PhD program
Mathematical and Computer Modelling

Mathematical and Computer Modelling

QUALIFICATION

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

MODEL OF GRADUATING STUDENT

ON1. Conduct scientific research and obtain new fundamental and applied results, plan scientific and analytical research in accordance with the approved direction of research in the field of specialization.
ON2. Use the concepts, mechanisms and patterns of physical, chemical and technological, natural, biological and random processes when developing conceptual and theoretical models of scientific problems solved.
ON3. Use multiprocessor computing techniques and methods of mathematical, numerical and computer modeling during the analysis and solution of applied and engineering problems, exposing the use of skills to expand their knowledge based on information and educational technologies.
ON4. Create a project and develop recommendations for the implementation of research results in the production and financial industries by methods of mathematical modeling and numerical experiments.
ON5. Carry out an in-depth analysis of the problems, statement and justification of the problems, reveal their natural and scientific content during scientific and research activities, involve the corresponding mathematical apparatus for their solution.
ON6. create mathematical and computer models to solve the problems of biomedical processes, processes of physical chemistry, kinetics, financial processes, dynamics of multiphase turbulent flows.
ON7. Analyze, develop and conduct numerical experiments of constructed mathematical models of industrial, technological, non-stationary physical, chemical, biological, financial processes.
ON8. Develop stochastic finance models; choose approximate methods to model turbulence and techniques for closing the governing equations using a semi-empirical theory.
ON9. Conduct scientific research in the field of mathematical and computer modeling of temperature phenomena, complex systems, thermomechanical processes, as well as apply stochastic and simulation systems to solve research and applied problems.
ON10. Conduct research and experiments to apply mathematical and numerical tools of fundamental knowledge on numerical methods, financial mathematics, computational fluid dynamics, mechanics, turbulence modeling, physical, biomedical, and nonlinear technological processes and complex systems for solving applied problems.
ON11. Develop educational materials, educational and methodical complexes of disciplines in the field of mathematical and computer modeling, modern numerical methods; develop and introduce new innovative education technologies to pedagogical practice.
ON12. Carry out research with foreign partners in order to prepare results for the implementation of interstate programs in the field of mathematical modeling, mathematics and mechanics; participate in scientific seminars and conferences, maintain international communication with scientific community; work as a team, tolerate social, ethnic, religious and cultural differences, critically evaluate individual and team activities, identify ways and choose the means for self-development and enhancing skills.

Program passport

Speciality Name
Mathematical and Computer Modelling
Speciality Code
8D06104
Faculty
Mechanics and Mathematics

disciplines

Academic writing
  • Number of credits - 2
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of studying the discipline "Academic writing" is to develop PhD doctoral students' respective professional competencies aimed at developing the willingness and ability of scientific and pedagogical personnel to implement their own research projects, programs, and presenting their results in writing in accordance with the legislative norms of the Republic of Kazakhstan and international academic community, the ability to show publication activity in national and foreign language. As a result of studying the discipline, doctoral students will be able to: 1. Formulate productive research questions; to formulate the goal, objectives, subject and object of scientific work; prepare a description of the research in Kazakh, Russian or Englishlanguage in order to publish the results in a highly rated journal. 2. To navigate in the literature on the topic of research, use bibliographic resources and search engines for scientific work, including electronic databases; 3. Reasonably state the provisions of their study, based on facts and examples. 4. Prepare and submit documents for obtaining a patent and copyright . 5. Substantially conduct a discussion on the topic of research in order to disclose a research question and develop methodological tools for the implementation of a scientific project. Implement a scientific project in accordance with the requirements of competitive documentation or as part of initial research. 6. Write a review of a scientific project / article / dissertation.During the study of the discipline students will learn following aspects: the main aspects of compiling academic texts in Kazakh, Russian and English are considered in order to publish the results of scientific research in the form of dissertations, scientific articles or project applications. We study the features of writing project applications for tender documentation for funding of scientific research; patent applications and applications for obtaining copyright. This course includes the study of the main aspects for the formulation of goals, objectives, relevance of research, etc. Students will learn how to carry out comprehensive research, including interdisciplinary, on the basis of a holistic systemic scientific worldview, to learn how to describe the research work done in Kazakh, Russian and English.

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 form a holistic systemic understanding of philosophy as a special form of cognition of the world, its main sections, problems and methods of their study in the context of future professional activity. The training course forms the theoretical and methodological basis of research work.

