Graduate School of Matehematics and Computer Science  > Comprehensive Examination

Two subjects for the complex examination must be chosen from the following eight groups of subjects. The list after each group shows the combination of subjects that can be chosen for each group. It is not possible to choose both subjects from the same group.

Subjects of the comprehensive examination

Groups of subjects: Algebra and logics, Analysis, Differential equations and their solutions, Discrete mathetics and computer science, Geometry, Operation Reseachs, Number theory, Stochastics (jump to the groups of subjects)

Algebra and logics (1+2, 4+5+9, 8+15, 6+7, 3+10+11 or 12+13+15)

1. Groups
2. Group representations
3. Semigroups and automata
4. Non-commutative rings
5. Homological algebra
6. Commutative algebra
7. Algebraic geometry
8. Field theory
9. Lie algebras
10. Universal algebra
11. Lattice theory
12. Model theory
13. Proof theory
14. Non-classical logics
15. Linear algebra

Analysis (any two of the 9 topics in this group)

1. Measure and integral
2. Operator algebras
3. Matrix analysis
4. Complex analysis
5. Fourier analysis
6. Functional analysis
7. Linear systems
8. Approximation theory
9. Numerical methods

Differential equations and their solutions (any two of the 16 topics in this group)

1. Ordinary differential equations
2. Dynamical systems
3. Chaos and ergodic theory
4. Numerical dynamics
5. Functional differential equations
6. Dynamical models in biology
7. Control theory
8. Numerical methods for ordinary differential equations: stability, convergence, accuracy
9. Classical partial differential equations
10. Sobolev spaces
11. Linear elliptic equations
12. Linear parabolic and hyperbolic equations
13. Reaction-diffusion equations
14. Nonlinear hyperbolic equations
15. Numerical methods for partial differential equations: stability, convergence, accuracy
16. Large-scale linear systems

Discrete mathetics and computer science (any two of the 9 topics in this group)

1. Combinatorial analysis and graph theory
2. Matroid theory
3. Data structures
4. Models of computation
5. Linear programming
6. Stochastic programming
7. Combinatorial optimization
8. Machine learning
9. Data mining and its application

Geometry (any two of the 8 topics in this group)

1. Surface Modelling with Spline Functions
2. Geometric Modelling Algorithms
3. Lattice Geometry
4. Crystallographic Geometry
5. Non-Euclidean Geometry
6. Combinatorial Geometry
7. Differential Geometry
8. Riemannian Geometry

Operation reseach (at least one of the topics must be chosen from the set {1,2,3,4,5,8})

1. Linear programming
2. Nonlinear programming
3. Stochastic programming
4. Integer programming
5. Combinatorial optimization
6. Semidefinite programming
7. Global optimization
8. Convex analysis
9. Dynamic programming
10. Econometrics
11. Game theory
12. Optimal controll
13. Linear complementary problems
14. Numerical methods of Operations Research

Number theory (any two of the 7 topics in this group)

1. Combinatorial number theory
2. Additive number theory
3. Analytic number theory
4. Algebraic number theory
5. Modular forms
6. Class field theory
7. Cryptographic applications of number theory

Stochastics (any two of the 9 topics in this group)

1. Basics of probability
2. Martingales and limit theorems
3. Random walks and Markov processes
4. Stationary processes
5. Stochstic analysis
6. Information Theory
7. Basics of statistics
8. Statisstical hypothesis testing
9. Multivariate (statistical) analysis

Utolsó módosítás: 2025.03.20.