Applied Mathematics

Applied Mathematics

QUALIFICATION

  • First Stage of Higher Education - Bachelor of Natural Science

MODEL OF GRADUATING STUDENT

Program passport

Speciality Name
Applied Mathematics
Speciality Code
6B05405
Faculty
Mechanics and Mathematics

disciplines

Algorithms and Data Structures
  • Number of credits - 6
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose is formation of the ability to apply algorithms, data structures for solving various programming problems. As a result of studying, the following abilities of students will be formed: - create various programs using fundamental computational; - practically use the data structures; - analyze the effectiveness of algorithms.

Applied problems of continuum mechanics
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is forming students’ fundamental knowledge in continuum mechanics by describing the macroscopic motion of liquid, gaseous and solid deformable bodies for their further use when solving applied problems. As part of the study of the discipline, students will learn to formulate the basic laws and equations of continuum mechanics, and also acquire skills in constructing and solving mathematical models of deformable media using modern methods of mechanics.

Bases of Mathematical Modelling
  • Number of credits - 6
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: isto form students' basic knowledge of the basics of mathematical modeling, the ability to apply them to develop and analyze mathematical models of objects of various nature using mathematical tools and computer technologies. During the study of course, master students should be competent in: – correctly explain and formulate the meaning of the domain problem; – create mathematical models of the phenomena and processes under study in their professional activities; - draw an analogy between the processes from different areas of natural science; use the versatility and analogy of models to apply the results of the study of some models to others (economic, biological, physical, and other processes); - to classify mathematical models, choose methods for solving them, use the capabilities of computing equipment, applied and specialized programs to solve domain problems. - highlight the applied aspect in solving a scientific problem; visualize, correctly present and interpret the result; transfer the result of the research in the form of specific recommendations expressed in terms of the subject area of the phenomenon under study.

Computational methods of partial differential equations
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is for students to master the methods of numerical analysis necessary for effective and accurate solution of practical problems in various fields of science and technology. The computational methods of the PDEs are aimed at teaching students the use of numerical methods to solve mathematical modeling problems.

Computer technologies in mathematical modeling
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the subject is to form competencies that allow graduates to effectively apply computational tools in many different areas of science and production. The main competencies that students acquire after studying the subject (Wolfram Mathematica, COMSOL Multiphysics) are: Knowledge and understanding of the basics of programming languages and libraries; Ability to apply these languages and tools to develop and implement complex mathematical models and algorithms in selected areas. The ability to analyze and interpret the results obtained, to present these results in an accessible form.

Continuum Mechanics
  • Number of credits - 3
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: is the formation of students' fundamental knowledge of the mechanics of the material continuum, the presentation of which is carried out from a unified position of the scientific foundations of the theoretical description of the macroscopic motion of liquid, gaseous and solid deformable bodies. During the study of course, students should be competent in: - demonstrate fundamental knowledge of the main sections of the mechanics of the material continuum (continuity hypothesis, continuum kinematics, medium deformation theory, dynamics, thermodynamics and continuum electrodynamics, and applied aspects of continuum mechanics); - to formulate the basic laws, basic equations and theorems of continuum mechanics; - build mathematical models of classical liquid, gaseous and solid wrought media; - solve problems and exercises on the kinematics of a continuous medium and on the theory of deformations (the law of motion of a continuous medium, the equations of the trajectory, current lines and vortex line, components of the strain tensors, strain rates and internal stresses) - analyze the results and draw reasonable conclusions.

Database Design Techniques
  • Number of credits - 6
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is forming students’ ability to work with basic database design methods and their components. The discipline focuses at acquiring skills in working with basic methods of database design through the use of the SQL language, understanding the principles of their creation, operation and administration.

Differential Equations
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The aim of the discipline is to acquaint students with basic concepts and methods for solving ordinary differential equations. In the course of studying the course to form students' abilities: - Explain the basic concepts of ordinary differential equations (partial solution, general solution, common integral, special solution), understand the assertions and proofs of the main theorems; - Classify the types of differential equations of the first order, resolved with respect to the derivative; - Solve the main types of ordinary differential equations of the first order (equations with separable derivatives, homogeneous equations, linear equations, equations in full differentials) and linear equations and systems with constant coefficients

Discrete Mathematics
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The goal is the formation of knowledge and skills of future specialists in the use of apparatus and methods of discrete mathematics in the analysis, management and programming of modern processes and systems. As a result of studying the course, students should form the following abilities: - to formulate and prove the fundamentals of the statements of discrete mathematics; - solve problems in binary relations; - to solve the basic problems of the theory of numbers and graph’s theory; - to solve the main problems of Boolean algebra.

Foreign Language
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Purpose: to form the improvement of knowledge of foreign language communicative competence. The main methods of speech skills and foreign language communication skills are considered as a basis for the development of communicative competence; implementation of acquired speech skills in the process of searching, selecting and using material in English.

