Phd studies
Study program – Mathematics
Phd studies
Study program – Mathematics
Study length: 3 years (6 semesters)
Total number of ECTS: 180
This Study Program became active since the 2022/23. school year.
Note: The study program will be performed in serbian and english languages
Dictionary of terms:
-
- L – the number of classes of lectures
- RW – the number of classes of exercises
- ECTS – European Credit Transfer and Accumulation System
- Fall semester
- Spring semester
- Fall or spring semester
| 1st year | ECTS | ||
|---|---|---|---|
| L | RW | ||
| Elective course 1 | 4 | 6 | 9 |
| Elective course 2 | 4 | 6 | 9 |
| Preparation of a doctoral dissertation 1 | 0 | 2 | 12 |
| Elective course 3 | 4 | 6 | 9 |
| Elective course 4 | 4 | 6 | 9 |
| Preparation of a doctoral dissertation 2 | 0 | 2 | 12 |
| 60 |
| 2nd year | ECTS | ||
|---|---|---|---|
| L | RW | ||
| Elective course 5 | 4 | 6 | 9 |
| Elective course 6 | 4 | 6 | 9 |
| Preparation of a doctoral dissertation 3 | 0 | 2 | 12 |
| Elective course 7 | 4 | 6 | 9 |
| Special course 1 | 4 | 6 | 9 |
| Preparation of a doctoral dissertation 4 | 0 | 2 | 12 |
| 60 |
| 3rd year | ЕСПБ |
||
|---|---|---|---|
| L | RW | ||
| Scientific research work 1 | 0 | 10 | 4 |
| Preparation of a doctoral dissertation 5 | 0 | 10 | 26 |
| Scientific research work 2 | 0 | 10 | 4 |
| Preparation of a doctoral dissertation 6 | 0 | 10 | 26 |
| 60 |
| List of elective courses - M3 | ECTS |
||
|---|---|---|---|
| L | RW | ||
| Algebra 4 | 4 | 6 | 9 |
| Universal algebra | 4 | 6 | 9 |
| Commutative rings | 4 | 6 | 9 |
| Rings and modules | 4 | 6 | 9 |
| Algebraic geometry | 4 | 6 | 9 |
| Homology methods in algebra | 4 | 6 | 9 |
| Model-theoretical algebra | 4 | 6 | 9 |
| Non-commutative algebra | 4 | 6 | 9 |
| Introduction to Hopf algebras | 4 | 6 | 9 |
| Discrete mathematics | 4 | 6 | 9 |
| Introduction to the theory of representations | 4 | 6 | 9 |
| Automorphic forms and representations | 4 | 6 | 9 |
| Analytic number theory | 4 | 6 | 9 |
| Algebraic number theory | 4 | 6 | 9 |
| Elliptic curves and an introduction to Diophantine geometry | 4 | 6 | 9 |
| Special course - Algebra | 4 | 6 | 9 |
| Analysis 4 | 4 | 6 | 9 |
| Complex analysis 2 | 4 | 6 | 9 |
| Theory of manifolds | 4 | 6 | 9 |
| Global analysis | 4 | 6 | 9 |
| Morse theory | 4 | 6 | 9 |
| Symplectic manifolds | 4 | 6 | 9 |
| Chaos theory in dynamical systems | 4 | 6 | 9 |
| Contact dynamics | 4 | 6 | 9 |
| Hamiltonian dynamics | 4 | 6 | 9 |
| Hamiltonian dynamics with elements of Flore's theory | 4 | 6 | 9 |
| Flor's theory with applications in contact and Hamiltonian dynamics | 4 | 6 | 9 |
| Hardy's and Bergman's spaces | 4 | 6 | 9 |
| Whole functions | 4 | 6 | 9 |
| The premises of Soboljevo | 4 | 6 | 9 |
| Integral operators | 4 | 6 | 9 |
| Interpolation of operators | 4 | 6 | 9 |
| Matrix analysis | 4 | 6 | 9 |
| Algebras of operators | 4 | 6 | 9 |
| Non-commutative dynamics | 4 | 6 | 9 |