Mathematical and computer modeling of medical and biological processes
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: to form knowledge in solving actual scientific and applied problems related to modeling processes occurring in living organisms and systems, processing and system analysis of experimental data, to form knowledge in the field of the theory of dynamic systems and nonlinear dynamics applied to the problems of physics of living systems.

Mathematical modeling of non-stationary physical process
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The main purpose of the course: to form the ability to simulate non-stationary physical processes using mathematical methods. During the study of course, students should be competent in: - describing the finite-difference methods for the approximate solution of the equations of mathematical physics; - selecting a mathematical model for the physical problem in the form of multi-dimensional time-dependent differential equations; - creating numerical algorithms and programs for the implementation on PC; - analyzing the results, their physical meaning; - assessing the accuracy of computations. During the study of the discipline students will learn following aspects: the construction of a mathematical model of the physical process; the correct choice of the mathematical model and the numerical method; construction of difference schemes and algorithms for solving problems; construction of flowcharts and software code; analysis of the results of numerical simulation of problems of nonlinear physical processes.

Modern methods of mathematical modeling
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: to form the skills of applying theoretical and practical aspects of modern modeling methods for solving problems of applied mathematics, skills of using mathematics packages corresponding to tasks, to form skills to interconnect modules implemented in math packages with software implemented using high-level programming languages (Python, Java). Modern mathematical packages will be studied that allow solving applied problems of natural science.

Numerical simulation of unsteady three-dimensional turbulence flows
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The main purpose of the course: to form the ability to conduct numerical simulation of unsteady three-dimensional turbulent flows; to compile an analysis of the results, to organize a computational experiment. During the study of the course, students should be competent in: - describing a variety of physical processes and mathematical models; - applying numerical methods to solve equations of mathematical physics describing physical problems; - describing the issues of convergence, stability of the applied schemes and algorithms, computation errors; - conducting numerical simulation of unsteady three-dimensional turbulent flows, selecting the method for solving the problem, and also compiling an analysis of the results obtained. - organizing a computational experiment.

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.

Psychology of management
  • Number of credits - 3
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to provide scientific training of highly qualified specialists based on the study of fundamental concepts of management psychology, creating prerequisites for a theoretical understanding and practical application of the most important aspects of the field of management in the process of professional formation. The course is aimed at studying the patterns of development and functioning of mental processes, the basics of effective interaction and conflict resolution, self-development and self-presentation.

Scientific Research methods
  • Number of credits - 3
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of studying the discipline "Research Methods " is to develop the ability of doctoral students to conduct research based on the analysis, systematization and generalization of research results in the field of mathematical and computer modeling through the use of a set of research methods for solving specific applied problems . As a result of studying the discipline, doctoral students will be able to: 1. to abstract thinking, analysis, synthesis, the ability to improve and develop their intellectual and General cultural level; 2. to master and use new research methods in a new field of professional and research activities; 3. to use knowledge of modern problems of science and education in solving fundamental and applied problems; 4. to analyze the results of scientific research, apply them in solving specific applied problems, independently carry out scientific research; 5. to use individual creative abilities to independently solve research problems; 6. to carry out scientific research, create innovations, implement them in reality, analyze and reflect the results. During the study of the discipline students will learn following aspects: methodologies, methods, problems, principles, and trends that are necessary for specialists in mathematical and computer modeling to develop and implement scientific research and research projects to improve the efficiency of organizations, industries, and regions in various areas of the economy. This course introduces the categories and basic concepts of research methodology, forms and methods of scientific knowledge, principles and organization of research activities; the main problems of modern research practice, teaches to use various information resources, introduces the methodology of writing, registration and defense of dissertation work.

Data for 2022-2025 years

disciplines

Computer modeling in dynamic systems
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The main purpose of the course: to form the knowledge in the field of the theory of dynamical systems and nonlinear dynamics as applied to the problems of the physics of living systems; ability to solve applied problems; know the methods of identification of dynamic systems and decision making. During the study of course, students should be competent in: - describing: the main provisions of the qualitative theory of differential equations, the terms and approaches of the theory of dynamic systems; - solving theoretical problems of system analysis and systems theory, - formulating the tasks of analytical and numerical research of dynamic systems on the phase plane and in the three-dimensional phase space and choose adequate theoretical and numerical methods for their solution. - possessing an analytical method for analyzing the stability of equilibrium states of models of living systems, to own computer methods for analyzing stability in the phase space of a model system. - solving research and applied problems. During the study of the discipline, students will learn following aspects: concept of a dynamic system, linear and nonlinear dynamical systems, existence and uniqueness of the solution, phase space, phase trajectory and semi trajectory, singular points, search and analysis of the stability of equilibrium states in two-dimensional and three-dimensional systems, determination of the equilibrium state in living systems, elements of bifurcation theory, structural stability and bifurcation.