Functional Analysis
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: To form the ability to use the basic concepts and methods of functional analysis to solve the problems of modeling real processes in various fields of natural science and economics, and to form students' abilities: - Explain the key concepts of functional analysis (normed spaces; metric spaces; Banach spaces, Hilbert spaces, linear continuous operators and linear continuous functionals defined on these spaces, conjugate(dual) spaces, reflexive spaces, compact operators, closed operators, adjoint and self-adjoint operators, the spectrum of the operator and the resolvent set) in the context of the corresponding theory.

Fundamentals and Methodology of Programming
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to teach students algorithmization methods and the basics of programming in a high-level language; development of logical thinking among students; preparation for the perception of general professional disciplines. As part of the discipline, students will learn programming methodology, namely set of ideas, concepts, principles, methods and tools that determine the style of writing, debugging and maintaining programs.

Fundamentals of Relational Database Design
  • Number of credits - 6
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is forming students' abilities for designing relational databases and working with their main components. During the study of course, master students should be competent in: - analyze data and use normalization to create a relational database schema; - classify various databases and work successfully with them; - set and refine the data storage and indexing parameters and perform query optimization; - use the SQL language to create, manipulate and manage databases; - synthesize the knowledge to perform basic tasks of database administration.

General Physics
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Physics is a science that studies the laws of nature, the subject of its study is matter (in the form of matter and fields) and the most general forms of its movement, as well as the fundamental interactions of nature that control the movement of matter. Formation of students' knowledge and skills of using fundamental laws, theories of classical and modern physics, methods of physical research as the basis of a system of professional activity.

Information-Communication Technologies
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Рurpose: it consists in the formation of a new "digital" thinking, a critical understanding of the role and importance of modern information and communication technologies, the ability to apply information and communication technologies in various professional activities. They are being studied: the role of ICT in key sectors of society development is being studied. Architecture of computer systems. Software. Microsoft Office Internet technologies. Cloud and mobile technologies. Multimedia technologies. E-learning. Information technology in the professional field.

Kazakh (Russian) Language
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Рurpose: ensuring the qualitative assimilation of the Kazakh (Russian) language as a means of social, intercultural, professional communication through the formation of communicative competencies. The following are studied: the system of phonetic, lexical, grammatical means of language, ideas about language as a cultural phenomenon and about the specifics of speech culture; language as an element of the national linguistic picture of the world; the status of the Kazakh (Russian) language in the world space.

Linear algebra and analytical geometry
  • Number of credits - 6
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: to form the ability to use linear algebra to study mathematical objects. To form the ability to use the methods of vector algebra and the coordinate method to study objects of analytic geometry, to formulate and prove the key statements of linear algebra and analytic geometry.

Machine learning
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is forming students’ abilities and skills to develop, select and implement machine learning algorithms and methods for their further application when solving applied optimization problems. As part of the discipline, students will learn to select effective machine learning models, recognize and select optimal model parameters, evaluate their performance and applicability for various optimization problems.

Mathematical Analysis I
  • Number of credits - 6
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to study the basic fundamental concepts of mathematical analysis and the methods of differential calculus of a function of one real variable. During the study of course, students should be competent in: - Explain the concepts of mathematical analysis (sequence, limit, continuity, derivative) in the context of the relevant theory; - Calculate typical tasks using mathematical analysis methods - finding the supremum of numerical sets, examining the convergence of the sequence, finding the limit of function at a point, continuity of function at a point and on a set, the derivative of a function.

Mathematical analysis II
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Mathematical Analysis-II is a continuation of the acquaintance with the fundamental concepts of mathematics and prepares students for mathematical research methods. This discipline studies the theory of integrals, their applications - calculating the area of a flat figure, calculating the volume of a body, the arclength and the area of a body of rotation. The course also contains the study of the theory of series, sufficient signs of convergence of series with non-negative terms, uniform convergence of functional series and the expansion of functions in the power series.

Mathematical and computer modelling of Physical processes
  • Number of credits - 6
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: the acquisition of knowledge and skills for conducting scientific research in the field of modeling physical processes. In the course of studying the course, to form students' abilities: - knowledge of the basic physical laws, on the basis of which the compilation of mathematical models for physical processes is carried out; - drawing up mathematical models of physical processes; - to develop algorithms for solving the problem; - use of numerical methods for solving problems of modeling physical processes; - analyze the results.

