Work Programs of the disciplines
111 Mathematics
02 Mathematical studies (V.M. Boyko)
03 Philosophy of science and culture
Section 1
02 Functional analysis (V.L. Ostrovskyi)
01.01 Additional topics of operator theory (V.L. Ostrovskyi)
01.02 Complex analysis (S.A Plaksa)
01.03 Approximative characteristics of functions classes (A.S. Romanyuk)
01.04 Approximations of periodic functions by trigonometric polynomial (A.S. Serdyuk)
01.05 Hardy spaces theory. Extremal problems (V.V. Savchuk)
01.06 Basics of frame theory (V.L. Ostrovskyi)
01.07 Generalized functions (O.O. Murach)
01.08 Geometric methods of analysis
01.09 Functions with fractal properties (M.V. Pratsiovytyi)
01.10 Inverse spectral problems (L.P. Nizhnik)
01.11 Fractional calculus (A.N. Kochubei)
01.12 Methods and characteristics in problems of approximation of classes of smooth functions (V.S. Romanyuk)
01.13 Selected topics in functional analysis (V.S. Romanyuk)
01.14 Rational approximation theory (A.P. Golub)
01.15 Theory of orthogonal and biorthogonal polynomials (A.P. Golub)
01.16 The classic problem of moments and generalized moment representations (A.P. Golub)
Section 2
03 Modern methods of the theory of differential equations (V.I. Tkachenko)
02.01 Asymptotic methods in the theory of differential equations (V.I. Tkachenko)
02.02 Differential equations with impulse action (V.I. Tkachenko)
02.03 Noetherian boundary value problems (O.A. Boichuk)
02.04 Functional differential equation (G.P. Pelyukh)
02.05 Geometric dynamics of discrete time systems (O.O. Pokutnyi)
02.06 Boundary value problems for operator differential equations (O.O. Pokutnyi)
Section 3
03.01 Group methods of integration of differential equations (V.M. Boyko, A.G. Nikitin, R.O. Popovych, O.O. Vaneeva)
03.02 Algebraic methods of mathematical physics (V.M. Boyko, M.O. Nesterenko, R.O. Popovych, O.O. Vaneeva)
03.03 Supersymmetry and superintegrability of equations of mathematical physics (A.G. Nikitin)
03.04 Evolution equations of modern mathematical physics (V.I. Gerasimenko)
03.05 Infinite-dimensional analysis in mathematical physics and its application (O.L. Rebenko)
03.06 The method of equipped spaces in the theory of singular perturbations of self-adjoint operators (V.D. Koshmanenko)
03.07 Modeling of complex systems (V.D. Koshmanenko)
Section 4
04.01 Low-dimensional topology (S.I. Maksymenko)
04.02 Differential topology (S.I. Maksymenko, Y.O. Polulyak)
04.03 Algebraic topology (S.I. Maksymenko, Y.O. Polulyak)
04.04 Dynamical systems and their applications (I.Y. Vlasenko)
Section 5
05.01 Large deviations theory (A.A. Dorogovtsev)
05.03 Stochastic flows (A.Y. Pilipenko)
05.04 Mathematical models for polymer processing (A.A. Dorogovtsev)
05.05 Transformations of Gaussian measures and orthogonal decompositions (G.V. Riabov)
05.06 Mathematical models of diffusion in media with membranes (M.I. Portenko)
05.07 Additional topics of theory of random processes (A.A. Dorogovtsev)
Section 6
01 Representation theory (Y.A. Drozd)
06.01 Algebraic geometry (Y.A. Drozd)
06.02 Geometric and combinatorial group theory (Y.P. Sysak)
06.03 Homological algebra (Y.A. Drozd)
06.04 Derived categories and their applcations (V.V. Lyubashenko)
06.05 Associative rings and semigroups (Y.P. Sysak)
06.06 Differential graded categories (V.V. Lyubashenko)
06.07 A∞-categories (V.V. Lyubashenko)
113 Applied Mathematics
07.01 Mathematical models and methods in applied sciences (O.M. Timokha)
07.02 Computational methods in modern scientific research (A.P. Golub, V.B. Vasylyk)
Section 1
07.01 Methods without saturation of accuracy in computational mathematics (V.B. Vasylyk)
07.02 Numerical methods for solving problems for differential equations with operator coefficients (V.B. Vasylyk)
07.03 Approximate methods for solving Sturm-Liouville problems and their generalizations (V.l. Makarov, V.B. Vasylyk)
07.04 Iterative procedures in incorrect problems (S.G. Solodky)
07.06 General principles of regularization of unstable problems (E.V. Semenova)
07.07 Rational approximation theory (A.P. Golub)
07.08 Theory of orthogonal and biorthogonal polynomials (A.P. Golub)
07.09 The classic problem of moments and generalized moment representations (A.P. Golub)
Section 2
08.01 Modern problems of stability and quality of control system (A.G. Mazko)
08.02 Matrix methods of stabilization of dynamic systems (A.G. Mazko)
08.03 Mathematical models of nonlinear dynamics of bodies with a liquid (O.M. Timokha)
08.04 Variational principles in continuum mechanics (O.M. Timokha)
08.05 Projection methods of mathematical physics (O.M. Timokha)
08.06 Selected topics of stability of conservative systems (S.P. Sosnytskyi)
08.07 Decomposition and control in dynamic systems (V.V. Novytskyy)
08.08 Control of almost conservative mechanical systems (V.V. Novytskyy)