Development and research of methods of modeling the behavior of complex processes
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline:: the formation of knowledge and skills in the creation and study of mathematical simulation models of complex processes and systems. Build Ability: -use theoretical and experimental research to model complex processes; - develop algorithms and software for managing complex processes based on research; - to generate the received scientific knowledge in own scientific research.

Mathematical and computer modeling of chemical processes
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline:is to improve the professional training of the student in the field of modeling of chemical and technological processes, includes master degree students knowledge in the field of modeling, compiling and optimizing mathematical models, using modern mathematical software packages in modeling; formation of professional skills in modeling chemical and technological processes, in the analysis and processing of data using modern information technologies. During the study of course, master students should be competent in: - building mathematical models of the systems under study; - carrying out analytical research and optimization of the developed mathematical model; - realizing the developed mathematical models in computer form; - applying the methods of computational mathematics to solve specific problems of the processes of chemical technology; - knowing methods of constructing a mathematical model of typical professional problems and a meaningful interpretation of the results obtained; - using packages of applied programs for modeling of chemical and technological processes. During the study of the discipline master students will learn following aspects: The course is designed to expand the knowledge of basic concepts, techniques and methods of mathematical and computer modeling, consideration of modern technologies for constructing and researching mathematical models for chemical-technological processes. The course discusses the principles of the formation of mathematical models, methods for constructing physico-chemical models of chemical-technological processes, types of reactors and chemical-technological processes, methods for optimizing chemical-technological processes using empirical and / or physico-chemical models.

Mathematical and computer modeling of physical chemistry processes
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The main purpose of the course: to form the ability to develop a mathematical model for the problem of physical chemistry; algorithm and program for the numerical solution of the problem; to analyze the results, their physical meaning; to estimate the computation error. During the study of the course, students should be competent in: - selecting a mathematical model for the problem of physical chemistry in the form of differential equations of mathematical physics; - creating the numerical algorithm, the program for implementation on PC; - analyzing the results, their physical meaning; assessing the accuracy of calculations. - describing the various problems of physical chemistry and mathematical models; - applying numerical methods for solving equations of mathematical physics describing physical problems.

Mathematical and Computer Modeling of Unsteady Nonlinear Physical Processes
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: to develop skills for solving problems of studying non-stationary nonlinear physical processes by mathematical methods. In the course of studying the course, to form the abilities of undergraduates: – to make mathematical models of complex non-stationary nonlinear physical processes; – use numerical methods for the implementation of mathematical models of non-stationary nonlinear physical processes; - write a program code for the constructed mathematical model; – build a graph and analyze the results.

Mathematical modeling of thermophysical processes in multilayer environments
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: is the development and research of a complex of mathematical models for solving heat and mass transfer problems in automatic process control facilities, developing control systems for thermophysical processes in such conditions for obtaining high-quality, reliable products from composite materials and developing recommendations for improving technology.

Mathematical Models for Heat and Mass Transfer problems
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The main purpose of the course: to form the ability to apply a generalized method for calculating the heat and mass transfer of fluid flows and related processes; to compose an algorithm for the numerical solution of the problem, the implementation program on PC; to analyze the results, their physical meaning; to evaluate the error of calculations. During the study of the course, students should be competent in: - choosing a computational method for solving problems; - constructing numerical algorithms; - making the program for implementation on PC; - analyzing the results, their physical meaning; - assessing the accuracy of computations. During the study of the discipline, students will learn following aspects: main aspects of mathematical modeling of heat and mass transfer in electrical contacts, various methods of implementation on a PC.

Methods in inverse-problem and optimization
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The main purpose of the course: to form the ability of doctoral students to carry out the formulation of the problem, to select the method of solution; to analyze the results obtained, to prove it; to apply basic methods for solving inverse problems. During the study of the course, students should be competent in: - knowing the basic optimization methods for solving inverse problems; - being able to formulate the problem, to select the method of solution; - making an algorithm for the numerical solution of the problem, a program for implementation on a PC and carry out feedback; - being able to analyze the results obtained, their physical meaning; - estimate the error of calculations. During the study of the discipline, students will learn the following aspects: Conception of Inverse Problem. Inverse Problems for Two-Dimensional Parabolic and Elliptic Equations. The Connection between Inverse Problems for Parabolic, Elliptic and Hyperbolic Equations. Numerical Solution of Inverse Problems for Parabolic, Elliptic and Hyperbolic Equations. Boundary Inverse Problem for Parabolic Equation. Statement of Problem. Optimization Method of Solution. Functional of Solution. Principle of Maximum for Boundary Inverse Problem for Parabolic Equation. Adjoint Problem. Numerical Algorithm of Solution. Method of Quickest Descent. Iterative Method.