Mathematical modeling in Biomedicine
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to study of development of mathematical models for the of biomedical processes on the basis of differential equations of differential equations, the differential equilibrium in the individual production, using modern methods of simplification. During the study of course, students should be competent in: - Understanding the basic principles of the numerical taxonomy, fundamental systems and properties of dynamical systems, basic types of dynamical systems; - Provide information on the stability of the non-stationary point in the equilibrium equilibrium; - To develop of mathematical models for biological systems; - demonstrate knowledge of the basic qualitative features of a biological system in a mathematical model; - to build a proactive mathematical model of infectious disease; - analyze the antiviral model of the immune response; - apply a nonlinear system of hydrodynamics for mathematical modeling of blood flow in the vessels.

Mathematical Modeling of Chemical Prosesses
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: the formation of skills for solving problems in the study of chemical processes by mathematical methods. In the course of studying the course, to form abilities: - demonstrate knowledge of the basic techniques for modeling chemical processes; - demonstrate knowledge in the field of optimization of chemical processes; - apply numerical methods to solve modeling problems in chemistry. - to create a mathematical model for a simple task of a chemical-technological process.

Mathematical models in natural science
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: to develop the ability to develop mathematical models of natural science based on systems of ordinary differential equations, differential equations in partial derivatives, using modern numerical methods. During the course, the students' abilities to be formed: - to know the main concepts and properties of dynamic systems, the main types of dynamic systems; - develop mathematical models for biological systems; - use mathematical methods to describe and predict phenomena in nature in various conditions

Military Training
  • Number of credits - 6
  • Type of control - MC
  • Description - Military Training

Modern Computational Methods in Problems of Natural Science
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The goal is to develop students' knowledge of modern numerical methods for solving systems of differential equations, the formation of practical skills in designing cost-effective methods for finding solutions for systems of differential equations with structural features. Based on the results of training, students acquire the following skills: • to professionally master modern methods of computing and information processing , methods of searching and structuring information, effectively apply them to solve scientific, technical and applied problems; • have the ability to use modern computer technology in practice.

Module of socio-political knowledge (Culture)
  • Number of credits - 2
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Aim оf discipline: to develop the ability to explain and interpret subject knowledge in all fields of science, shaping of the discipline. Sociology and sociological perspectives, social structure, form of policy, organizational structure, institutions, the legal and organizational rules, content, purpose, value, policy, concept and essence of culture, semiotics of culture, psychology of personality, psychology of interpersonal communication will be studied.

Module of socio-political knowledge (Culture)
  • Number of credits - 2
  • Type of control - RK1+RK2 (100)
  • Description - Aim оf discipline: to develop the ability to explain and interpret subject knowledge in all fields of science, shaping of the discipline. Sociology and sociological perspectives, social structure, form of policy, organizational structure, institutions, the legal and organizational rules, content, purpose, value, policy, concept and essence of culture, semiotics of culture, psychology of personality, psychology of interpersonal communication will be studied.

Module of socio-political knowledge (Political science)
  • Number of credits - 2
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Aim оf discipline: to develop the ability to explain and interpret subject knowledge in all fields of science, shaping of the discipline. Sociology and sociological perspectives, social structure, form of policy, organizational structure, institutions, the legal and organizational rules, content, purpose, value, policy, concept and essence of culture, semiotics of culture, psychology of personality, psychology of interpersonal communication will be studied.

Module of socio-political knowledge (Political science)
  • Number of credits - 2
  • Type of control - RK1+RK2 (100)
  • Description - Aim оf discipline: to develop the ability to explain and interpret subject knowledge in all fields of science, shaping of the discipline. Sociology and sociological perspectives, social structure, form of policy, organizational structure, institutions, the legal and organizational rules, content, purpose, value, policy, concept and essence of culture, semiotics of culture, psychology of personality, psychology of interpersonal communication will be studied.

Module of socio-political knowledge (Psychology)
  • Number of credits - 2
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Aim оf discipline: to develop the ability to explain and interpret subject knowledge in all fields of science, shaping of the discipline. Sociology and sociological perspectives, social structure, form of policy, organizational structure, institutions, the legal and organizational rules, content, purpose, value, policy, concept and essence of culture, semiotics of culture, psychology of personality, psychology of interpersonal communication will be studied.

Module of socio-political knowledge (Psychology)
  • Number of credits - 2
  • Type of control - RK1+RK2 (100)
  • Description - Aim оf discipline: to develop the ability to explain and interpret subject knowledge in all fields of science, shaping of the discipline. Sociology and sociological perspectives, social structure, form of policy, organizational structure, institutions, the legal and organizational rules, content, purpose, value, policy, concept and essence of culture, semiotics of culture, psychology of personality, psychology of interpersonal communication will be studied.

Module of socio-political knowledge (Sociology)
  • Number of credits - 2
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Aim оf discipline: to develop the ability to explain and interpret subject knowledge in all fields of science, shaping of the discipline. Sociology and sociological perspectives, social structure, form of policy, organizational structure, institutions, the legal and organizational rules, content, purpose, value, policy, concept and essence of culture, semiotics of culture, psychology of personality, psychology of interpersonal communication will be studied.

