Magistracy
Speciality Code:
7M05406
Speciality Name:
Pure and applied mathematics
Faculty:
Mechanics and Mathematics
Qualification:
 Scientific and pedagogical direction  Master of Natural Sciences
 Model of graduating student
 Mandatory disciplines
 Elective disciplines
 Professional

Stochastic analysis
 Number of credits: 5
 Type of control: [RK1+MT1+RK2+Exam] (100)
 Description: The purpose of teaching this discipline is to thoroughly familiarize undergraduates with basic concepts, results, and some of the most important, both theoretical and practical, applications of the modern theory of stochastic analysis. The objectives of the course are: Successful mastering of the main results of this discipline by undergraduates so that they can subsequently use them effectively in the course of their future scientific and educational activities; Acquisition of practical skills in educational and scientific literature in various sections of the course under study; Learning Outcomes: The undergraduate who successfully mastered the program of this course: Receives skills in the application of methods of the theory of stochastic analysis and stochastic calculus and is able to apply these methods to solve typical standard problems; Receives a clear understanding of the relationship of this discipline with other disciplines of the selected educational program; Will be able to freely navigate in the main directions of further development of topics of this discipline. Random function. Basic concepts of the general theory of stochastic processes; Convergence; Continuity; Derivatives; Integrals; Conditional expectation with respect to partitions and sigma algebras Fundamentals of the theory of martingales Diffusion process; The direct and inverse Kolmogorov equations; Connection of diffusion processes with the Cauchy problem for partial differential equations of parabolic type.

Introduction to theory of linear differential operators
 Number of credits: 5
 Type of control: [RK1+MT1+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 finitedimensional and cases of infinitedimensional spaces.

Differential calculus on Banach spaces
 Number of credits: 5
 Type of control: [RK1+MT1+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

Select Heads of Analysis and Differential Equalizations
 Number of credits: 5
 Type of control: [RK1+MT1+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.

Foreign Language (professional)
 Number of credits: 5
 Type of control: [RK1+MT1+RK2+Exam] (100)
 Description: The purpose of the discipline: the acquisition and improvement of competencies in accordance with international standards of foreign language education, allowing the use of a foreign language as a means of communication for the successful professional and scientific activities of the future master. able to compete in the labor market, as new knowledge, technologies are available through a foreign language, mastering a professional foreign language serves as a tool in mastering new competencies

History and philosophy of science
 Number of credits: 3
 Type of control: [RK1+MT1+RK2+Exam] (100)
 Description: The course "History and Philosophy of Science" introduces the problem of science as an object of special philosophical analysis, 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. The maintenance of a course includes detection of specifics and interrelation of the main problems, subjects of philosophy of science and history of science; studying consciousness of science in its social and philosophical foreshortenings; consideration of a phenomenon of science as professions, social institute and direct productive force; disclosure of disciplinary selfdetermination of natural, social and technical science, their communities and distinction.

Master’s dissertation preparation and defense (MDPaD)
 Number of credits: 12
 Type of control: Master Dissertation
 Description: The main purpose of "The implementation of a Master Thesis": the formation of master students in preparation for the defense of the thesis for the Master in specialty (by industry). During the study of course, master student's should be competent in: 1. demonstrate the progress of solving problems arising in the course of research activities and requiring indepth professional knowledge; 2. to argue for carrying out theoretical or experimental research within the framework of the tasks, including a mathematical (simulation) experiment; 3. can choose the necessary research methods, modify existing methods and develop new methods, based on the tasks of the specific study; 4. to use foreign languages for independent work on normative sources and scientific literature; 5. formulate the goals and objectives of the dissertation research, determine the scientific novelty and practical significance of the results of research activities; to develop a structurally methodological scheme for performing research.

Pedagogy of higher education
 Number of credits: 5
 Type of control: [RK1+MT1+RK2+Exam] (100)
 Description: The purpose of disciplinemastering the basics of professional and pedagogical culture of higher school teacher, the formation of competencies, skills and teaching activities in universities and colleges. The following issues are studied: the role of pedagogical science in the system of Sciences; the system of higher professional education in Kazakhstan; methodology of pedagogical science; didactics of higher education; design of TLAstrategy of education, the use of traditional and innovative methods and forms of education.

