency and replication
  1. Databases—query languages
  • Relational model, entity–relationship model, transformation from ER to relational model
  • Relational algebra, SQL, Datalog
  • Recursion inquery languages
  • Procedural elements in query langauges (variables, control structures, subprograms, cursors, exceptions)
  1. Databases—query execution
  • Index structures, sparse and dense index, B+ tree, bitmap index, dynamic hashing
  • One-pass and two-pass algorithms, sort based and hash-based algorithms
  • Join methods
  • Cost of operations
  • Query execution plans
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