The doctoral program in Mathematics is designed according to the planned research topics of doctoral students, as well as qualification training courses in this field of science. The purpose of the doctoral program is to train scientists, who would be capable of independently carrying out research and experimental development and solving scientific problems of Mathematics.

## Research topics

Research topics of doctoral students in Mathematics:

- Algebraic Number Theory
- Analytical Number Theory
- Random Processes Theory
- Differential Equations and Numerical Methods
- Risk Theory
- Didactics of Mathematics
- Geometric Groups Theory
- Combinatorics and Graph Theory
- Mathematical Statistics
- Mathematical Models of Hydrodynamics
- Limits Theorems
- Probability Theory

The study program consists of two blocks for subjects: compulsory block and elective block. The compulsory block consists of the subject for all the doctoral students and it reflects the main research topics for doctoral students, providing them with access to the general qualifications required for research. An elective block offers the subjects from which the rest of the program may be chosen and it is based on the research topics of Mathematics. With the approval of the PhD Committee, students can choose the subject in other fields of science.

## Study plan

Compulsory block

- Algebra
- Functional Analysis
- Mathematical Analysis
- Probability Theory and Mathematical Statistics

Elective block

- Algebraic Combinatorics
- Algebraic Number Theory
- Algebraic Numbers, Polynomials and Diophantine Analysis
- Analytical Number Theory
- Analytical and Probabilistic Combinatorics
- Approximation Methods
- Asymptotic Statistics
- Random Processes
- Finite Population Statistics
- Application of Bayesian Models in Statistics
- Multidimensional Statistics
- Non-self-adjoint boundary eigenvalue problems
- Numerical Methods of Differential Equations
- Mathematics of Insurance
- Zeta-functions
- Econometrics
- Spatial Statistics
- Function Theory of Complex Variable
- Time Series Analysis
- Markov’s Chains
- Equations in Mathematical Physics
- Modular Shapes and Elliptic Curves
- Navier - Stokes Equation Theory
- Dependency Measures and Copulas
- Weak Measure Convergence
- Fluid and Gas Mechanics
- Statistics
- Statistical Data Analysis
- Stochastic Analysis
- Theory of Stochastic Differential Equations
- Modern Numerical Methods
- Probabilistic Number Theory
- Limits Theorems of Probability Theory

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