Modern Methods of Stability Theory
 Number of credits: 5
 Type of control: [RK1+MT1+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.

Psychology of management
 Number of credits: 3
 Type of control: [RK1+MT1+RK2+Exam] (100)
 Description: The purpose of the discipline is to provide scientific training for highly qualified specialists on the basis of studying the fundamental concepts of management psychology, capable of understanding the current state of the theory and practice of management psychology in an amount optimal for use in subsequent professional activities; apply and describe psychological methods of studying individuals and social groups (communities) in order to increase management efficiency;

Boundary Value Problems for Ordinary Differential Equations
 Type of control: [RK1+MT1+RK2+Exam] (100)
 Description: We study boundary value problems for ordinary differential equations of arbitrary order with a small parameter with the highest derivative. Estimates of solutions and solutions of perturbed problems are given. We will obtain asymptotic expansions of solutions with a work of degree of accuracy with respect to a small parameter. As a result of the training, the undergraduates will be introduced to the methods of investigating boundaryvalue problems for ordinary differential equations with a small parameter with the highest derivative. Be able to detect the influence of a small parameter on the asymptotic behavior of solutions, to determine the order of growth of solutions at the point of the initial jump. To have skills in solving boundary value problems for ordinary differential equations

Generalized Functions
 Type of control: [RK1+MT1+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

Elements of Algebraic Geometry
 Type of control: [RK1+MT1+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 Calgebras. 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.

Linearly ordered models and the number of countable models of the complete ordered theory
 Type of control: [RK1+MT1+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

Algebraic geometry and the theory of models
 Type of control: [RK1+MT1+RK2+Exam] (100)
 Description: The goal of this course is to introduce undergraduates into the modern theory of models using the methods of the theory of models to solve problems of algebraic geometry. In particular, the theory of omegastable theories, the rank of Morley, is presented. Classification theorems for complete theories from the point of view of various rank functions for formula sets. BaldwinZaksla theorems on stable groups and properties of decreasing formula subgroups are presented.

Functional methods for solving partial differential equations
 Type of control: [RK1+MT1+RK2+Exam] (100)
 Description: Master modern methods for proving the existence of generalized solutions of boundary value problems for elliptic and parabolic equations. VishikLaxMilgram theory. Variational theory of boundary value problems. Galerkin method for parabolic equations. Prior estimates

Algebraic Systems
 Type of control: [RK1+MT1+RK2+Exam] (100)
 Description:

Combinatorical Enumeration
 Type of control: [RK1+MT1+RK2+Exam] (100)
 Description: The purpose of the discipline is to study: sampling, resetting, combination, resetting 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+MT1+RK2+Exam] (100)
 Description: The main objective of this course is the formation of undergraduates of a common settheoretic and logicalalgebraic culture, as a scientifictheoretical and ideological and methodological basis for mastering the syntactic and semantic components of formal languages of classical calculus, as well as the formation of undergraduates knowledge systems abilities and skills of application in logicalmathematical practice of methods, technologies and canonical constructions peculiar to modern model theory ..

Strongly Minimum Theories
 Type of control: [RK1+MT1+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: pseudoflatness; categorical in all infinite capacities; replacement lemma, examples of strongly minimal algebraic structures.

Representation Theory
 Type of control: [RK1+MT1+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 Operator AssaultLioville
 Type of control: [RK1+MT1+RK2+Exam] (100)
 Description: The theory of SturmLiouville operators on a finite interval. Properties of eigenfunctions. Operator SturmLiouville. 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 onedimensional formulation. The theory of SturmLiouville operators on a finite interval. Properties of eigenfunctions. SturmLiouville 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 onedimensional formulation

Functional Spaces and Embedding Theorems
 Type of control: [RK1+MT1+RK2+Exam] (100)
 Description:

Theory of rings and fields
 Type of control: [RK1+MT1+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.

Fundamental solutions of equations of mathematical physics
 Type of control: [RK1+MT1+RK2+Exam] (100)
 Description: Summary of classifications of second order equations; differential equations of hyperbolic, ally, and parabolic types; fundamental solutions of equations of every type; methods for solving boundary value problems for equations of hyperbolic, elliptic and parabolic types. Differential partial differential equations of hyperbolic, elliptic, and parabolic types. Application of the method of characteristics to the study of oscillations in electric lines. Potential theory. Spherical functions. Helmholtz equation. Application of the Fourier method to the solution of boundary problems for equations of parabolic type.

