Magistracy
Speciality Code:
7M06105
Speciality Name:
Mathematical and Computer Modelling (PFUR)
Faculty:
Mechanics and Mathematics
Qualification:
- Scientific and pedagogical direction - Master of Engineering Sciences
- Model of graduating student
- Mandatory disciplines
- Elective disciplines
- Professional
ON1 To make reviews, substantiated conclusions and recommendations on the basis of systematization and analysis of scientific and technical information on the topic of scientific research in the chosen field;
ON2 to develop curricula for mathematical disciplines for inclusion in the educational process, to present the material orally and in writing;
ON3 to teach mathematics and special subjects in educational institutions, professional educational organizations and educational institutions of higher education;
ON4 Integrate knowledge gained in various disciplines to solve research problems of natural science;
ON5 to critically evaluate modern scientific concepts and theories in the field of applied mathematics to determine the object and subject of independent research;
ON6 to conduct research in the field of modeling natural and technological processes based on classical and modern modeling methods and to obtain new scientific and applied results independently and as part of a research team;
ON7 to make mathematical models to describe the processes under study, to assess the accuracy and reliability of the results of mathematical modeling;
ON8 to develop software packages for solving problems in the field of modeling natural science processes on the basis of modern programming languages, high-performance technologies;
ON9 to develop and apply mathematical methods, system and application software for solving problems of scientific and design and technological activities;
ON10 to plan and carry out numerical experiments, analyze and interpret the results obtained, make reasonable conclusions and predictions of the behavior of the objects under study;
ON11 to build research activities on the basis of ethical and legal norms in relations between people, to bear personal responsibility for the quality of work and scientific accuracy of the results;
ON12 to objectively assess the level of their own educational background and realize the need to form new competencies, build a personal trajectory of further professional training and growth.
ON2 to develop curricula for mathematical disciplines for inclusion in the educational process, to present the material orally and in writing;
ON3 to teach mathematics and special subjects in educational institutions, professional educational organizations and educational institutions of higher education;
ON4 Integrate knowledge gained in various disciplines to solve research problems of natural science;
ON5 to critically evaluate modern scientific concepts and theories in the field of applied mathematics to determine the object and subject of independent research;
ON6 to conduct research in the field of modeling natural and technological processes based on classical and modern modeling methods and to obtain new scientific and applied results independently and as part of a research team;
ON7 to make mathematical models to describe the processes under study, to assess the accuracy and reliability of the results of mathematical modeling;
ON8 to develop software packages for solving problems in the field of modeling natural science processes on the basis of modern programming languages, high-performance technologies;
ON9 to develop and apply mathematical methods, system and application software for solving problems of scientific and design and technological activities;
ON10 to plan and carry out numerical experiments, analyze and interpret the results obtained, make reasonable conclusions and predictions of the behavior of the objects under study;
ON11 to build research activities on the basis of ethical and legal norms in relations between people, to bear personal responsibility for the quality of work and scientific accuracy of the results;
ON12 to objectively assess the level of their own educational background and realize the need to form new competencies, build a personal trajectory of further professional training and growth.
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Psychology of management
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Formation of knowledge about the fundamental concepts of management psychology for the practical application of the most critical aspects of management in professional interaction. Basic principles of management psychology, personality in management interactions, management of personality behavior, modern ideas, psychology of managing group phenomena, motivation, and practical reflection.
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High-performance computational processes in problems of mathematical physics
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The goal is to develop skills in applying methods for solving problems of mathematical physics on high-performance systems. During the study of course, students should be competent in: - Analyze the complexity of the calculations and evaluate the possibility of parallelization - apply the principles of development of parallel methods; - know the architecture of parallel computing systems; - apply graph models of programs. Dependency graphs and minimal graphs; - develop parallel algorithms using MPI, OpenMP, CUDA technologies; - develop parallel algorithms using POSIX Threads; - develop parallel algorithms using PVM (Parallel Virtual Machine).
