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PhD program

Mathematical and Computer Modelling

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PhD program
Educational programs
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

Mathematical and computer modeling of medical and biological processes

Mathematical modeling of nonstationary physical processes

Modern methods of mathematical modeling

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

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 2021-2024 years

disciplines

Computer modeling in dynamic systems

Computer modeling of complex system using Python

Type of control - [RK1+MT+RK2+Exam] (100)
Description - The main purpose of the course: to form the ability to create complex computer models based on the Python platform. During the study of the course, students should be competent in: - demonstrating fundamental, systemic knowledge in the development of computer modeling of complex systems within the framework of modern scientific knowledge paradigms; - conducting a critical analysis, evaluation and synthesis of new, complex ideas, problems, approaches and trends in determining specific requirements in developing a computer model; - working with the test results and processing the experimental results with the methods of mathematical processing of experimental data; - critically evaluating the results of scientific research, modern theories, problems and approaches, new trends in the study of the model and the obtained modeling data; - differentiating the priorities of educational and research activities, correlating their own scientific interests with social, ethnic values, the needs of production and society; - presenting the results of educational and research activities in the form of scientific reports, abstracts, abstracts of articles, physical and mathematical comments, doctoral dissertations, educational research and scientific projects; - conducting independent research of scientific problems with a projection on promising new directions in computer modeling of complex systems using Python. During the study of the discipline, students will learn the following aspects: Computer simulation of complex thermo-physical processes. Python programming language. Python-based software design. Designing user interfaces. Confidentiality and ethical standards. Ergonomics and accessibility.

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: is the formation of knowledge and skills in creating and exploring mathematical simulation models of complex processes and systems. During the study of course, master students should be competent in: - to demonstrate deep knowledge of the current state and trends in the development of scientific knowledge in the field of mathematical modeling of complex processes; - to consider complexes of mathematical models of the behavior of complex processes; - use theoretical and experimental studies to simulate complex processes; - develop algorithms and software for managing complex processes based on research; - to generate the received scientific knowledge in own scientific research. During the study of the discipline master students will learn following aspects: Models of data structures; understanding of DBMS classification methods depending on implemented data models and methods of their use; studying the ways of storing data at the physical level, the types and methods of organizing file systems; detailed study of the relational data model and DBMS implementing this model, the language of SQL queries; An understanding of the problems and the main ways to solve them with the collective access to data; study of the capabilities of DBMS supporting various models of data organization, advantages and disadvantages of these databases in the implementation of various data structures, the means of these DBMS; understanding the stages of the life cycle of the database, support and maintenance; Obtaining an idea of specialized hardware and software tools oriented to building databases of large volumes of storage.

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

Mathematical and computer modeling of temperature phenomena

Type of control - [RK1+MT+RK2+Exam] (100)
Description - The main purpose of the course: to form the ability to develop a computer-aided mathematical model of a steady-state temperature field in structural elements with simultaneous presence of heterogeneous local heat sources. During the study of the course, students should be competent in: - identifying specific requirements, opportunities and problems in the development of a mathematical model of temperature phenomena; - systematizing and interpreting scientific theories and concepts of the latest trends in mathematical and computer modeling; - applying general programming knowledge in the field of computer modeling; - critically evaluate the results of scientific research, modern theories, problems and approaches, new trends in the study of thermal processes and temperature phenomena; - differentiating the priorities of educational and research activities, correlating their own scientific interests with social, ethnic values, the needs of production and society; - presenting the results of educational and research activities in the form of scientific reports, abstracts, abstracts of articles, physical and mathematical comments, doctoral dissertations, educational research and scientific projects; - building a research process on the topic of the thesis, reasonably submit the research results in scientific discussions and publications in rating journals in international databases of Thomson Reuters or Scopus, as well as in national and international peer-reviewed publications. During the study of the discipline, students will learn the following aspects: Modeling of complex thermo-physical processes and temperature phenomena. Programming languages. Software design. Designing user interfaces. Confidentiality and ethical standards. Ergonomics and accessibility. Principles and methods of applying the fundamental laws of energy conservation in the study of temperature phenomena in the bearing elements of the structure, taking into account the simultaneous presence of local dissimilar heat sources.

Mathematical and Computer Modeling of Unsteady Nonlinear Physical Processes

Mathematical modeling in Biomedical Engineering

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. During the study of course, master students should be competent in: - identify specific requirements, opportunities and problems in the development of a mathematical model of thermophysical processes in multilayer environments; - systematize and interpret scientific theories and concepts of the latest trends in mathematical and computer modeling; - apply general programming knowledge in the field of computer modeling; - critically evaluate the results of scientific research, modern theories, problems and approaches, new trends in the study of thermal processes in multilayer environments; - to differentiate the priorities of educational and research activities, correlating their own scientific interests with social, ethnic values, the needs of production and society. - present the results of educational and research activities in the form of scientific reports, abstracts, abstracts of articles, physical and mathematical comments, master's theses. During the study of the discipline master students will learn following aspects: Identification of physico-chemical factors that determine the temperature fields in the process of polymerization of composite materials and their accounting in mathematical models. Statement and solution of mathematical problems describing the temperature fields in the process of polymerization in the automatic recycling plant with regard to phase transitions and multi-stage.Development of finite-difference schemes and calculation of spatio-temporal distributions of temperature fields in the automated process control system.Analysis of the contribution of various processes to the temperature fields in the automated process control system and the development of algorithms and programs for managing thermophysical processes, the development of new installations (devices) for automatic control systems at all stages of product manufacturing. Development of a methodology for identifying during the process of manufacturing the sources of the degradation process. Identify the effeerature, time, heating rate and pressure on the quality of the material being manufactured.Development of recommendations for the management of the polymerization process in the automated process control system.