Dissertation Writing
 Type of control: Защита НИР
 Description:

Research Seminar III
 Type of control: Защита НИР
 Description:

Scientific Internship
 Type of control: Защита НИР
 Description: The main purpose of "Scientific Internship": is the formation in the students of the ability to independently conduct research and development in the professional sphere using modern research methods and information and communication technologies on the basis of a foreign university. During the study of course, student should be competent in:  to substantiate the fundamentals of the methodology for performing scientific research, planning and organizing a scientific experiment, processing scientific data;  to argue methods of solving research and practical problems, including in interdisciplinary areas;  can analyze alternative solutions to research and practical problems and assess the potential benefits of implementing these options;  apply theoretical knowledge on methods of collecting, storing, processing and transmitting information using modern computer technologies;  choose the methods of presentation and methods of information transfer for different contingents of listeners.

Research practice
 Type of control: Защита практики
 Description: The main purpose of the discipline: the formation of pedagogical competence, the ability of pedagogical activity in universities and colleges based on the knowledge of the didactics of the higher school, the theory of education and management of education, analysis and selfassessment of teaching. During the study of course, master students should be competent in:  classify teaching methods based on criteria: traditionalistic  innovation; activity of cognitive activity; didactic goal and focus on results;  apply strategies and methods of training and education adequate to the goals;  develop research projects on topical issues of education and present the results in the form of presentations, articles, etc.;  describe different approaches to university management (university management  linear, structural, matrix): structure, quality, reputation;  evaluate and manage the processes of the organization of education, aimed at improving the structure, quality, reputation based on modern management approaches;  develop the provisions of the academic and research policy of the organization of education.

Research Seminar I
 Type of control: Защита НИР
 Description: The main purpose of "Research Seminar": the formation of master students in the skills of scientific research work. During the study of course, master student's should be competent in: 1. is able to competently substantiate the main directions of scientific research on the topic of dissertational work; 2. formulate a research problem, put a scientific problem and choose appropriate research methods; 3. can apply theoretical and experimental research methods in professional activity; 4. analyze the results of scientific research at each stage of the dissertation preparation; 5. are able to evaluate and draw conclusions on the main provisions of their research activities.

Research Seminar II
 Type of control: Защита НИР
 Description: The main purpose of "Research Seminar": the formation of master students in the skills of scientific research work. During the study of course, master student's should be competent in: 1. is able to competently substantiate the main directions of scientific research on the topic of dissertational work; 2. formulate a research problem, put a scientific problem and choose appropriate research methods; 3. can apply theoretical and experimental research methods in professional activity; 4. analyze the results of scientific research at each stage of the dissertation preparation; 5. are able to evaluate and draw conclusions on the main provisions of their research activities.

Teaching Internship
 Type of control: Защита практики
 Description: The purpose of teaching practice is to prepare for scientific and pedagogical activities in higher education, the acquisition and consolidation of practical skills for the implementation of the teaching and educational process in higher education, including the teaching of special disciplines, the organization of educational activities of students, scientific and methodological work on the subject.As a result of pedagogical practice, the undergraduate will have the skills of structuring and transforming scientific knowledge into educational material, oral and written presentation of the subject material, a variety of modern educational technologies, methods of drawing up tasks, exercises, etc.

Publication in the Proceedings of International Conferences
 Type of control: Защита НИР
 Description: The main purpose of "Publication in the Proceedings of International Conferences": is the formation of master candidates in the possibility of presenting the results of research work to the scientific community, receiving feedback, and exchanging experience in the field of professional activity. During the study of course, master student's should be competent in: 1. demonstrate current trends in scientific research; 2. to argue the annotated results of research in scientific journals, materials of international conferences and symposia; 3. they can apply new, scientifically grounded, theoretical or experimental results that allow solving a theoretical and applied problem; 4. analyze scientific results, the data of their colleagues and opponents in the sphere of the chosen professional activity; 5. generate ideas for the use of proposed developments in scientific research of the professional field of activity.