Research activities along with educational is the main activity of the Department of Fundamental Mathematics and acts as a mandatory element of the educational process in the implementation of educational programs.
The main tasks of the department in the field of scientific activity are the implementation of fundamental research of modern problems of mathematics, the implementation of innovative activities, the use of the latest scientific achievements and technologies in teaching, improving the level of professional training of students, training scientific and pedagogical workers, the implementation of the results of research in the educational process and practical activities.
Every year, the faculty of the department publishes textbooks, teaching aids and monographs, scientific articles and other publications on topical problems of modern mathematics.
More and more students are involved in the scientific life of the department. For this, research institutes at the university closely cooperate:
1. "Eurasian Mathematical Institute" - Academician of the National Academy of Sciences of the Republic of Kazakhstan,
Director - Professor, Doctor of Physical and Mathematical Sciences. R. Oinarov.
http://www.enu.kz/ru/nauka/nauchno-issled-podr/nii-evraziyskiy-matematicheskiy-institut/
2. "Institute of Theoretical Mathematics and Scientific Computations".
Director - Professor, Doctor of Physical and Mathematical Sciences N. Temirgaliyev.
http://www.enu.kz/ru/nauka/nauchno-issled-podr/nii-teoreticheskoy-matematiki-i-nauchnyh-vychisleniy/
The scientific directions of the teaching staff of the department are:
1) General theory of boundary value problems.
2) Study of the problem of strong solvability of equations of gas and hydrodynamics, development of approximate methods for solving equations of mathematical physics and systems of algebraic equations, mathematical problems of theoretical physics
3) Solvability of singular linear and nonlinear differential equations and partial differential equations, smoothness and approximation properties of their solutions, spectral properties of operators.
4) Research of the properties of operators of the type of fractional differentiation in various functional spaces (the fractional differentiation operator plays an important role in various problems of analysis, especially in questions of applied mathematics.
5) Research of weighted additive and multiplicative estimates of "intermediate" operators, which are important in the theory of embedding, in the theory of differential equations and in computational mathematics.
6) Spectral properties of differential operators with variable coefficients. Problems of interpolation of weighted Sobolev spaces. Approximation issues for two-weight Hardy operators.
7) Interpolation theory, approximation theory of function spaces.
8) Multiplicative orthogonal Fourier series
9) Continuous and discrete mathematics in organic unity in the context of research areas.
10) Probabilistic-statistical studies of distribution estimates.
Seminars of the department:
The department conducts a weekly scientific seminar "Functional analysis and its applications" under the guidance of the academician of the National Academy of Sciences of the Republic of Kazakhstan, professor, doctor of physical and mathematical sciences R. Oynarov, professor, doctor of physical and mathematical sciences K. Ospanov and professors, Doctor of Physical and Mathematical Sciences E. Nursultanov, where the faculty and doctoral students of the Department of Fundamental Mathematics and guests make presentations on topical topics.
Significant results of scientific activity
The problem of exact constants in the inequalities of Nikol'skii and Remez is solved. The global and local properties in the Hilbert transforms are studied.
The factors in the Lebesgue and Lorentz spaces are studied. Sufficient conditions are obtained, the accuracy of the results is shown.
A new concept of the tensor product of functionals is defined and various variants of classes of functions based on the involvement of trigonometric Fourier coefficients are proposed. Their applications are shown in problems of numerical integration both in terms of inaccurate information and in terms of exact information. The exact orders of the errors arising in this case are found for various classes of functions, both previously known and new.
For different classes of functions, exact orders of deviation in the class of Smolyak's quadrature formulas from the true value of the integral are obtained.
The exact orders of calculating the Fourier coefficients by means of Smolyak's quadrature formulas are obtained and their applications to the restoration of functions are given.
Research work of students for 2020.
Research work of undergraduates for 2020.
Research work of doctoral students for 2020.