PhD courses
Speciality Code:
8D05405
Speciality Name:
Computational Sciences and Statistics
Faculty:
Mechanics and Mathematics
Qualification:
- Scientific and pedagogical direction - Doctor of Philosophy (PhD)
- Model of graduating student
- Mandatory disciplines
- Elective disciplines
- Professional
Conduct scientific research and obtain new fundamental and applied results, critically analyze and evaluate the results obtained, formulate sound conclusions even in conditions of incomplete or limited information;
Write scientific articles in foreign and domestic journals and inform the wide scientific community of advanced topics and research results at international and national conferences, seminars and workshops, critically assessing their significance;
Write independent scientific projects and applications, setting a theoretical or practical computational problem or a solution method that is relevant to society, implement and correct, if necessary, the process of independent scientific research;
Determine the direction and intensity of their professional development in the chosen scientific field, be able to work in a team and contribute to the development of the team and society as a whole.
Conduct research in the field of methodology of computational experiments based on approximating differential equations by methods of finite differences, volumes and / or elements.
Conduct a fundamental analysis of computational methods and difference schemes for convergence and correctness, including in the case of high-performance algorithms;
Create and use correct structured, curvilinear, unstructured computational grids in computational problems
Develop parallel computing algorithms for engineering problems and implement them in high-performance systems, develop quantum computing algorithms.
Use the methods of mathematical statistics on real data for the selection of parameters, adaptation and testing of computing systems based on real experiments
Use data mining methods based on deep learning, reinforcement learning to adapt the computational algorithm to effectively predict results
Write scientific articles in foreign and domestic journals and inform the wide scientific community of advanced topics and research results at international and national conferences, seminars and workshops, critically assessing their significance;
Write independent scientific projects and applications, setting a theoretical or practical computational problem or a solution method that is relevant to society, implement and correct, if necessary, the process of independent scientific research;
Determine the direction and intensity of their professional development in the chosen scientific field, be able to work in a team and contribute to the development of the team and society as a whole.
Conduct research in the field of methodology of computational experiments based on approximating differential equations by methods of finite differences, volumes and / or elements.
Conduct a fundamental analysis of computational methods and difference schemes for convergence and correctness, including in the case of high-performance algorithms;
Create and use correct structured, curvilinear, unstructured computational grids in computational problems
Develop parallel computing algorithms for engineering problems and implement them in high-performance systems, develop quantum computing algorithms.
Use the methods of mathematical statistics on real data for the selection of parameters, adaptation and testing of computing systems based on real experiments
Use data mining methods based on deep learning, reinforcement learning to adapt the computational algorithm to effectively predict results
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Curvilinear adaptive meshes
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose: familiarization with the fundamental concepts and methods of using curvilinear adaptive grids in numerical methods for solving differential equations and other problems of mathematical modeling. The main emphasis is on the development and application of algorithms that allow the construction and efficient use of curvilinear grids.
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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.
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Advanced Statistics
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The course is aimed at teaching mathematical methods of data analysis and statistical modeling for solving various problems in applied areas. In general, the course provides the necessary knowledge and skills for the effective use of data analysis and machine learning methods in their scientific work.
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Academic writing
- Number of credits: 2
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of studying the discipline 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 in the field of robotics and mechatronics, 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. The discipline includes 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.
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Finite element methods
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The discipline is devoted to finite element methods (FEM) for the numerical solution of linear and nonlinear partial differential equations (PDE). The most important finite elements are introduced, for example, high-order polynomials on tetrahedra and hexahedrons, as well as isoparametric elements. Throughout the course, a formal language is used to analyze elliptical problems, for example, to prove existence and uniqueness, and to analyze errors. The student will know: proof of the theorem in the formal language used to analyze the finite element method; analytical and numerical solutions of elliptic partial differential equations. The student will be able to: independently formulate, implement and use various finite element methods for linear and nonlinear differential equations; solve systems of equations, resulting from the finite element method in a numerically efficient manner; obtain general error estimates for finite element methods; use fundamental equations in applications; present the results both orally and in writing; numerically evaluate the effectiveness of the finite element method.
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Scientific Research methods
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of studying the discipline is the formation of doctoral PhD students ideas about the methods of scientific research in robotics and mechatronics, the formation of research competence and their willingness to apply the knowledge and skills in organizing their own scientific research and the organization of scientific research in their professional activities. As part of the study of the discipline are considered: Methodology and methodology of scientific research in robotics and mechatronics; The main methods of finding information for scientific research; Planning of research work; Mathematical foundations of experimental design; Procedures for the preparation, execution and defense of doctoral dissertations.
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Intelligent systems for process forecasting
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The goal of the discipline is to teach students methods of forecasting processes using machine learning and mathematical statistics. In the course of studying the discipline, students will become familiar with the concepts of deep learning, reinforcement learning, generative adversarial GANs. Students will learn how to apply mining methods to select the parameters of a mathematical model for effective forecasting by approximating real data. They will also get acquainted with the latest works in the field of simulation simulation based on the results of preliminary runs of a numerical model, based on finding values in nodes and cells based on the work of an intelligent system, without direct calculation.