Module of socio-political knowledge (Sociology)
  • Number of credits - 2
  • Type of control - RK1+RK2 (100)
  • Description - Aim оf discipline: to develop the ability to explain and interpret subject knowledge in all fields of science, shaping of the discipline. Sociology and sociological perspectives, social structure, form of policy, organizational structure, institutions, the legal and organizational rules, content, purpose, value, policy, concept and essence of culture, semiotics of culture, psychology of personality, psychology of interpersonal communication will be studied.

Module of socio-political knowledge (Sociology/ Political science/ Culture/ Psychology)
  • Number of credits - 8
  • Type of control - RK + Exam (100)
  • Description - Aim оf discipline: to develop the ability to explain and interpret subject knowledge in all fields of science, shaping of the discipline. Sociology and sociological perspectives, social structure, form of policy, organizational structure, institutions, the legal and organizational rules, content, purpose, value, policy, concept and essence of culture, semiotics of culture, psychology of personality, psychology of interpersonal communication will be studied.

Numerical methods
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: to study the students with numerical methods for solving problems of analysis and algebra, with the principles of constructing algorithms; teaching students to skillfully apply methods of numerical solution of problems of analysis and algebra; to teach future specialists the basic theoretical knowledge and practical skills for comparing the numerical methods of algebra and analysis; to analyze of numerical results. In the course of studying the course, to form students' abilities: – solving the main problems of analysis and algebra; – know the basic principles of constructing algorithms; – application of methods of computational mathematics for the numerical solution of problems of analysis and algebra; – substantiation of the correctness of problems, comparative numerical analysis of the results of problems.

Object-Oriented C++ Programming
  • Number of credits - 6
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The aim of the discipline is forming the students' ability to develop programs in modern C++ programming language with its further use in various fields of professional activity. As a result of studying the discipline, the student will be able to: - demonstrate acquired knowledge in the field of object-oriented programming and their understanding; - explain the main principles underlying the creation of various applications in C++ programming language; - combine various tools of C++ programming language (classes, methods, packages, interfaces, etc.) to develop effective programs and software packages; - justify the purpose and use of the main components of C++ programming language; - synthesize, interpret and evaluate the learning outcomes of the discipline for their further application in professional activities.

Partial Differential Eguations
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - To form the ability to solve problems for partial differential equations and know the basic theory. The content of the discipline is aimed at studying the classification of partial differential equations and bringing them to canonical form, Fourier methods, thermal potentials, the continuation method and Green's functions, the maximum principle, the Cauchy problem, mixed problems, the Duhamel principle.

Philosophy
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Purpose: to form a systematic understanding of philosophy and its main problems and methods in the context of future professional activities. The main content of ontology and metaphysics is considered in the context of the historical development of philosophy; the importance of key worldview concepts in the modern world.

Physical Training
  • Number of credits - 2
  • Type of control - РК(с оценкой)
  • Description - The purpose of the discipline is the formation of social and personal competencies of students, ensuring the targeted use of the appropriate means of physical culture and sports for preservation, preparation for professional activities. As a result of studying the discipline, the graduate should know the role of physical culture in human development.

Probability Theory and Mathematical Statistics
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: is studying the discipline is to master the basic probabilistic and mathematical-statistical concepts; development of logical and algorithmic thinking; mastering the main methods for solving probabilistic and mathematical statistical problems. During the study of course, students should be competent in: - explain the key concepts of probability theory and mathematical statistics; - solve typical problems (calculating the probability of event; checking events for independence; investigating a random variable; estimating an unknown parameter of the general population; checking statistical hypotheses) by methods of probability theory and mathematical statistics; - streamline the solution of applied problems using the properties of probability, numerical characteristics of random variables and the statistical properties of estimators; - to classify the basic concepts of probability theory and mathematical statistics (events, random variables, estimators, hypotheses); - describe the study of events, random variables (general population) by methods of probability theory and mathematical statistics; - design the process of studying an applied problem using the methods of probability theory and mathematical statistics.

Theoretical mechanics
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Purpose: to acquire skills in building mathematical models of processes occurring in nature and technology, their analysis using mathematical methods; Will be studied: determination of the kinematic characteristics of a material point and a mechanical system motion; study of the balance of various systems of forces; solution of the problem of dynamics based on Newton's second law, etc.

Theory of Finite Difference Schemes
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to study the approximation and stability of difference schemes in the numerical solution of differential equations. Students are introduced to the basic concepts, algorithms, and theoretical aspects of constructing and analyzing difference schemes necessary for effective modeling of processes in science and technology.

