- Abstract differential equations with applications in mathematical physics
- Asymptotic methods in nonlinear problems of mathematical physics
- Group analysis of differential equations In the course we consider integrations of ODEs that admit sufficiently large Lie algebras of point transformations, as well as contact transformations that generalize point transformations. We consider the connection between the generalized symmetries of the Euler-Lagrange equations and the conservation laws.
- Supplementary chapters of mathematical physics (nonlinear functional analysis)
- Additional chapters of numerical methods Application of numerical methods for various applications
- Linear and nonlinear functional analysis
- Magnetohydrodynamics and dynamo theory
- Mathematical problems of diffraction theory Mathematical models of wave processes in non-uniform environments, their full mathematical justification. Main analytical and numerical algorithms of creation of models and their research
- Mathematical modeling of plasma – computer experiment
- Mathematical modeling of plasma – fundamentals of kinetics
- Differential inequality method in nonlinear problems
- Nonlinear elliptic and parabolic equations of mathematical physics
- Fundamentals of algebra and differential geometry
- Category Theory Basics
- Parabolic equations Parabolic equations
- Application of spectral theory in mathematical physics
- Programming of scientific applications in the language C++
- Methods of finite differences in mathematical physics
- Special functions of mathematical physics This course is a restored course, created by prof. A.F. Nikiforov. A unified approach to constructing particular solutions to generalized hypergeometric equation is proposed. The generalized hypergeometric equation is an often used equation of mathematical and theoretical physics.
- Special practical work. Differential schemes
- Stochastic differential equations
- Theoretical Basics of Big Data Analytics and Real Time Computation Algorithms The course will briefly review specific challenges of Big Data Analytics, such as problems of extracting, unifying, updating, and merging information and specific needs in processing data, which should be highly parallel and distributed. With these specific features in mind we will then study more closely a number of mathematical tools for Big Data analytics, such as regression analysis, linear estimation, calibration problems, real time processing of incoming (potentially infinite) data
- Catastrophe theory and its applications in physics
- Functional analysis
- Extremal problems
- Elliptic equations