Master degree program
Applied and Computational Mathematics

Applied and Computational Mathematics

QUALIFICATION

  • Scientific and pedagogical direction - Master of Natural Sciences

MODEL OF GRADUATING STUDENT

Program passport

Speciality Name
Applied and Computational Mathematics
Speciality Code
7M05409
Faculty
Mechanics and Mathematics

disciplines

Conjugate equation methods for geophysics problems
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to form undergraduates’ knowledge of the basics of applying the theory of conjugate equations to solve problems in geochemistry and geophysics; understanding of issues of stability, convergence of discrete analogues of geophysical problems; ability to solve numerically integral Fredholm equations of the first kind by projection methods with bases in the form of wavelets. Coupled equation methods for the magnetotelluric sensing problem will be studied. The issues of creating a module for a geographic information system for geochemical and geophysical problems will be resolved.

Foreign language (professional)
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to form practical skills in various types of speech activity in a foreign language. The training course builds the ability to perceive, understand and translate information in the modern global space, participate in scientific events to test their own research. The discipline is aimed at improving competencies in accordance with international standards of foreign language education.

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 be considered on the basis of historical dynamics and in a historically changing socio - cultural context. Introduces the problems of the phenomenon of Science, which is a subject of special philosophical analysis, forms knowledge about the history and theory of Science, the laws of the development of Science and the structure of scientific knowledge, the features of science as a specialty and social institution, the role of Science in the development of society.

Mathematical foundations of computer graphics
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: to form the ability to develop and apply the basic mathematical and graphical tools of computer graphics for their successful application in graphic programming; determine the criteria for the classification and organization of graphic systems and models; combine and effectively use various computer graphics tools to create graphics programs and program modules; synthesize, interpret and critically evaluate various types of graphic information.

Modern computational methods for applied problems
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Thepurpose of the discipline: to form students' ability to apply modern methods of numerical solution of hydrodynamic equations, practical application of the main stages of mathematical modeling of hydrodynamic processes, including the physical formulation of the problem, the choice of a mathematical model and the formulation of the initial-boundary-value problem, the construction of a network model, the choice and development of grid approximations, teach the construction of various algorithms for constructing finite difference and finite element meshes..

Modern methods of applied mathematics
  • 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.

Modern technologies of parallel programming
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: to form knowledge on the technology of parallel programming in the environments OpenMP, MPI; have skills in setting up a computing cluster in Linux, Windows operating systems. Graduates will have in-depth knowledge of parallel computing, - to understand systems with massive parallelism; - work on computing clusters; - apply OpenMP, MPI technologies in Fortran, C++ programming languages.

Organization and Planning of Scientific Research (in English)
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline to form the ability to apply practical skills in the organization and planning of scientific research. The discipline studies: forms and methods of planning, organization and design of scientific articles and dissertations; forms of summarizing the results of scientific research in presentations, speeches, projects, articles.

Pedagogy of Higher education
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose is the formation of the ability of pedagogical activity through the knowledge of higher education didactics, theories of upbringing and education management, analysis, and self-assessment of teaching activities. The course covers the educational activity design of specialists, Bologna process implementation, acquiring a lecturer, and curatorial skills by TLA-strategies.

Psychology of Management
  • Number of credits - 3
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The course reveals the subject, the basic principles of management psychology, personality in managerial interactions, personal behavior management, psychology of managing group phenomena and processes, psychological characteristics of the leader's personality, individual management style, psychology of influence in management activities, conflict management.

Data for 2021-2024 years

disciplines

Application of graphics packages in solution applied problems
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: to form knowledge about various graphic packages for modeling and visualization; practical drawing techniques and types of drawings (construction, engineering, etc.). During the study, knowledge will be given on: tools and innovations of three-dimensional modeling in 3ds max; inverse kinematics and the Character Studio module; work with atmospheric effects; visualization in Mental Ray; work with global illumination; scripting language MAXScript

Computational methods for solution of continuum dynamics problems
  • 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

Finite element method in applied problems
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to form the abilities of undergraduates: -describe the finite element method (FEM); -determine the order of approximation of the FEM, ways to improve it; build finite element schemes of higher approximation order; - solve 2D-3D boundary value problems using FEM; -know the algorithms for constructing finite element meshes; -use modern finite element software packages; - apply the basic methods for describing the calculation areas; -develop programs for the implementation of the FEM.

