PhD program
Mathematics

Mathematics

QUALIFICATION

  • Scientific and pedagogical direction - Doctor of Philosophy (PhD)

MODEL OF GRADUATING STUDENT

ON 1.To apply innovative educational technologies and methods for teaching special subjects in universities; to develop assessment tools, methodological instructions;
ON 2. To obtain new results based on the conducted research and analytical work in relevant fields of science and apply these results to solve practical problems in the form of participation in research projects and tenders, conference presentations, publishing articles in journals with nonzero impact factor;
ON 3. To develop new mathematical methods for solving extremal problems and boundary value problems for nonlinear differential equations and mathematical physics;

ON 4. Competently use linguistic and cultural linguistic knowledge for communication in a multilingual and multicultural Kazakh society and in the international arena;

ON 5. Apply mathematical and computer modeling knowledge and skills, use modern programming, as well as modern software packages for solving problems in the field of insurance and financial risks;

ON 6. To construct different mathematical and economic models of the object under study based on the principles and tools of mathematical methods for making management decisions in the field of forecasting in the financial and insurance sectors;

ON 7. To conduct research on the numbering of specific classical objects, as well as finding analogs of the numbering theory problems;

ON 8. Planning stages an application research process using mathematical and statistical methods;
ON 9. To expand a theory of insurance risk assessment and improve the tools of this theory, which is a system of mathematical models and statistical methods;

ON 10. Synthesize new and complex ideas, hypotheses, techniques based on the results of research work;

ON 11. To create mathematical and sequential models of mathematical physics and filtration processes;
ON 12. To conduct a dialogue on topics in the competent field with equal status, as well as with the broad scientific community and society.

Program passport

Speciality Name
Mathematics
Speciality Code
8D05401
Faculty
Mechanics and Mathematics

disciplines

Academic writing
  • Number of credits - 2
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - In the course, doctoral students will be acquainted with the following topics related to the search for information in scientific data bases, analysis, working with genres academic writing: -Main genres of academic writing.. -Scientific databases. -The structure of the academic community. -Reference in scientific and scientific-technical information environment. -Features of the analytical review. -Review and types of reviews. -Report of a scientific event.

Actual problems of mathematics
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The aim of the course is to familiarize doctoral students with modern problems and the achievements of mathematics. In the course of studying the course, form the abilities of doctoral students: - understand the statements and the importance of modern open mathematical problems; - estimate the existing difficulties facing researchers of the open problems of pure and applied mathematics. - Critically evaluate the current state of theories of differential equations and mathematical analysis.

PhD thesis writing and defence
  • Number of credits - 12
  • Type of control - Докторская диссертация
  • Description - The main purpose of "PhD thesis writing and defence": of a doctoral dissertation is the formation of the doctoral students' ability to disclose the content of research work for the defense of the thesis. During the study of course, doctoral student's should be competent in: 1. to substantiate the content of new scientifically grounded theoretical and experimental results that allow to solve a theoretical or applied problem or are a major achievement in the development of specific scientific directions; 2. explain the assessment of the completeness of the solutions to the tasks assigned, according to the specifics of the professional sphere of activity; 3. they can analyze alternative solutions for solving research and practical problems and assess the prospects for implementing these options; 4. apply the skills of writing scientific texts and presenting them in the form of scientific publications and presentations. 5. to plan and structure the scientific search, clearly highlight the research problem, develop a plan / program and methods for its study, formalize, in accordance with the requirements of the State Educational Establishment, the scientific and qualification work in the form of a thesis for a scientific degree Doctor of Doctor of Philosophy (PhD) on specialty «8D07502 – Standardization and certification (by industry)». During the study of the discipline doctoral student will learn following aspects: Registration of documents for presentation of the thesis for defense. Information card of the dissertation and registration-registration card (in the format Visio 2003). Extract from the minutes of the meeting of the institution, in which the preliminary defense of the thesis took place. Cover letter to the Higher Attestation Commission. Expert conclusion on the possibility of publishing the author's abstract. Expert opinion on the possibility of publishing a dissertation. Minutes of the meeting of the counting commission. Bulletin for voting. A shorthand record of the meeting of the dissertational council. List of scientific papers. Response of the official opponent. A review of the leading organization. The recall of the scientific adviser.