Variation Calculus and Optimization Methods
  • Number of credits - 5
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is the study by students of the simplest variational problem; theories of the first and second variations; variational problem with higher derivatives; convex programming; the global minimum theorem; linear and non-linear programming. Know the necessary, as well as sufficient conditions of the first and second order of the local minimum points of differential functions; theory of simplest and isoperimetric variational problems; theory of mathematical programming; Pontryagin's principle for the optimal control problem.

Нistory of Kazakhstan
  • Number of credits - 5
  • Type of control - [РК1+MT+РК2+ ГЭК] (100)
  • Description - The purpose of the discipline is to give objective knowledge about the main stages in the development of the history of Kazakhstan from ancient times to the present. Expected learning outcomes: 1) demonstrate knowledge and understanding of the main stages in the development of the history of Kazakhstan; 2) to correlate the phenomena and events of the historical past with the general paradigm of the world-historical development of human society through critical analysis; 3) to possess the skills of analytical and axiological analysis in the study of historical processes and phenomena of modern Kazakhstan; 4) be able to objectively and comprehensively comprehend the immanent features of the modern Kazakh model of development; 5) Systematize and give a critical assessment of historical phenomena and processes in the history of Kazakhstan. During the study of the discipline students will learn following aspects: Ancient people and the formation of a nomadic civilization, Turkic civilization and the Great Steppe, Kazakhstan in modern times (XVIII - early XX centuries), Kazakhstan as part of the Soviet administrative-command system, Kazakhstan in the world community (1991-2022).

Data for 2021-2024 years

disciplines

Abais Teaching
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The goal of the discipline is to form in future specialists the ability to self-knowledge, the use of Abai's doctrine as the basis of spirituality and intellectuality of modern Kazakhstan, the application of their professional knowledge, understanding and abilities through the prism of humanism and education in order to strengthen the unity of the country and civil solidarity of society.The following will be studied: the concept of the teachings of Abai; sources of teaching; components of Abai's doctrine; categories of Abai's doctrine; assessment tools of the teachings of Abai; the essence and meaning of Abai’s doctrine.

Al-Farabi and Modernity
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Aim of the discipline is to form students' ideas about the scientific and philosophical heritage of the great Turkic thinker Abu Nasr al-Farabi in developing the world and national culture. Learning outcomes: explain the main philosophical contents al-Farabi's heritage and his influence on the formation of Turkic philosophy; influence European Renaissance.

Applications of Computational Fluid Dynamics
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The aim of the discipline is to generate knowledge in a number of applications of hydrodynamics, such as convective heat and mass transfer, wind energy, biofluid mechanics and aerodynamics of road vehicles. At the same time, the course is aimed at deepening the understanding of physics and the basic equations of hydrodynamics. In the course of studying the course, to form students' abilities: - demonstrate knowledge about the features of the flow around road vehicles; - apply the concepts of fluid mechanics and thermodynamics to model the transfer of heat and mass.

Applied problems of control theory
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The main goal of the discipline "Applied Problems of Control Theory" is the formation of knowledge and skills in applying the basic concepts and methods of mathematical control theory among students, a detailed study features of the application of methods of control theory, depending on the considered applied task. The tasks of studying the discipline are:  study of the basic concepts of management theory;  development of the main and special sections of the management theory;  study of methods for solving problems of control and observation in linear systems;  study of methods for solving problems of stabilization and optimal stabilization program movements of linear and nonlinear systems;  development of skills for independent solution of practical problems;  study of the possibilities of application software packages in solving problems of theory management.

Applied problems of stability of elastic systems
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to study the fundamentals of systemic understanding and solution of problems of stability of deformable systems with the choice of criteria for their static and dynamic stability, analysis methodology and methods for solving them. Within this discipline, students will gain skills in solving, analyzing and interpreting the results obtained; adjustments and recommendations in terms of the subject area of the process being studied.

Applied stochastic models
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to develop knowledge about the use of stochastic methods for solving queuing models in economics and finance. When studying the discipline, students will study the following aspects: normal probability density, statistical inference, statistical research methods, testing statistical hypotheses, testing hypotheses about means, nonparametric tests, various types of regression, correlation, analysis of variance, analysis of covariance.

Basics of financial literacy
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to form rational financial behavior in students based on building a direct connection between understanding financial information and their practical application for making competent and informed decisions regarding personal finances and increasing their economic security, as well as the ability to critically evaluate and analyze processes related to protection their rights and interests as consumers of financial services through the use of financial instruments, including digital technologies.

Coding and pattern recognition theory
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The goal is to develop knowledge of the theoretical foundations of pattern recognition and the development of computer programs that implement various pattern recognition algorithms and study their effectiveness. During the training, knowledge will be given on the basic concepts of Bayesian theory, with an emphasis on nonparametric methods for constructing classifiers. Approaches to classifying a sample consisting of unlabeled vectors are discussed. Machine learning problems for image recognition and artificial neural networks (types and architectures) are considered.

