- Mathematical Analysis - functional analysis, constructive theory of function, linear and complex analysis;
- The Algebra and Number Theory - number theory, group theory, algebraic K theory, Galois theory;
- High Geometry - algebraic and geometric topology, topology of real and complex manifolds, Rimann geometry;
- Differential Equations - stability theory, theory of smooth dynamic systems, qualitative theory;
- Mathematical Physics - nonlinear partial differential equations, spectral theory of differential operations as methods;
- Theory of Probability and Mathematical Statistics - limit theorems, stochastic processes, mathematical statistics;
- Computational Mathematics - numerical methods of solutions of differential and integral equations, theory of approximations;
- Statistical Modelling - simulation modelling and statistical simulation, applied statistics, theory of optimization and design of experiment;
- Theoretical Cybernetics - theory of learning and identification systems, robototechniques, automate theory, m.m. of als.;
- Applied Cybernetics - control and circuits, applied theory of dynamic system, stability theory, dimension theory.
- Operations Research - discrete, linear and nonlinear programming theory of optimal control, differential combinatorical theory problems;
- Computer Science - computer languages and methods of translator constructions, artificial intellect languages and expert systems;
- Parallel Algorithms - parallel algorithms, wavelets.
- Software Engineering - software technologies, software design and automated systems;
- Analitical information Systems - models and techniques for information storage, retrieval, processing, and analytics.
- Theory and Applied Mechanics - theory of vibrations of mechanic systems and solids, vibrations under stochastic forces, theory of automatic control and regulation, robototechniques;
- Hydroaeromechanics - gas dynamics and theory of shock waves, theory of carrier surfaces, airodynamics of rarefied gases;
- Hydroelasticity - dynamics of elastic shells in continuous medium;
- Elasticity Department - problems of material strength and fracture, crack theory, problems of mechanics of Solids;
- Physical Mechanics - physical principles of mechanics of Solids, Fluids and Gases, dynamics of plasma, biophysics;
- Astrophysics - theoretical astrophysics, observer astrophysics, radio astrophysics;
- Celestial Mechanics - gravitational field of celestial body, the evolution of the solar systems, stellar astronomy, the evolution of the systems three stars;
- Astronomy - space astronomy, radio astronomy;
- General Mathematics & Informatics - mathematical cources for non-mathematics specialities.