Scientific Research methods
  • Number of credits - 3
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The method of scientific research as a way of knowing objective reality, which is a certain sequence of actions, techniques and operations to achieve the goals of their scientific research. The concept of a method, methodology and methodology of scientific research. Classification of research methods. General, general scientific and special research methods. Universal and private research methods.

Spectral theory of operators and analytical methods research of differential operators
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Purpose of the discipline– To familiarize with methods of the theory of linear operators and spectral expansions connected with differential operators. Tasks of the discipline– to acquaint with the main results of the spectral theory of linear operators. To study the analytical methods of investigating the spectral decomposition generated by differential operators.

Data for 2021-2024 years

disciplines

Bonus-malus system and its application in insurance
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - It describes the main difficulties in the practical solution of optimal control problems. The existence and uniqueness of the optimal control, the sufficiency of optimality, correctness, extreme challenges, the bifurcation of extremals. In the course of the course, the students will be able to formulate doctoral dissertation: Contextualize mathematical methods for modeling Bonus-Malus systems. Formulate conditions for the existence and uniqueness of solutions of stochastic differential equations and systems of equations.

Computable Numberings in the Arithmetical Hierarchy
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The course aims to show that arithmetical and hyperarithmetical hierarchies provide a natural measure of the complexity of sets of natural numbers that occur both in mathematics itself and in its applications, measured by the complexity of their description in the first-order language. The course tasks to studythe Tarski-Kuratovsky algorithm; to evaluate the algorithmic complexity of arithmetic sets; to evaluate the algorithmic complexity of sets relative to the hyperarithmetical hierarchy.

ControIIability Theory for Dynamical Systems
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the course “Theory of Controllability of Dynamical Systems” is the study of the theory and main problems of controllability of dynamic systems and methods for their solution. In the course of studying the course to form the ability of doctoral students: know and understand the basics of theories of controllability of dynamic systems for independent research and development to solve a number of boundary problems of controllability and optimal control.

Definability and Computability
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Purpose of the discipline– Familiarization with the notion of enumerability of sets in an arithmetic hierarchy is equivalent in the broadest sense of their natural definability in arithmetic. Tasks of the discipline-Consists in a new approach to the proof of Gödel's incompleteness theorem, based on the systematic use of formulas with bounded quantifiers and the application of the Gandhi fixed point theorem.

Embedding theorems and the theory of function spaces
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Purpose of the discipline– To familiarize us with the functional spaces of Sobolev and Nikol'skii and the corresponding imbedding theorems. Tasks of the discipline– To introduce the functional spaces of Sobolev and Nikol'skii and the basic inequalities between their norms, and, as a consequence, to obtain corresponding embedding theorems.

Generalized theory of Lyapunov exponents
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the course "Theory of generalized Lyapunov exponents" - the study of the theory and the main problems of generalized Lyapunov exponents of differential equations and methods of their solution. In the course of the study course is to give the doctoral students ability: know and understand the basics of the theory of generalized Lyapunov exponents for self-conducting research on the theory of differential equations.

Mathematical Analysis on Manifolds
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - To familiarize operators of exterior differential forms on smooth manifolds and integrate them. In the course of studying the course to form the ability of doctoral students: - Describe the basic concepts and definitions of the theory of entire functions of many variables; - Build metric spaces and their completion; - Implement a variational method for solving integrals of a k-form along a manifold.

Mathematical Models of Nonequilibrium Filtration Processes
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - We consider a process non stationary filtrational flow of uniform droplet-compressible monophase fluid in isotropic weakly-deformable porous environment. There are a various models to describe this process. The most popular is a model of classical elastic regime. But this model describes only non-stationary “equilibrium” filtration.

Models of random environment theory
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - n the course, we will consider some mathematical problems in the theory of random media: the infinitesimal (generating) operator of a random process; The method of random trajectories for solving parabolic equations; Solution of the Cauchy problem for the heat equation in a random environment perturbed by the "white noise" process; Finding the distributions of various additive functional from the Wiener process.

Modern problems of stochastic analysis
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to familiarize students with the basics of modern stochastic analysis and the theory of martingales, as well as some of their applications. The objectives of the discipline are for students to successfully master the basic concepts of the theory being presented; Acquiring practical skills in working with educational and scientific literature based on the fundamentals of stochastic calculus.

Modern Problems of the Theory of Mathematical Physics
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the course "Modern Problems of the Theory of Mathematical Physics" is the study of the theory and the main nonlinear problems of mathematical physics and methods for their solution. In the course of studying the course to form the ability of doctoral students: To know and understand the basics of the theory of functional analysis and the equations of mathematical physics for independent research on nonlinear equations.

