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 yearECTS
Elective course 1469
Elective course 2469
Preparation of a doctoral dissertation 10212
Elective course 3469
Elective course 4469
Preparation of a doctoral dissertation 20212
2nd yearECTS
Elective course 5469
Elective course 6469
Preparation of a doctoral dissertation 30212
Elective course 7469
Special course 1469
Preparation of a doctoral dissertation 40212
3rd yearЕСПБ

Scientific research work 10104
Preparation of a doctoral dissertation 501026
Scientific research work 20104
Preparation of a doctoral dissertation 601026
List of elective courses - M3ECTS

Algebra 4469
Universal algebra469
Commutative rings469
Rings and modules469
Algebraic geometry469
Homology methods in algebra469
Model-theoretical algebra469
Non-commutative algebra469
Introduction to Hopf algebras469
Discrete mathematics469
Introduction to the theory of representations469
Automorphic forms and representations469
Analytic number theory469
Algebraic number theory469
Elliptic curves and an introduction to Diophantine geometry469
Special course - Algebra469
Analysis 4469
Complex analysis 2469
Theory of manifolds469
Global analysis469
Morse theory469
Symplectic manifolds469
Chaos theory in dynamical systems469
Contact dynamics469
Hamiltonian dynamics469
Hamiltonian dynamics with elements of Flore's theory469
Flor's theory with applications in contact and Hamiltonian dynamics469
Hardy's and Bergman's spaces469
Whole functions469
The premises of Soboljevo469
Integral operators469
Interpolation of operators469
Matrix analysis469
Algebras of operators469
Non-commutative dynamics469
Spectral theory469
Geometric theory of harmonic functions469
Classical harmonic analysis469
Quasiconformal and harmonic mappings469
Differential operators469
Pseudodifferential operators469
Compact and non-self-conjugate operators469
Banach algebras469
Hilbert modules469
K theory C* algebra469
Pseudoholomorphic curves in symplectic manifolds469
Fredholm mappings in global analysis469
Contact manifolds and holomorphic curves469
Symplectic and Hamiltonian actions469
Near-complex structures and holomorphic curves469
Linear topological spaces469
Theory of distributions469
Functional analysis469
Nonlinear functional analysis469
Stability of solutions of ordinary differential equations469
Qualitative analysis of ordinary differential equations469
Complex dynamic systems469
Asymptotic analysis469
Fixed point theory469
Geometric theory of functions 2469
Analysis on manifolds469
Special course - Analysis and differential equations469
Riemannian geometry A469
Riemannian geometry B469
Groups in geometry A469
Groups in geometry B469
Non-Euclidean geometries469
Regular polytopes469
Geometry of discrete groups469
Complex manifolds469
Spectral geometry469
Differential geometry of vector layers469
Differential geometric methods in statistics469
Discrete differential geometry469
Geometry in computer science469
Geometry in astronomy469
Geometric modeling in industry and design469
Symmetry groups469
Groups of transformations469
Homogeneous spaces469
Representations of Lie groups and algebras469
Symplectic geometry469
Stochastic differential geometry469
Theory of submanifolds469
Special course - Geometry469
Model theory469
Theory of computability469
Evidence theory469
Theory of sets469
Mathematical logic in computing469
Non-classical logic469
Theoretical computing469
Theory of automata and formal grammar469
Boolean algebras469
Applied logical theories469
Non-standard analysis469
Special course - Mathematical logic and theoretical computing469
Selected chapters of the theory of extremal problems469
Numerical analysis 3469
Finite element method with applications469
Finite difference method469
Theory of approximations with applications469
Game theory469
Regularization methods469
Discrete optimization469
Pontryagin's maximum principle469
Theory of location problems with applications469
Metaheuristic methods - advanced concepts469
Spectral theory of graphs with applications469
Algorithms on graphs and their applications469
Combinatorial graph theory with applications469
Special course - Applied mathematics469
Algebraic combinatorics469
Dynamic systems469
Data structures469
Algebraic topology469
Differential topology469
Topological combinatorics469
Discrete and computational topology469
Function spaces469
PL topology469
K - theory469
Vector layers and characteristic classes469
Homotopy theory469
Low dimensional topology469
Cohomology of groups469
Spectral arrays469
Selected chapters from general topology469
Selected chapters in algebraic topology469
Cohomological operations469
The theory of cobordism469
Equivariant topologies and applications469
Special course - Topology469
Mathematical statistics469
Bayesian data analysis469
Theory of random processes469
Reliability theory469
Theory of mass catering469
Spectral theory of random processes469
Gaussian random processes469
Stationary random processes469
Time series analysis469
Statistics of random processes469
Stochastic differential equations469
Stochastic financial mathematics469
Statistical hypothesis testing469
Linear statistical models469
Non-parametric statistics469
Information theory469
Coding theory469
Ergodic theory469
Stochastic analysis469
Probability measures in metric spaces469
Theory of extreme values469
Risk theory - advanced concepts469
Special Course - Probability and Statistics469
Fluid mechanics469
Integrable dynamical systems and solitons469
General Relativity and Cosmological Models (NEW)469
Dynamics of body systems469
Analytical mechanics469
Educational Software - Advanced Concepts469
Research methodology in teaching mathematics and computer science with practicum469


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