Mathematical Models for Heat and Mass Transfer problems

Mathematical models of two-phase process control

Methods in inverse-problem and optimization

Methods of parametrization in the statistical dynamics of turbulence

Modeling of financial risks

Modeling of nonlinear deformable systems and processes

Nonlinear Theory of Deformable Media

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.

Numerical methods in chemical kinetics

Numerical methods of high order accuracy

Numerical simulation of unsteady three-dimensional turbulence flows

Physical nonlinearity in problems of dynamics

Random processes and financial mathematics

Simulation Modeling of Complex Systems

Type of control - [RK1+MT+RK2+Exam] (100)
Description - The main purpose of the course: to form the ability to create simulation models for solving applied and research problems based on various modern platforms. During the study of the course, students should be competent in: - demonstrating fundamental, systemic knowledge in the field of simulation modeling of applied and research problems; - conducting critical analysis, evaluation and synthesis of new and complex ideas, problems, approaches and trends in the application of simulation systems; applying general programming knowledge in application development; - generating new and complex goals, proposing new hypotheses and solutions of scientific problems in the field of principles for constructing simulation models of systems and processes of their functioning; - applying the methods of system dynamics and discrete event modeling for the development of simulation models; - working skills in the instrumental environment of simulation modeling using the means of visual development of the model; - differentiating the priorities of educational and research activities, correlating their own scientific interests with social, ethnic values, the needs of production and society; - presenting the results of educational and research activities in the form of scientific reports, abstracts, abstracts of articles, physical and mathematical comments, doctoral dissertations, educational research and scientific projects. During the study of the discipline, students will learn the following aspects: Development of simulation models of processes and systems, development of decision support systems, automation of production processes. Software design. Designing user interfaces. Confidentiality and ethical standards. Ergonomics and accessibility. Project management.

Stochastic models and the theory of calculations in stochastic financial models

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. During the study of course, master students should be competent in: – using the main types of special functions, their integral representations, asymptotics for solving problems of mathematical physics, – applying the theory of generalized functions to the solution of applied problems of mathematics and programming. – knowing the methodology of the study of functions, the rules of action in terms of calculating infinitely small quantities and the transition to integrated systems. – to be able to differentiate and integrate, investigate series and sequences for convergence, solve extremal problems, construct graphs of functions, solve equations and inequalities. – possessing the methods of formulation, analysis and solution of problems of differential and integral calculus, skills of independent solution of problems of theoretical and applied nature. During the study of the discipline master students will learn following aspects: Fundamentals of the theory of generalized functions and operations on them; fundamentals of integral Fourier and Laplace transforms in the space of generalized functions and methods for constructing solutions of partial differential equations. Generalized functions of one variable, operations with them. The main functions of many variables. The space of the main functions. Generalized functions of many variables, operations with them.

Turbulence modeling techniques (RANS)

Type of control - [RK1+MT+RK2+Exam] (100)
Description - The main purpose of the course: to form the ability of doctoral students to choose the right approximate methods of modeling turbulence based on the Reynolds method. During the study of the course, students should be competent in: - quantitatively analyzing the obtained numerical results; having a clear idea of the algorithm for solving problems; - selecting and justifying the methods chosen; having the culture of thinking; understanding the importance and the main problems of the discipline; - closing the system of equations for the averaged values; - building a numerical algorithm for solving differential equations; - writing the code, analyzing the results of numerical simulation of turbulent flows. The objective of the discipline is oriented the doctoral correct choice of approximate methods for solving problems. Since the module as a whole is focused on methods for solving nonlinear partial differential equations, which are characterized by discontinuous solutions (for hyperbolic type equations), large gradient domains (“boundary layers”), etc., a lot of attention is paid to building monotone (majorant) schemes. During the transition from model equations to linear systems and nonlinear equations, the course actively uses the characteristic properties of hyperbolic type equations and similar splitting methods for other types of equations, the integral-interpolation method (integral identity method) and other effective ways of generalizing schemes with preserving properties. During the study of the discipline students will learn the following aspects: semi-empirical theory of turbulence, the characteristic properties of statistical moments of higher order, obtained on the basis of equations for Reynolds stresses; one-parameter, two-parameter models of turbulence; building semi-empirical models for Reynolds stresses in the field of external forces.

Turbulence modeling: LES-approach

Data for 2021-2024 years

INTERNSHIPS

Pedagogical

Research

Data for 2021-2024 years