| Spectral theory | 4 | 6 | 9 |
| Geometric theory of harmonic functions | 4 | 6 | 9 |
| Classical harmonic analysis | 4 | 6 | 9 |
| Quasiconformal and harmonic mappings | 4 | 6 | 9 |
| Differential operators | 4 | 6 | 9 |
| Pseudodifferential operators | 4 | 6 | 9 |
| Compact and non-self-conjugate operators | 4 | 6 | 9 |
| Banach algebras | 4 | 6 | 9 |
| Hilbert modules | 4 | 6 | 9 |
| K theory C* algebra | 4 | 6 | 9 |
| Pseudoholomorphic curves in symplectic manifolds | 4 | 6 | 9 |
| Fredholm mappings in global analysis | 4 | 6 | 9 |
| Contact manifolds and holomorphic curves | 4 | 6 | 9 |
| Symplectic and Hamiltonian actions | 4 | 6 | 9 |
| Near-complex structures and holomorphic curves | 4 | 6 | 9 |
| Linear topological spaces | 4 | 6 | 9 |
| Theory of distributions | 4 | 6 | 9 |
| Functional analysis | 4 | 6 | 9 |
| Nonlinear functional analysis | 4 | 6 | 9 |
| Stability of solutions of ordinary differential equations | 4 | 6 | 9 |
| Qualitative analysis of ordinary differential equations | 4 | 6 | 9 |
| Complex dynamic systems | 4 | 6 | 9 |
| Asymptotic analysis | 4 | 6 | 9 |
| Fixed point theory | 4 | 6 | 9 |
| Geometric theory of functions 2 | 4 | 6 | 9 |
| Analysis on manifolds | 4 | 6 | 9 |
| Special course - Analysis and differential equations | 4 | 6 | 9 |
| Riemannian geometry A | 4 | 6 | 9 |
| Riemannian geometry B | 4 | 6 | 9 |
| Groups in geometry A | 4 | 6 | 9 |
| Groups in geometry B | 4 | 6 | 9 |
| Non-Euclidean geometries | 4 | 6 | 9 |
| Regular polytopes | 4 | 6 | 9 |
| Geometry of discrete groups | 4 | 6 | 9 |
| Complex manifolds | 4 | 6 | 9 |
| Spectral geometry | 4 | 6 | 9 |
| Differential geometry of vector layers | 4 | 6 | 9 |
| Differential geometric methods in statistics | 4 | 6 | 9 |
| Discrete differential geometry | 4 | 6 | 9 |
| Geometry in computer science | 4 | 6 | 9 |
| Geometry in astronomy | 4 | 6 | 9 |
| Geometric modeling in industry and design | 4 | 6 | 9 |
| Symmetry groups | 4 | 6 | 9 |
| Groups of transformations | 4 | 6 | 9 |
| Homogeneous spaces | 4 | 6 | 9 |
| Representations of Lie groups and algebras | 4 | 6 | 9 |
| Symplectic geometry | 4 | 6 | 9 |
| Stochastic differential geometry | 4 | 6 | 9 |
| Theory of submanifolds | 4 | 6 | 9 |
| Special course - Geometry | 4 | 6 | 9 |
| Model theory | 4 | 6 | 9 |
| Theory of computability | 4 | 6 | 9 |
| Evidence theory | 4 | 6 | 9 |
| Theory of sets | 4 | 6 | 9 |
| Mathematical logic in computing | 4 | 6 | 9 |
| Non-classical logic | 4 | 6 | 9 |
| Theoretical computing | 4 | 6 | 9 |
| Theory of automata and formal grammar | 4 | 6 | 9 |
| Boolean algebras | 4 | 6 | 9 |
| Applied logical theories | 4 | 6 | 9 |
| Non-standard analysis | 4 | 6 | 9 |
| Special course - Mathematical logic and theoretical computing | 4 | 6 | 9 |
| Selected chapters of the theory of extremal problems | 4 | 6 | 9 |
| Numerical analysis 3 | 4 | 6 | 9 |
| Finite element method with applications | 4 | 6 | 9 |
| Finite difference method | 4 | 6 | 9 |