Modeling of nonlinear deformable systems and processes
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The main purpose of the course: forming the ability of doctoral students to obtain the basic relations and characteristics of nonlinear deformable media for their practical application while modeling of applied problems of the elasticity theory. During the study of course, students should be competent in: - demonstrating a deep understanding and ability to develop mathematical models of nonlinear deformable systems and processes; - understanding and explaining the basic principles underlying the nonlinear mathematical models of deformable systems and processes; - properly applying the methodological apparatus of the nonlinear theory of deformable media to solve nonlinear mathematical models; - critically analyzing and evaluating the results of modeling of nonlinear deformable systems and processes; - integrating knowledge on modeling of nonlinear deformable systems and processes to solve important applied problems and determining the significance of products of their own and other scientific activities. During the study of the discipline students will learn the following aspects: concept of deformation functional; construction of the functional of elastic deformation for a nonlinear medium at various approximations; variation principles; application of variation principles for the development of nonlinear mathematical models; selection of methods and finding solutions to models of nonlinear applied problems; visualization of the research results.

Nonlinear Theory of Deformable Media
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The main purpose of the course: forming the doctoral knowledge on the theory of nonlinear deformable media for practical application while modeling processes and phenomena at the new qualitative level. During the study of the course, students should be competent in: - demonstrating a deep understanding and ability to apply the conceptual apparatus of the V.V. Novozhilov nonlinear theory of deformable media; - competently operating with the basic equations of the nonlinear theory of deformable media; - classifying nonlinear problems, boundary conditions, external and internal forces; - conducting a critical analysis of the strain-stress state of various deformable media in nonlinear formulation; - creating a holistic scientific work using the basic relations, principles and methods of the V.V. Novozhilov nonlinear theory. During the study of the discipline students will learn following aspects: fundamentals of the V.V. Novozhilov nonlinear theory, strain-stress state of the medium in nonlinear formulation; basic assumptions of the nonlinear theory; equations of media and boundary conditions; physical meaning of the V.V. Novozhilov simplifications; application of the nonlinear theory for modeling of various processes and phenomena.

Numerical methods for solution of the Navier-Stokes Equations
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: to form knowledge about the problems of the numerical solution of the Navier-Stokes equations. Methods for the numerical solution of the Navier-Stokes equations in the case of an incompressible fluid on a spaced grid will be shown. The methods for solution the variables in the function - vorticity parameters are shown. The solution methods for a viscous compressible fluid are studied, in particular, the McCormack method, the Bima-Warming method, the Godunov method, the TVD scheme During the study of course, master students should be competent in: – deriving the Navier-Stokes equations of a viscous compressible flow, to made dimensionless the parameters characterizing the motion of a viscous fluid. – creating a mathematical model of hydrodynamic processes, including the physical formulation of the problem, –formulating initial-boundary problems. – demonstrating knowledge of the basic finite difference, finite element and finite volume approaches to solving boundary value problems for the Navier-Stokes equations. – mading the program of the constructed numerical schemes for solving problems of hydrodynamics, to obtain results and to be able to interpret the mechanisms of the physical process. During the study of the discipline master students will learn following aspects: derivation of the Navier-Stokes equations, conservation laws, and basic hypotheses. Problems of numerical solution of equations. Numerical methods for solution of the Navier-Stokes equations in the case of incompressible fluid. The methods for solution the variables in the function - vorticity parameters are shown. Solutions for viscous compressible fluid, Mac-Cormac method, Bima-Warming method, Godunov method, TVD schemes, explicit implicit integration methods.

Theory of Generalized and Special Functions
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline:to introduce students to the mathematical apparatus of the theory of generalized functions and various operations on them. Outlines the basics of the theory of generalized functions and operations on them. It also presents the basics of integral Fourier and Laplace transforms in the space of generalized functions and methods for constructing solutions of partial differential equations.

Data for 2022-2025 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 2022-2025 years