theory of differential equations, dynamical systems and nonlinear oscillations
mathematical physics, methods of functional and nonlinear analysis
probability theory and mathematical statistics
theory of functions of real and complex variables
algebraic and topological structures
computational mathematics, analytical mechanics and dynamics of mechanical systems
Theory of partial differential equations and operators, constructive and geometric theory of functions, theory of stochastic processes and mathematical statistics
Rigid body dynamics, stability and control theory, rock mechanics
Modeling, identification and recognition of control systems
methods of nonlinear functional analysis, linear algebra, differen¬tial geometry and topology
nonclassical problems of the theory of differential and integral equations and mathematical physics
mathematical and thermodynamic modeling and investigation of coupled processes of different nature in complex technical and medical-biological structures
methods of determination and optimization the stress-strain state and limit equilibrium of structurally in homogeneous systems with regard to problems of estimation the in strength, prediction of resource and function reliability
conducting scientific researches and developments on modern trends and problems of mathematical modeling
development of methods of computational experiment and optimization in relation to the problems of creating new models of technology and technology;
development of new forms and methods of mathematical education, training and advanced training of scientific personnel focused on the implementation of international projects and programs
creation of new information technologies and information support of scientific activity, international exchange of information in the field of mathematical modeling and computational experiment