Random parabolic equations and systems of equations
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to present probabilistic and statistical methods for analyzing the asymptotic behavior of solutions and issues of averaging parabolic equations and systems of partial differential equations. The objectives of the discipline are to study the method of random trajectories, which allows you to write out solutions to the equations under consideration in the form of a conditional mathematical expectation along the trajectories of a solution associated in a certain way with the original equation of a stochastic differential equation (or system of equations).

Sequential Models of Mathematical Physics
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The aim of the course is the familiarization of doctoral students with methods of justification of determining of mathematical models, the forms of its solutions. Studying this course, it is necessary to form the ability of doctoral students: - Know and understand the different forms of solutions of problems of mathematical physics; - Justify the methods for constructing mathematical models of physical processes; - Apply and justify the methods of practical solving of mathematical physics problems.

Singularly Perturbed Partial Differential Equations of Hyperbolic Type
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The aim of the course "Singularly Perturbed PartialDifferential Equations of Hyperbolic Type" is the study of the basic of the asymptotic theory of singularly perturbed partial differential equations of hyperbolic type and methods for solving such equations. In the course of studying the course to form the ability of doctoral students: to know and understand the basic of the theory of singularly perturbed partial differential equations of a hyperbolic type for independent research.

Spectral theory of operators and analytical methods research of differential operators
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Purpose of the discipline– To familiarize with methods of the theory of linear operators and spectral expansions connected with differential operators. Tasks of the discipline– to acquaint with the main results of the spectral theory of linear operators. To study the analytical methods of investigating the spectral decomposition generated by differential operators.

Statistical estimation methods and mathematical forecasting methods
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to familiarize with mathematical methods of demographic forecasting and assessment of the risks of morbidity and mortality. The tasks of the discipline are to study the basic methods of demographic forecasting with a view to their further application in insurance practice. In the course of the course, the students will be able to formulate doctoral dissertation: the purpose of the discipline is to teach students the principles of risk management in insurance, decision-making in risk situations for various types of insurance schemes.

System Nonlinear Differential Equations
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The aim of the course is to study the basic of the theory of systems of nonlinear differential and integro-differential equations with a small parameter with the highest derivative and methods for solving such equations. In the course of studying the course to form the ability of doctoral students:to know and understand the basic of the theory of nonlinear differential and integro-differential systems with a small parameter for independent research on self-research in this area.

The Category of Numbered Sets
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Purpose of the discipline– To present a theory-categorical approach for the analysis of facts and results on the numbering of concrete classical objects, as well as finding analogues of problems of number theory in topology and other areas of mathematics. From the point of view of category theory, the main problems of number theory are considered. Tasks of the discipline–To study the problems of number theory in topology and other fields of mathematics.

The Mathematical Theory of Viscous Incompressible Fluid
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The aim of the course "Mathematical problems of the dynamics of a viscous incompressible fluids" is the study of the basic theory and the main problems of a viscous incompressible fluids and methods for solving them. In the course of studying the course to form the ability of doctoral students:know and understand the basic theory of the dynamics of a viscous incompressible fluids for to independent research scientific works on the theory of Newtonian fluids.

The methods of statistical evaluation of insurance premiums and reserves, taking into account the quality of data
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to familiarize with the methods of statistical evaluation of insurance premiums and reserves taking into account the quality of the data. The task of the discipline is to study the basic methods of calculating premiums and reserves in insurance with a view to their further application in insurance practice.

The theory of generalized Lyapunov Exponents
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the course "Theory of generalized Lyapunov exponents" - the study of the theory and the main problems of generalized Lyapunov exponents of differential equations and methods of their solution. In the course of the study course is to give the doctoral students ability: know and understand the basics of the theory of generalized Lyapunov exponents for self-conducting research on the theory of differential equations.

Theory of Extremal Problems in Banach Space
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to familiarize methods ofsolving extremum problems in Banach spaces During the study of course, students should be competent in: • calculation of functional gradients defined on the set of solutions of ordinary differential equations, parabolic equation, hyperbolic equation; • formulation optimality conditions for a variety of extreme tasks and control their performance; • analyze mathematical models of control processes and justify the correct choice of the method of solving problems (analytical, numerical, analytical-numerical).

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