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Hight Performance Computing
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The goal of the discipline is to develop the ability to manage technologies for organizing parallel computing on multiprocessor computers with distributed or shared RAM. As a result of studying the discipline, form the doctoral students' abilities: to consider methods of logical representation of the structure of multiprocessor computing systems; analyze the available computational schemes and carry out their decomposition; analyze the complexity of the main data transmission operations; simulate parallel programs; form models of computing systems. Within the discipline the following aspects are considered: General characteristics of data transmission mechanisms. Analysis of the complexity of the basic data transfer operations. Generalized data transfer from one processor to all other processors on the network. Generalized data transfer from all processors to all processors on the network. Methods of logical representation of the topology of the communication environment. Estimation of the complexity of data transfer operations for cluster systems. Simulation of parallel programs. Parallel algorithms development technique. The distribution of subtasks between the processors should be performed in such a way that the presence of information links. Methods for solving partial differential equations. Organization of parallel computing for systems with shared memory. Computing system model formation. Statement of the computational problem and the choice of a parallel solution method. Determination of graphical forms of monitoring the process of parallel computing. Estimation of the complexity of data transfer operations for cluster systems. Simulation of parallel programs. Parallel algorithms development technique. The distribution of subtasks between the processors should be performed in such a way that the presence of information links. Methods for solving partial differential equations. Organization of parallel computing for systems with shared memory. Computing system model formation. Statement of the computational problem and the choice of a parallel solution method. Determination of graphical forms of monitoring the process of parallel computing. Estimation of the complexity of data transfer operations for cluster systems. Simulation of parallel programs. Parallel algorithms development technique. The distribution of subtasks between the processors should be performed in such a way that the presence of information links. Methods for solving partial differential equations. Organization of parallel computing for systems with shared memory. Computing system model formation. Statement of the computational problem and the choice of a parallel solution method. Determination of graphical forms of monitoring the process of parallel computing. Methods for solving partial differential equations. Organization of parallel computing for systems with shared memory. Computing system model formation. Statement of the computational problem and the choice of a parallel solution method. Determination of graphical forms of monitoring the process of parallel computing. Methods for solving partial differential equations. Organization of parallel computing for systems with shared memory. Computing system model formation. Statement of the computational problem and the choice of a parallel solution method. Determination of graphical forms of monitoring the process of parallel computing.
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Unstructured grids
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The goal of the discipline is to teach the student to write and use computational grids without a specific structure for use in control volume and finite element methods. In the course of studying the discipline, students will learn various algorithms for constructing unstructured meshes based on Delaunay triangulation and Voronoi diagrams. Methods for implementing mesh refinement adaptation in unstructured meshes will also be discussed. Cases of constructing and using hybrid mesh structures will be studied together with structured hybrid meshes.
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Computability theory
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The objectives of mastering the discipline are: formation of knowledge about the main results of classical mathematical logic and the theory of algorithms; development of logical and algorithmic intuition both in mathematics and in computer science; formation and development of understanding of the level of rigor of the computational algorithm. As a result of mastering the discipline, the student must: Know the concepts: computability, decidability, enumerability, logical calculus, truth and provability of first-order formulas; - important theorems of the theory of algorithms. Be able to: - apply the methods of mathematical logic and the theory of algorithms to solve practical problems - use the language of mathematical logic to represent knowledge about subject areas; - explore Boolean functions, get their representation in the form of formulas; - to construct minimal forms of Boolean functions; - to determine the completeness and basis of the system of Boolean functions; - to solve problems of synthesis of finite automata; - to determine the temporal and capacitive complexity of algorithms. Own: - basic methods of converting logical expressions and bringing them to normal forms; - methods of proof in propositional calculus and predicate calculus
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Big Data & High Performance Statistical Computing
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose: teaching doctoral students methods and technologies for processing, analyzing and interpreting large amounts of data using high-performance computing and statistical methods. They will be able to use various technologies and programming languages to work with big data and methods that require significant computing resources.
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Intelligent systems for monitoring and forecasting processes
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose: to acquaint with the principles, methods and applications of intelligent systems for monitoring and forecasting various processes. The course is aimed at developing students' understanding of the theoretical foundations and practical methodologies used in the development, implementation and use of intelligent systems in monitoring and forecasting tasks.
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Quantum Computing
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of studying the course "Quantum Computing" is to expand the knowledge of doctoral students in the field of quantum computing and quantum technologies, as well as to develop skills in designing and programming complex quantum algorithms to solve more complex problems.
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Finite element methods
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose: to form advanced knowledge in the field of the finite element method for research work. As a result, doctoral students should: be able to develop algorithms, conduct research and analyze the results of scientific experiments, master the skills of research work in the field of the finite element method.
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Quantum Computing
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The goal of the discipline is to study the basics of quantum computing, quantum computational models and efficient quantum algorithms. The course is aimed at expanding and deepening the education of students in the field of computer science, the formation of their systems thinking by studying approaches to the problems of building quantum computing. In the course of studying the discipline, the necessary definitions and concepts are introduced, based on the postulates of quantum mechanics, quantum computational algorithms are studied, well-known quantum algorithms are considered in detail, demonstrating the power of quantum computing in comparison with classical ones. At the end of the course, the student must master the basic concepts of quantum informatics, such as the concept of a qubit, transformations and measurements of a quantum system, know the basic laws of quantum computing,
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Curvilinear adaptive meshes
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The discipline is devoted to methods of constructing curvilinear structured computational grids adapted to the values of a certain function, the gradient of a function or to the direction of a vector field. Including cases of adaptation to the solution of the problem considered and solved in parallel with the construction are considered. During the study of the discipline, students will become familiar with the methods of equidistribution, Godunov-Thompson, and the inverse Beltrami equation. They will also learn how to independently construct curvilinear structured adaptive computational grids based on solving differential equations using finite difference methods.
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Pedagogical
- Type of control: Защита практики
- Description: Aim оf discipline: formation of the ability to carry out educational activities in universities, to design the educational process and conduct certain types of training sessions using innovative educational technologies.
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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.