Computational Fluid Dynamics
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to formulate the practical skills of the application of l steps of the mathematical modeling of hydrodynamic processes, including the physical position, the choice of mathematical model and the principal task of the formulation, the expansion of the nether model, the development of auxiliary approximations. During the study of course, students should be competent in: - apply methods of the formation of finite-dimensional, continental-dimensional and continental elementary sets; - construction of netting schemes with finite dimensional, finite dimensions of finite element and hydrodynamics for typical tasks of heat transfer; - demonstrate of the possibility of solubility of hydrodynamics and thermodynamics.

Computer Graphics in OpenGL
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: is to forming the ability of students to work with basic tools and methods of computer graphics for creation and visualization of graphic objects with the use of software and hardware tools. During the study of course, students should be competent in: - demonstrate the understanding and ability to apply the basic methodological principles of graphical programming for creatingand analyzingtwo- and three-dimensional objects; - determine the criteria for classification and organization of graphical systems and models; - effectively use various approaches of image visualization applyingmodern graphical tools; - apply methods of computer graphics in their professional activities; - synthesize, interpret and critically evaluate various types of graphic information.

Ecology and Human Life Safety
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The goal of the discipline is to form a number of key competencies based on modern concepts of environmental management, implementing the principles of harmonious optimization of human interaction with nature. The following will be studied: the principles of sustainable development, conservation and reproduction of natural resources to ensure the safety of human life, methods for assessing and minimizing risks, protecting against dangers, including during travel, measures to eliminate the consequences of accidents, anthropogenic disasters, natural disasters, environmental protection and rational environmental management.

Entrepreneurship
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Purpose: formation of practical skills for carrying out entrepreneurial activities. Student able to: use market opportunities that correspond to their interests and abilities; make an initial decision about business; work effectively within the framework of legal norms; evaluate the potential market opportunities of a startup.

Functional Analysis
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: To form the ability to use the basic concepts and methods of functional analysis to solve the problems of modeling real processes in various fields of natural science and economics, and to form students' abilities: - Explain the key concepts of functional analysis (normed spaces; metric spaces; Banach spaces, Hilbert spaces, linear continuous operators and linear continuous functionals defined on these spaces, conjugate(dual) spaces, reflexive spaces, compact operators, closed operators, adjoint and self-adjoint operators, the spectrum of the operator and the resolvent set) in the context of the corresponding theory.

Fundamentals of Atmospheric Modelling
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: is to formulate of the ability of developing of the mathematical modeling dynamics of atmospheric processes, to describe the space structure in the atmosphere, the task of self - determinate determination, with the help of quantitative equations in the analytic models, using the modern computational technique. During the study of course, students should be competent in: -to declare the fundamentality of the atmospheric phenomena originating from the law of hydrodynamics and thermodynamics; - to formulate and solve the problem, connected with diverse processes that are in the atmosphere; - to solve on the task that is related to the value of the analytic models, as it is used in the modern computing technique.

High Performance Computing
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: isto provide solid introduction to modern serial and parallel computer architectures, parallel programming technologies and efficient optimization strategies for scientific high performance computing. During the study of course, master students should be competent in: - demonstrate knowledge of computer architecture, parallel programming methods; - demonstrate optimization of data alignment; - knowledge of the effectiveness of parallel programming;

Intelligent data analysis
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: the formation of students' knowledge about the basic provisions, principles and methods of data mining for further application in practice in order to detect hidden information, dependencies and patterns in the databases under study. In the course of studying the course, to form students' abilities: - classify and generalize the characteristics and objects of the considered classes, data; - choose appropriate data analysis methods for solving a specific problem; - recognize emerging patterns and relationships in large datasets; - create models and apply them in practice.

Inverse Problems of Mathematical Physics
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Students will know how to solve inverse problems by restoring unknown coefficients or the right-hand side of the equation. Know: the characteristic features of inverse problems; basic statements of coefficient inverse problems; basic mathematical models of inverse problems for the equation of mathematical physics. To be able: to formulate typical inverse problems of interpretation of geophysical measurements data; to set tasks for the numerical realization of the basic types of inverse problems for the heat equation, the wave equation, and the Laplace equation.

Legal Bases of Corruption Control
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to form a responsible attitude and the ability to demonstrate in practice the application of the principles and norms of anti-corruption legislation in order to prevent corruption offenses, to form intolerance towards corruption, an anti-corruption culture in everyday life and at the workplace, civil liability. The following will be studied: anti-corruption legislation, the system and activities of anti-corruption subjects, causes and conditions conducive to corruption, anti-corruption policy, international experience in combating corruption.

Mathematical modeling of deformable media
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: is forming students' basic knowledge of the mechanics of solid deformable media, the ability to model the deformed state of the environment using mathematical tools and computer technologies. During the study of course, students should be competent in: - explain correctly and formulate the meaning of the subject area problem; - apply fundamental basic knowledge in the specialty for mathematical modeling of applied problems in the field of solid media deformation; - implement effective numerical methods and calculation algorithms for computer modeling of the deformed state of the environment.

