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

Differential calculus on Banach spaces
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The goal of teaching the discipline is to learn the basics of modern mathematical analysis on Banach spaces, stochastic analysis and the theory of martingales, as well as some of their applications. Banach spaces, metric spaces. Full metric spaces. Convergence on metric space. Neighborhood. Compactness. Differentiability. Vaserstein metric - a natural metric on a space of probability measures in a metric space

Foreign Language (professional)
  • Number of credits - 6
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to form practical skills in various types of speech activity in a foreign language. The training course builds the ability to perceive, understand and translate information in the modern global space, participate in scientific events to test their own research. The discipline is aimed at improving competencies in accordance with international standards of foreign language education.

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 purpose of the discipline is to be considered on the basis of historical dynamics and in a historically changing socio - cultural context. Introduces the problems of the phenomenon of Science, which is a subject of special philosophical analysis, forms knowledge about the history and theory of Science, the laws of the development of Science and the structure of scientific knowledge, the features of science as a specialty and social institution, 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.

Modern Methods of Stability Theory
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Outline the theoretical foundations of the modern theory of stability of solutions of ordinary differential equations based on the second Lyapunov method, or the method of Lyapunov functions. The purpose of studying the discipline: familiarization with the theory of sustainability, including some of its modern directions; acquisition of skills for analyzing stability and other properties of dynamic systems with continuous time. The objectives of the discipline: the formation of knowledge and skills on the basic methods of studying stability and stabilization, the methods of their application to the problems of stability of controlled systems. The main classical theorems of the Lyapunov function method. Mathematical theory of sustainability. Definitions of stability and asymptotic stability according to Lyapunov, exponential stability. Stability of sets, stability in a part of variables, stability under constantly acting perturbations.

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 to form the ability to apply practical skills in the organization and planning of scientific research. The discipline studies: forms and methods of planning, organization and design of scientific articles and dissertations; forms of summarizing the results of scientific research in presentations, speeches, projects, articles.

Pedagogy of Higher education
  • Number of credits - 5
  • 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.

Select Heads of Analysis and Differential Equalizations
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - To form the ability to use the theory of a singular differential equation with a piecewise constant argument for the study of objects of natural science. The content of the discipline is directed to studyThe analytical formula for the solution, the unperturbed problem, the theorem on passage to the limit, the initial jump of the solution, the uniform asymptotic expansion of the solution.

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 - To develop the ability to study boundary value problems for ordinary differential equations of arbitrary order with a small parameter at the highest derivative. Will be studied: - Estimation of the difference between solutions of singularly perturbed and unperturbed problems. -asymptotic expansions of solutions with any degree of accuracy in a small parameter; - influence of a small parameter on the asymptotic behavior of solutions; - the order of growth of solutions at the point of the initial jump.

Combinatorical Enumeration
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to study: sampling, re-setting, combination, re-setting with repetition; combinations with repetitions; binomial coefficients, their properties; binomial theorem; polynomial theorem; inclusion and exclusion formula, generating functions. Calculations with formal power series. Rational generating functions and linear recurrence relations with constant coefficients.

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.

Elements of Algebraic Geometry
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Algebraic set, Zariski topology. Irreducibility, affine and projective algebraic variety. Dimension. Regular and rational mappings. In this section, we introduce the basic concepts of universal algebraic geometry. For more detailed information. All the definitions given below can be formulated for an arbitrary algebraic system in an arbitrary functional language. However, for convenience, all concepts of universal algebraic geometry will be immediately given for Boolean C-algebras. In this course, based on the constructions of algebraic geometry, the methods of studying algebraic geometry study the Zariski topology, algebraic varieties in affine and projective spaces.

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.

Generalized Functions
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Purpose: the study and mastery of undergraduates the concept of a generalized function. A generalized function or distribution is a mathematical concept that generalizes the classical concept of a function. The need for such a generalization arises in many physical and mathematical problems. 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 (spatial) density of a simple or double layer, the intensity of an instantaneous source. Regular and singular generalized functions. Operations Linear operations on generalized functions, as extensions of basic operations on functionals: change of variables, product, differentiation. Properties

Group representation theory
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Group representation means homomorphism from group to group of automorphisms of an object. Group representation theory is divided into subtheories depending on the type of group represented: Finite groups, compact groups, linear algebraic groups. Group representations make it possible to reduce many group-theoretic problems to linear algebra problems. The theory of group representation allows us to move on to the representation of abstract algebraic objects such as associative algebras or Lie algebras, which will be studied later.

Linearly ordered models and the number of countable models of the complete ordered theory
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to form the ability to work with formulas containing a linear order, and properties of formula sets such as convexity, mutual density of formula sets, to work with types. Counting the number of countable models having formula linear or partial order

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

Spectral theory of the Sturm-Liouville operator
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The theory of Sturm-Liouville operators on a finite interval. Properties of eigenfunctions. Operator Sturm-Liouville. Types of boundary conditions. Recovery of a differential operator from spectral data. Reduction of the inverse problem of the quantum theory of scattering to a one-dimensional formulation. The theory of Sturm-Liouville operators on a finite interval. Properties of eigenfunctions. Sturm-Liouville operator. Types of boundary conditions. Restoration of a differential operator from spectral data. Reduction of the inverse problem of the quantum theory of scattering to a one-dimensional formulation

Strongly Minimum Theories
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the study of the discipline masters is to possess the following competencies:To create undergraduates strong knowledge, including concepts and theorems of strongly minimal theories; Achieve an understanding of the fundamentals of the theory of strongly minimal structures. This course examines the basic concepts and properties of highly minimal theories: pseudo-flatness; categorical in all infinite capacities; replacement lemma, examples of strongly minimal algebraic structures.

Theory of rings and fields
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The course is an introduction to field theory, which is one of the main subjects in algebra, computer science and cryptography. The course will cover the main topics on field theory and ring theory. During the course, we formulate the basic concepts and results that have become classic today and are trying to describe current trends and achievements.

Data for 2021-2024 years

INTERNSHIPS

Pedagogical
  • Type of control - Защита практики
  • Description - Formation of practical, educational-methodical skills of conducting lectures, seminars, creatively apply scientific, theoretical knowledge, practical skills in teaching activities, conduct training sessions in the disciplines of the specialty; own modern professional techniques, methods of training, use in practice the latest theoretical, methodological advances, make educational, methodological documentation.

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