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Discrete Mathematical Models
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose - the formation of skills to conduct studies of smooth curves on the plane and in space, regular surfaces, calculate polynomial invariants and invariants with values on graphs for classical and virtual knots and links. During the study of course, students should be competent in: - Know the basic concepts and methods of differential geometry and topology; - to conduct studies of smooth curves in the plane and in space, as well as regular surfaces; - calculate the main polynomial invariants and invariants with values on graphs for classical and virtual knots and links; - to find polynomials of volume for the simplest polyhedron; - apply the methods of knot theory and convex polyhedrons.
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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.
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Foreign Language (professional)
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose is to acquire and improve competencies by international standards of foreign language education and to communicate in an intercultural, professional, and scientific environment. A master's student must integrate new information, understand the organization of languages, interact in society, and defend his point of view.
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History and Philosophy of Science
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose: Understanding of modern philosophy as a system of scientific knowledge, including worldview in rational-theoretical comprehension. The discipline includes aspects of the evolution and development of scientific thinking, historical moments, the contribution of scientists and scientific schools to the formation of science, and ethical and social aspects of scientific activity.
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Mathematical Control Theory
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The goal is to develop skills for constructing a mathematical model of the problem under consideration, formalizing and choosing the method of its research, the development of the student’s mathematical culture and its preparation for the independent use of the knowledge gained. During the study of course, students should be competent in: - know the basic concepts of the theory of mathematical control; - apply research methods and properties of controlled systems; - apply the principles of program management; - apply the criteria for the quality of controlled systems; - apply frequency sustainability criteria.
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Mathematical models in economics and ecology
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The goal is to develop the skills of applying the methods of mathematical modeling in the problems of economics and ecology, to build and explore the simplest mathematical models for economic problems and environmental problems. The evolution and disasters of ecosystems, economic models and their dynamics will be studied. During the study of course, students should be competent in: - Build models of economical processes; - apply methods for studying the stability of dynamic systems; - apply the Holling – Tanner model; - know limit cycles for equations of economic models of the Rayleigh type.
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Nonlinear problems of mathematical physics
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline: The objectives of the development of the discipline "Nonlinear problems of mathematical physics" - acquaintance with the methods of mathematical modeling of physical processes; - acquaintance with modern analytical methods for studying nonlinear problems of mathematical physics; -acquisition of skills to use the modern mathematical apparatus in research and applied activities. In the course of studying the course to form undergraduates' abilities: - Explain the key concepts of generalized functions in the context of the relevant theory; - Calculate problems (generalized solutions, ordinary differential operators, inverse scattering problems, soliton solutions) using modern methods of the theory of generalized functions; - To prove the solvability of applied problems using the theory of generalized functions; - Solve theoretical and applied problems of physics, mechanics, etc .; - Describe the solution of the problems of nonlinear equations of mathematical physics by the methods of the theory of generalized functions and the theory of functional spaces. - Design the process of studying an applied problem using the methods of the theory of generalized functions; - To work in a team, reasonably defend the correctness of the choice of a solution to a problem. As a result of training, undergraduates should know: the physical meaning of the classical nonlinear equations of mathematical physics; Basic ideas and methods of the spectral theory of ordinary differential operators; The main ideas of the inverse scattering method. To be able to: Build mathematical models of physical and other phenomena; Use the ideas of the inverse problem method to study solutions of nonlinear equations of mathematical physics. Possess: Skills of joint application of various mathematical methods; The skills of combining analytical and approximate methods in the study of complex mathematical and applied problems.
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Pedagogy of Higher Education
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose: To provide pedagogical theories and practical strategies for effective teaching in higher education, fostering critical thinking, and academic success. The course explores instructional methods, curriculum design, assessment techniques, and classroom management strategies preparing educators to create inclusive and stimulating learning environments.