Mathematical modeling of hydro-gas dynamics
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: is to form the ability of numerical modeling of the dynamics of incompressible, compressible fluid described by the Navier-Stokes equations. During the study of course, master students should be competent in: - to possess methods of analytical and numerical study of mathematical models of hydrodynamics; - describe the dimensional and dimensionless forms of writing equations, the conservative form of equations; - possess the main methods for solving the Navier-Stokes equation of compressible fluid, incompressible fluid.

Mathematical modeling of physical processes
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: the acquisition of knowledge and skills for conducting scientific research in the field of modeling physical processes. In the course of studying the course, to form students' abilities: - knowledge of the basic physical laws, on the basis of which the compilation of mathematical models for physical processes is carried out; - drawing up mathematical models of physical processes; - to develop algorithms for solving the problem; - use of numerical methods for solving problems of modeling physical processes; - analyze the results.

Mathematical models of deformable media
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to form in students basic knowledge of the basic laws and relationships of the deformed state of a continuous medium; the ability to model and solve it using mathematical tools and computer technologies. As a result of the training, students will gain skills in applying fundamental basic knowledge, effective methods and calculation algorithms when solving problems in the subject area; working in a team to develop self-development and improve your qualifications.

Mathematical models of nonlinear processes
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the subject to develop the ability to mathematically model the dynamics of non-linear processes; formation of the ability to independently solve problems related to quantitative assessment within the framework of constructed mathematical models using modern computer technology. In the course of studying the subject, students develop the following skills: - to explain the features of non-linear processes based on the general laws of fluid mechanics and thermodynamics; - to formulate and solve simple problems related to non-linear processes occurring in the atmosphere.

Methods of scientific research
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The goal of the discipline is to develop skills in cognitive activity in the field of science. To use methods of scientific research for understanding and assimilating information. To be able to describe the object of research. To master methods of search, processing of scientific information, systematization, analysis, synthesis to obtain an objective content of scientific knowledge. To apply analytical and practical research methods and argumentation systems for justification, assertion, evaluation.

Modern data visualization packages
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is forming students’ ability to successfully utilize modern graphics packages for data visualization with with their further application in various fields of professional activity. As part of the study of the discipline, students will learn the basic tools and techniques of data visualization, as well as learn to create and manipulate various types of graphs for clear and convenient presentation of the results of scientific computation.

Numerical methods in optimization
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to form a basis for students to develop professional competencies in the field of numerical optimization methods, namely, mastery of numerical methods for solving problems of optimization of objective functions without restrictions and with restrictions of various types, development of the ability to apply optimization methods to find extremum points of functions without restrictions and with their availability; – developing the ability to implement numerical methods for solving optimization problems in various integrated mathematical environments.

Numerical methods of inverse problems
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline is to introduce the theory of inverse and ill-posed problems, to teach how to perfectly apply widespread numerical methods used in many inverse problems. Students will get acquainted with the basic numerical algorithms for solving inverse and ill-posed problems and will master methods for solving inverse problems for equations of mathematical physics. They will also have the skills to optimally select methods for numerically solving inverse problems.

Operations Research
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the subject is to form the following competencies in the student: apply mathematical methods and tools for modeling complex systems and decision making; System analysis and optimization skills, including linear programming, dynamic programming, network analysis and other methods; To apply acquired knowledge and skills to solve complex problems in practice in various areas such as production, transport, logistics, economics, finance and others.

Parallel Computing Methods
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: isto provide solid introduction to modern serial and parallel computer architectures, parallel programming technologies and efficient optimization strategies for scientific high performance computing. During the study of course, master students should be competent in: - demonstrate knowledge of computer architecture, parallel programming methods; - demonstrate optimization of data alignment; - knowledge of the effectiveness of parallel programming;

Parallel programming with MPI and Open MP
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: is to create and develop the ability to program and apply the parallel programming technologies OpenMP and MPI. During the study of course, master students should be competent in: - demonstrate knowledge of Open MP and MPI technology; - demonstrate knowledge of MPI and OpenMP directives; - construct an optimal parallel algorithm; - choose the right MPI and OpenMP directives; - identify similarities and differences of OpenMP and MPI technologies.

Python Programming
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: isacquisition of programming skills and creating applications in the Python scripting language, useful for developers, data analysts, web programmers, etc. During the study of course, students should be competent in: - demonstrate acquired knowledge in the field of scenario programming and their understanding; - Explain the principles underlying the writing of various applications in the Python programming language; - to classify the approaches used for developing applications, web interfaces, data analysis scenarios, and successfully apply them in practice; - justify the purpose and use of the main components of the Python programming language. - to synthesize, interpret and evaluate the results of studying the discipline with a view to their further application in professional activities.