Fundamentals of modeling gas dynamics problems
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: the formation of students' knowledge in the areas of theoretical and applied gas dynamics. The course examines the elements of thermodynamics, the equations of state of perfect and real gases, the laws of conservation and the ratio on strong discontinuities, the ratio of parameters on an oblique jump, the change in entropy. The method of characteristics for the equations of gas dynamics, one-dimensional unsteady gas flow.

Main problems of modeling turbulent flows
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: to form students' basic knowledge of the theory of turbulence and its principles. The concepts of turbulence are given, methods for describing the structures of turbulent flows are described. The basic principles of the Kolmogorov theory of developed homogeneous isotropic turbulence are given, in particular, concepts of the scale of turbulence, the spectrum of turbulent pulsations are given, the essence of the energy-containing and dissipative region of wave numbers.

Mathematical methods for modeling dynamic nonlinear physical problems
  • 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 methods for modeling environmental problems
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The goal is to develop skills in solving problems of atmospheric processes based on the integration of a system of hydrothermodynamic equations for the purpose of short-term and medium-term weather prediction, developing the ability to independently solve theoretical and applied problems in the field of hydrodynamic modeling of natural processes using modern computational methods and devices.

Mathematical methods for modeling natural sciences problems
  • 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, in the field of the theory of dynamical systems and nonlinear dynamics in application to the problems of physics of living systems.

Mathematical methods for solution of turbulent flows problems
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: the formation of undergraduates' knowledge about the methods of modeling turbulent flows. Problems of closure of the Reynolds-averaged Navier–Stokes equations. Concepts of Reynolds stresses and turbulent viscosity. The main turbulence models will be shown, in particular, models with one turbulence energy balance equation, two-parameter models, models with equations for the transfer of the Reynolds stress tensor components.

Methods for solving inverse and ill-posed problems of mathematical physics
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of discipline: formation of undergraduates core competencies based on in-depth study of research methods and inverse ill-posed problems. During the study of the discipline, master students will learn following aspects: familiarity with the concept of students and research methods of inverse and ill-posed problems, the development of complex mathematical apparatus of ownership and the formation of skills and abilities to self-intensive research and scientific and exploration activities.

Modeling of processes in multiphase environments
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: to form knowledge with the current state of the theory of single-phase and multi-phase flows. The basics of classification of two-phase flows are presented. The strategy of building a generalized mathematical model of multiphase flows using the Eulerian and Lagrangian approaches is described. Models of specific problems of the dynamics of multiphase media with phase transitions are shown. Derivation of the equations of motion and energy of a heterogeneous medium with phase transitions.

Solution methods of deformable systems stability problems
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: to form the ability of undergraduates: - demonstrate a systematic understanding of the process of modeling the stability of deformable systems; - critically evaluate the choice of criteria for static and dynamic stability of systems in relation to deformable media; - choose the methodology for analyzing the stability of deformable systems and methods for solving; - correct the process of solving and visualizing the stability of the systems under study using modern application packages

Data for 2021-2024 years

INTERNSHIPS

Pedagogical
  • Type of control - Защита практики
  • Description - Formation of practical, educational-methodical skills of conducting lectures, seminars, creatively apply scientific, theoretical knowledge, practical skills in teaching activities, conduct training sessions in the disciplines of the specialty; own modern professional techniques, methods of training, use in practice the latest theoretical, methodological advances, make educational, methodological documentation.

Research
  • Type of control - Защита практики
  • Description - The purpose of the practice: gaining experience in the study of an actual scientific problem, expand the professional knowledge gained in the learning process, and developing practical skills for conducting independent scientific work. The practice is aimed at developing the skills of research, analysis and application of economic knowledge.

Data for 2021-2024 years