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Appliеd problems in mathematical modeling
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the course is to form the skills of constructing mathematical models describing natural science and humanitarian processes. Basic information will be presented on models of mathematical physics, on methods for solving problems that reduce to dynamic systems, differential equations, and systems of partial differential equations. Particular attention is paid to the study of the concept of constructing mathematical models, which are analytical, numerical algorithms, as well as their compositions. During the study of course, students should be competent in: - build mathematical models describing physical, chemical, biological, social, economic processes and phenomena, and leading to differential integral equations; - apply methods of analytical problem solving, methods of numerical solution of problems resulting from the simulation of these processes; - know the properties of the processes being modeled for different types of problems of partial differential equations; - choose the right mathematical model for the studied process; - correctly set the corresponding models of mathematical tasks; - find solutions to the main types of tasks; - analyze the solutions and give a competent interpretation of their decisions.
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Nonlocal boundary problems
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The goal is to form the ability to apply basic qualitative research methods, to study non-classical problems for partial differential equations, including elliptic equations with nonlocal boundary conditions and boundary problems for functional differential equations. During the study of course, students should be competent in: - To know the basic types of non-local boundary value problems for elliptic equations, the formulation of boundary value problems for functional differential equations, the concept and basic properties of Sobolev spaces and weighted spaces, the Fredholm solvability property, the effect of breaking smoothness of solutions. - to investigate the solvability and regularity of solutions of non-local boundary value problems for elliptic equations, as well as boundary value problems for some classes of functional differential equations in various functional spaces; - apply basic qualitative research methods as a theory of Banach algebras, a localization technique, a method of cutting functions, a method of a priori estimates, the construction of regularizators, a method of continuation with respect to a parameter.
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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.
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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.
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Mathematical models of the theory of elasticity
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline: formation the ability to correctly build mathematical models and algorithms for the study of dynamic processes in deformable solids and media. Acquaintance with physico-mathematical models of deformable solids, methods for solving model boundary-value problems, with the basics of conducting various numerical experiments to study the dynamics of mechanical properties, and features of computer technology. During the study of course, master students should be competent in: - studying the concepts of deformations of the continuum, measures and stress tensors, their properties, concepts of geometrically linear and non-linear approaches; - deriving stress tensors, moment voltages, - knowing the basics of nonequilibrium thermodynamics of the continuum, the concepts of material stability and design; - applying the basic concepts of nonlinear mechanics of continuous media for the formulation of mathematical formulation of problems in research and development activities. - analyzing the mathematical statement made, to linearize the task, to record the initial and boundary conditions; During the study of the discipline, master students will learn following aspects: Models for the study of dynamic processes in deformable solids and media. Physical and mathematical models of deformable solids, methods for solving model boundary value problems. The concepts of deformations of the continuum, measures and strain tensors, their properties, the basics of the thermodynamics of the continuum, the concepts of material stability and design.
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Continuous Mathematical Models
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of teaching a discipline is to develop skills for constructing a mathematical model of the problem under consideration, formalizing and choosing the method of its research for describing and solving applied problems, developing a student’s mathematical culture for mastering other basic mathematical courses. The basic concepts of mathematical models of physical, engineering and other systems, approaches to obtaining models, methods of their research will be presented. During the study of course, students should be competent in: - to know the basic concepts of mathematical models of physical, engineering, etc. systems, - apply the principles of constructing mathematical models; - to apply numerical and analytical methods for the study of continuous mathematical models; - possess the skills of formalization and choice of the method of studying mathematical models.
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Control systems with consequences
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The goal is to develop skills for solving linear and nonlinear differential equations with delay, optimal control problems in systems with aftereffect, application of dynamic models with delay by the method of steps and the operational method; method of reducing to a non-local boundary value problem. During the study of course, students should be competent in: – solve linear and nonlinear differential equations with aftereffect; – solve optimal control problems in systems with aftereffect; – build dynamic models with aftereffect; – apply methods of reducing initial equations to a non-local boundary value problem.
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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.