Scientific Research Methods
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Рurpose: to form a methodological and scientific culture, a system of knowledge, skills and abilities in the organization and conduct of scientific research. General scientific research methods are studied, including methods of searching, processing, systematization, analysis, synthesis, generalization and argumentation of scientific information to obtain the objective content of scientific knowledge.

Signal processing and spectral analysis
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: the formation of knowledge and practical skills on the methods of analysis and processing of signals of various origins; study of the main spectral methods, methods of analysis of numerical sequences; study of definitions and applications of various types of wavelet analysis. In the course of studying the course, to form students' abilities: – demonstrate knowledge of the fundamentals of spectral methods and wavelet analysis. - demonstrate knowledge of the typical properties of signals, the theoretical foundations of time series analysis, the limits of applicability of methods, their advantages and disadvantages; - master the techniques of working in one of the mathematical packages (Mathcad, Mathlab).

Software Development
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: is forming students' ability to design, develop and test new software for its further use in various fields of professional activity. During the study of course, master students should be competent in: – demonstrate the acquired knowledge in the field of software development (methods, stages, elements and tools of software development, life cycle models, software requirements, etc.) and their understanding; - understand and explain the principles underlying software development; - classify the approaches used for developing software, and successfully apply them in practice; - justify the purpose and use of various programming languages to create specific applications; - create software with the requirements of the modern market; - synthesize, interpret and evaluate the learning outcomesof the discipline with a view to their further application in professional activities for software development.

Software packages for solving applied problems
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the subject is to develop students' practical skills in using software tools such as MATLAB, R, Python (with libraries NumPy, SciPy, Pandas), SAS, SPSS, designed to solve specific applied problems in various fields. Students will study their capabilities, features and use them for process modeling, data analysis and decision-making in various fields of activity.

Statistical analysis in applications
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the subject "Statistical Analysis in Applications" is to form the following skills and competencies: apply statistical methods and analyze data in scientific and applied fields; Skills in the analysis and interpretation of statistical data, including sample characteristics, distributions, correlations and regression analysis; apply statistical analysis in various fields, such as business, economics, medicine, sociology and others.

System Administration of Operating Systems (Linux)
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The purpose of the discipline: is the formation of a holistic system view of the OS, its purpose, architecture, main components, practical solution of problems arising in the system management of operating systems, critical thinking and understanding of the key concepts of interaction between components of operating systems. During the study of course, students should be competent in: - describe the main components of operating systems, understand their capabilities, purpose, requirements for their system maintenance; - explain the architecture of Linux OS; - demonstrate the management of processes and types of inter-process interaction; - to investigate the work of the network subsystem;

Theory of Dynamical Systems
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - The aim of the discipline is the formation of knowledge and skills on the basic concepts and results of the modern theory of dynamical systems. These include: classification of trajectories and their limit sets, roughness and structural stability, typical bifurcations, regular dynamics and chaos, familiarity with mathematical models of the most important processes in natural science. Formation of competencies necessary for the application of knowledge and skills of construction, as well as qualitative and quantitative research of mathematical models of complex dynamic systems operating in continuous or discrete time, as well as evaluation of initial data for the development of mathematical models of a real process.

Web Programming
  • Type of control - [RK1+MT+RK2+Exam] (100)
  • Description - Purpose: formation of a trained knowledge of web programming abilities and skills to develop web applications. The purpose of the discipline is achieved by solving problems of the web. Objective: The study of discipline is achieved through the following objectives: learn the basics of operation, configuration and administration software that implements Web services, to give an idea about the basic principles and structure of Web technologies.

Data for 2021-2024 years

INTERNSHIPS

Educational
  • Type of control - Защита практики
  • Description - Сonsolidation of the received theoretical knowledge, professional orientation of students; familiarization and study of the organization of activity, structure, directions of scientific activity of the department, faculty, university. - use knowledge of physical laws and theories to explain the structure of matter, forces and interactions in nature, the origin of fields; use acquired knowledge in practice and in everyday life;

Pre-diploma
  • Type of control - Защита практики
  • Description - The goal of the practice is to form the ability to integrate the theory and methodology of technological and chemical disciplines to solve practical problems related to future professional activities. The practice is aimed at the formation of an independent solution to real problems in the field of chemical technology of inorganic substances using the competencies obtained in the course of mastering the educational program.

Production
  • Type of control - Защита практики
  • Description - Consolidation of theoretical and practical knowledge obtained at the university, familiarization with the organization and production technology, the acquisition of practical skills and professional experience in the field of study. As a result of the internship, the student will be able to study and analyze the necessary information, to carry out the necessary calculations using modern technical means.

Data for 2021-2024 years