| Theory of approximations with applications | 4 | 6 | 9 |
| Game theory | 4 | 6 | 9 |
| Regularization methods | 4 | 6 | 9 |
| Discrete optimization | 4 | 6 | 9 |
| Pontryagin's maximum principle | 4 | 6 | 9 |
| Theory of location problems with applications | 4 | 6 | 9 |
| Metaheuristic methods - advanced concepts | 4 | 6 | 9 |
| Spectral theory of graphs with applications | 4 | 6 | 9 |
| Algorithms on graphs and their applications | 4 | 6 | 9 |
| Combinatorial graph theory with applications | 4 | 6 | 9 |
| Special course - Applied mathematics | 4 | 6 | 9 |
| Algebraic combinatorics | 4 | 6 | 9 |
| Dynamic systems | 4 | 6 | 9 |
| Optimization | 4 | 6 | 9 |
| Data structures | 4 | 6 | 9 |
| Algebraic topology | 4 | 6 | 9 |
| Differential topology | 4 | 6 | 9 |
| Topological combinatorics | 4 | 6 | 9 |
| Discrete and computational topology | 4 | 6 | 9 |
| Function spaces | 4 | 6 | 9 |
| PL topology | 4 | 6 | 9 |
| K - theory | 4 | 6 | 9 |
| Vector layers and characteristic classes | 4 | 6 | 9 |
| Homotopy theory | 4 | 6 | 9 |
| Low dimensional topology | 4 | 6 | 9 |
| Cohomology of groups | 4 | 6 | 9 |
| Spectral arrays | 4 | 6 | 9 |
| Selected chapters from general topology | 4 | 6 | 9 |
| Selected chapters in algebraic topology | 4 | 6 | 9 |
| Cohomological operations | 4 | 6 | 9 |
| The theory of cobordism | 4 | 6 | 9 |
| Equivariant topologies and applications | 4 | 6 | 9 |
| Special course - Topology | 4 | 6 | 9 |
| Mathematical statistics | 4 | 6 | 9 |
| Bayesian data analysis | 4 | 6 | 9 |
| Theory of random processes | 4 | 6 | 9 |
| Reliability theory | 4 | 6 | 9 |
| Theory of mass catering | 4 | 6 | 9 |
| Spectral theory of random processes | 4 | 6 | 9 |
| Gaussian random processes | 4 | 6 | 9 |
| Stationary random processes | 4 | 6 | 9 |
| Time series analysis | 4 | 6 | 9 |
| Statistics of random processes | 4 | 6 | 9 |
| Stochastic differential equations | 4 | 6 | 9 |
| Stochastic financial mathematics | 4 | 6 | 9 |
| Statistical hypothesis testing | 4 | 6 | 9 |
| Linear statistical models | 4 | 6 | 9 |
| Non-parametric statistics | 4 | 6 | 9 |
| Information theory | 4 | 6 | 9 |
| Coding theory | 4 | 6 | 9 |
| Ergodic theory | 4 | 6 | 9 |
| Stochastic analysis | 4 | 6 | 9 |
| Probability measures in metric spaces | 4 | 6 | 9 |
| Theory of extreme values | 4 | 6 | 9 |
| Risk theory - advanced concepts | 4 | 6 | 9 |
| Special Course - Probability and Statistics | 4 | 6 | 9 |
| Fluid mechanics | 4 | 6 | 9 |
| Integrable dynamical systems and solitons | 4 | 6 | 9 |
| General Relativity and Cosmological Models (NEW) | 4 | 6 | 9 |
| Dynamics of body systems | 4 | 6 | 9 |
| Analytical mechanics | 4 | 6 | 9 |
| Educational Software - Advanced Concepts | 4 | 6 | 9 |
| Research methodology in teaching mathematics and computer science with practicum | 4 | 6 | 9 |
Адреса: Студентски трг 16, 11000 Београд
Телефон: (+381) 11 2027 855 (10-14h)
(+381) 64 8650 003 (10-14h)
Е-пошта: upis@matf.bg.ac.rs