Master degree program
Pure and Applied Mathematics

Pure and Applied Mathematics

QUALIFICATION

  • Scientific and pedagogical direction - Master of Natural Sciences

MODEL OF GRADUATING STUDENT

1.The use of innovative pedagogical technologies and methods in teaching mathematical subjects; development of assessment tools, instructions;
2.Providing practical explanations and analysis of the degree of complexity of spectral problems based on deep systematic knowledge in the subject area;
3.Develop logical schemes of manipulators, critically evaluating the dynamics of robotic, algebraic systems
4.Competent use of language and linguistic knowledge for communication in a multilingual and multicultural society of the Republic of Kazakhstan and in the international arena;
5.Develop software packages for solving problems in the natural sciences, using modern programming languages and computer modeling;
6.Transformation of models using linear and non-linear operators in various functional and topological spaces;
7.Conduct research on the sustainability of the operation of electric power systems;
8.Designing the process of applied research using mathematical and statistical methods;
9.Creation of search algorithms for various queries in the database using numbering theory;
10.Planning and conducting experiments, assessing the accuracy and reliability of simulation results;
11.Create constructive methods for solving boundary value problems of integro-differential equations;
12.Conducting laboratory and numerical experiments, assessing the accuracy and reliability of simulation results in their scientific research.

Program passport

Speciality Name
Pure and Applied Mathematics
Speciality Code
7M05406
Faculty
Mechanics and Mathematics

disciplines

Foreign Language (professional)
  • Number of credits - 6
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose is to acquire and improve competencies by international standards of foreign language education and to communicate in an intercultural, professional, and scientific environment. A master's student must integrate new information, understand the organization of languages, interact in society, and defend his point of view.

Generalized functions
  • Number of credits - 6
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Purpose: studying and mastering the concept of a generalized function by undergraduates. The concept of a generalized function makes it possible to express in a mathematically correct form such idealized concepts as the density of a material point, a point charge, a point dipole, the density of a simple or double layer, etc.

History and Philosophy of Science
  • Number of credits - 3
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The course forms knowledge about the history and theory of science; on the laws of the development of science and the structure of scientific knowledge; about science as a profession and social institution; оn the methods of conducting scientific research; the role of science in the development of society.

Introduction to theory of linear differential operators
  • Number of credits - 9
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - To study the basic concepts of the general theory of linear operators in functional spaces and their basic properties. With specific examples to demonstrate all the input definitions and properties. Consider cases of finite-dimensional and cases of infinite-dimensional spaces.

Organization and Planning of Scientific Research (in English)
  • Number of credits - 6
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to train masters in conducting scientific research, carrying out scientific and methodological work, socializing young students and their participation in the corporate governance system of Organization of higher and postgraduate education (OHPE). Undergraduates learn to interact with OHPE stakeholders, participate in research projects.

Pedagogy of Higher education
  • Number of credits - 3
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose is the formation of the ability of pedagogical activity through the knowledge of higher education didactics, theories of upbringing and education management, analysis, and self-assessment of teaching activities. The course covers the educational activity design of specialists, Bologna process implementation, acquiring a lecturer, and curatorial skills by TLA-strategies.

Psychology of Management
  • Number of credits - 3
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The course reveals the subject, the basic principles of management psychology, personality in managerial interactions, personal behavior management, psychology of managing group phenomena and processes, psychological characteristics of the leader's personality, individual management style, psychology of influence in management activities, conflict management.

Stochastic analysis
  • Number of credits - 6
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of teaching the discipline is to thoroughly familiarize undergraduates with the basic concepts, both theoretical and practical, applications of modern theories of stochastic analysis. Successful assimilation by undergraduates of the main results of this discipline so that they can use them effectively in the course of their future scientific and pedagogical activities.

Data for 2021-2024 years

disciplines

Algebraic geometry and the theory of models
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - To introduce undergraduates into modern model theory, which uses the application of model theory methods to solve problems of algebraic geometry. In particular, the theory of omega-stable theories, the rank of Morality is presented. Classification theorems of complete theories for formal sets. Boldwin-Zakisla theorems on stable groups and properties of decreasing formula subgroups.

Algebraic Systems
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to formalize the concepts of an algorithm and an algorithmically unsolvable problem. The main topics of the course: primitive recursive and partially recursive functions; Turing computable functions, universal Turing machine; Church's thesis; computably enumerable sets; universal functions, diagonal designs; creative, productive, simple and maximal sets.

Boundary Value Problems for Ordinary Differential Equations
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - We study boundary value problems for ordinary differential equations of arbitrary order with a small parameter at the highest derivative. Asymptotic expansions of solutions with a work degree of accuracy in a small parameter will be obtained.

Complete theories, types and models
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The objective of the course is to form a general set-theoretic and logical-algebraic culture among undergraduates, as a scientific-theoretical and ideological-methodological basis for mastering the syntactic and semantic components of the formal languages of classical calculus, a system of knowledge, skills and skills of applying methods and technologies in logical and mathematical practice.

Functional methods for solving partial differential equations
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Undergraduates must master modern methods of proving the existence of generalized solutions to boundary value problems for elliptic and parabolic equations. Presentation of the Vishik-Lax-Milgram theory. Variational theory of boundary value problems. Galerkin's method for parabolic equations. Prior estimates

Functional Spaces and Embedding Theorems
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Aims and objectives of the discipline: the main goal of the course is to master the basics of the modern theory of functional spaces and its applications to the problems of modern mathematical and functional analysis. The study of basic integral inequalities and their application. Teaching undergraduates the basics of the theory of approximation using differentiable functions.

Fundamental solutions of equations of mathematical physics
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Presentation of classifications of equations of the second order; differential equations of hyperbolic, elliptic and parabolic types; fundamental solutions of equations of each type; methods for solving boundary value problems for equations of hyperbolic, elliptic and parabolic types. Application of the method of characteristics to the study of oscillations in electric lines. Potential Theory.

Representation Theory
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - To form the ability to use representation theory to the problems of algebras, not necessarily associative. In algebra, group representations play an important role. The content of the discipline is aimed at studyingdifferent bases of commutative rings, theorems on passage to the limit, uniform decomposition of homomorphisms

Data for 2021-2024 years

INTERNSHIPS

Pedagogical
  • Type of control - Защита практики
  • Description - Aim оf discipline: formation of the ability to carry out educational activities in universities, to design the educational process and conduct certain types of training sessions using innovative educational technologies.

Research
  • Type of control - Защита практики
  • Description - The purpose of the practice: gaining experience in the study of an actual scientific problem, expand the professional knowledge gained in the learning process, and developing practical skills for conducting independent scientific work. The practice is aimed at developing the skills of research, analysis and application of economic knowledge.

Data for 2021-2024 years