8D05401 - MATHEMATICS

Passage of accreditation (year of passage, period of passage).

Based on the results of the evaluation conducted by the external expert commission of the non-profit organization “Independent Kazakhstani Accreditation Center,” the educational program “8D05401 – Mathematics” has been accredited for a period of 7 years. Registration number: HE-SA No. 00510, validity period: June 17, 2025 – June 16, 2032.

Training period: 3 years.

Degree awarded: doctor of philosophy (PhD) in the educational program “8D05401 – Mathematics»

Purpose of the Educational Program. The purpose of the educational program "8D05401 – Mathematics" is to train competitive, highly qualified scientific and teaching staff for higher education, postgraduate education and the scientific field with in-depth scientific, pedagogical and research training.

Field of professional activity: 

• the science; 
• education; 
• scientific and production sphere, economics and management.

Objects of professional activity: research organizations, engineering and design bureaus, firms and companies; educational organizations (higher education institutions, etc.); organization management of the relevant profile; organizations of various forms of ownership, using the methods of mathematics in their work.

Subject of professional activity: scientific research in areas using mathematical methods and computer technologies; solving various applied problems using mathematical modeling of processes and objects and software; development of effective methods for solving problems of natural science, technology, economics and management; software and information support of scientific, research and management activities; teaching of mathematical disciplines, organization of the educational process in higher educational institutions and other educational institutions.

Functions and types of professional activity

Types of professional activity: 

• scientific research;
• pedagogical;
• administrative and managerial.

In accordance with the types of professional activity, a graduate of the OP "8D05401-Mathematics" can perform the following functions: 

Scientific research activities:

• conducting scientific research using mathematical methods and computational technologies to solve fundamental problems of mathematical modeling of processes and objects;
• constructing and studying mathematical models, developing algorithms and research methods within the scope of ongoing fundamental and applied research projects;
• developing knowledge-intensive mathematical and modern high-performance computing technologies, information technologies, and software packages for solving applied problems in the field of natural sciences.

Teaching Activities:

• organizing the educational process and teaching mathematical disciplines in institutions of higher and postgraduate education;
• supervising research activities of bachelor’s, master’s, and doctoral students;
• developing educational and methodological materials for institutions of higher and postgraduate education.

Administrative and Management Activities:

• organizing the work of research groups, teams, institutes, and other units;
• organizing and conducting scientific and scientific-methodological seminars and conferences.

List of specialist positions. 

Graduates of the doctoral program can carry out professional activities in accordance with the received fundamental and specialized training in the specialty in the position: 

• researcher (senior, leading, chief) employee in research institutes, laboratories, design and design bureaus, etc.;
• teacher of mathematics in higher educational institutions and other educational organizations; 
• mathematical analyst, chief specialist in production and management organizations that use mathematical methods in their work, in insurance companies, financial structures; 
• head of the university.

Learning Outcomes of the Educational Program:

1. To plan, coordinate, implement, and forecast research results; to critically analyze, evaluate, and compare various scientific theories and ideas.
2. To demonstrate deep and comprehensive knowledge of the fundamental areas of mathematics, including Sobolev space theory, non-commutative operator analysis, stochastic analysis, the theory of reducibility of systems of differential equations, and the theory of dynamical systems; to apply scientific research methods to solve current problems in modern mathematics.
3. To apply theoretical and applied research methods in the field of systems of partial differential equations for the study of vector field directions, boundary value problems for hyperbolic-type equations with nonlocal conditions, and multiperiodic and almost periodic solutions of applied problems for parabolic-type equations.
4. To generate original scientific ideas and synthesize the results of research and analytical work in the form of a doctoral dissertation; to be competent in conducting scientific projects and research in the professional field.
5. To apply methods for finding periodic solutions of differential and integro-differential equations with multidimensional time, to address issues of stability of multiperiodic solutions and holomorphy with respect to a small parameter; to generate new ideas in the context of scientific research in differential equation theory and artificial intelligence.
6. To formulate and solve modern scientific and practical problems in mathematics; to organize and conduct research and experimental work in the chosen field.
7. To plan and forecast one's further professional development; to possess skills for acquiring new knowledge in a specialized field and in the theory and methodology of professional education; to apply modern information and innovative technologies, including digital learning technologies and artificial intelligence technologies, in the educational process.
8. To use modern data analysis methods, demonstrating skills in searching, collecting, processing, storing, and transmitting scientific information using modern information and innovative technologies.
9. To construct and evaluate phase portraits of dynamical systems, distinguish deterministic chaos from non-deterministic systems, and solve problems of qualitative analysis of a dynamical system.

Internship and Practical Training Bases:

Institute of Mathematics and Mathematical Modeling of the SC MSHE RK, Scientific Center for Applied Mathematics and Informatics, Zhubanov University, Karakalpak State University named after Berdak, V.I. Romanovsky Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, Grozny State Oil Technical University, Faculty of Nuclear Sciences and Physical Engineering of the Czech Technical University in Prague, etc.