MAJORS IN MATHEMATICS AND MECHANICS

Algebra and Mathematical Logic
Group theory; Lie groups, semi-simple Lie groups and algebras; rings and ideals; structural theory of Jordan algebras. Set theory: constructible sets. Algorithm theory.
Calculus
Computational Mathematics Splines. Monte Carlo method and turbulence. Numerical solutions of ordinary and stochastic equations. Digital filters. Numerical methods in linear algebra. Statistical methods for solving problems of mathematical physics. Approximation theory and computer graphics.
Computational Methods For Mechanics Of Contiuuous Media Differential approximations method.Numerical analysis; numerical methods for viscous fluid dynamics problems, Exact solution in continuum mechanics. Wave hydrodynamics in complex-shaped areas. Exact solutions of nonlinear kinetic equations.
Computational Systems
Computer architectures; parallel computation. Database management systems. Design of real-time network operation system.
Geometry And Topology
Riemann Geometry. General theory of relativity: axiomatic approach. Differentiable Riemannian manifolds. Integral geometry: tensor analysis and Riemann geometry; theory of generalized functions and Fourier transform. Chronometry. Convex and visible compacts. Cobordism theories. Algebraic topology.
Hydrodynamics
Free-boundary problems in fluid dynamics. Microgravity. Self-generated oscillations. Scattering theory: Dirichlet and Neumann problems. Seiche in harbors. Musical instruments. Mufflers. Antennas.
Differential Equations
Operator methods. Differential equations in ecology. Well-posed boundary value problems with broken boundaries; initial and boundary value problems for Navier-Stokes equation for compressible viscous fluids.
Analysis
Analysis of weak derivatives. Klein groups. Quasiconformal mappings. Nonstandard analysis. Analysis on nilpotent groups. Potential theory and differential equations. Theory of orbifolds.
Mathematical Methods For Geophysics
Computational methods for oceanic currents; ocean dynamics problem. Hydrothermodynamical modeling of the ocean. Numerical methods in atmospheric problems. Numerical methods in environmental problems. Mathematical methods in seismology, geophysics, and tomography. Inverse problems for differential equations of mathematical physics.
Mechanics Of Deformable Solids
Mechanics of the geosphere. Nonlinear problem of elasiticity theory. Cracks and fracture. Experimental methods of mechanics of deformable solids.
Applied Mathematics
Applied complex analysis: singular integral equations. Dynamics of inclusions within vibrating liquids.
Probability And Statistics
Limit theorems in probability and statistics and their applications. Central limit theorem in functional spaces; large deviations; boundary problems; queuing theory.
Theory Of Functions
Geometric theory of functions. Inverse and ill-posed problems.
Theoretical Cybernetics
Graph theory. Operations research. Combinatorics. Discrete extreme value problem. Game theory. Discrete analysis. Optimal process theory. Mathematical economics. Languages for modeling. Statistical decision theory. Algebraic coding theory. Pattern recognition.
Theoretical Mechanics
Elasticity and plasticity. Diffusion models in ecology. Boundary value problems on Riemann surfaces.