Bachelor courses
Speciality Code:
6B05402
Speciality Name:
Mathematics
Faculty:
Mechanics and Mathematics
Qualification:
- First Stage of Higher Education - Bachelor of Natural Science
- Model of graduating student
- Mandatory disciplines
- Elective disciplines
- Professional
ON1. Demonstrate mathematical literacy, logical thinking and knowledge of the basic concepts and laws of mathematics, master the mathematical language in the subject area;
ON2. To find methods for solving scientific problems in new and unfamiliar contexts based on mathematical methods;
ON3. Use mathematical programming methods and develop new programs to optimize computational processes and production planning;
ON4. Analyze mathematical models and substantiate the correctness of the choice of the method of solving problems (analytical, numerical, laboratory experiment);
ON5. Summarize the results of research and analytical work in relevant fields of science in the form of participation in research projects and speeches at conferences;
ON6. Classify technologies, methods and techniques of teaching mathematics based on the main achievements in the field of mathematics teaching methods.
ON7. Choose modern mathematical methods and apply them in solving problems of natural science;
ON8. To substantiate the behavior of the observed process on the basis of the theory of differential and integral calculus;
ON9. To make mathematical models of the object under study on the basis of the principles and tools of mathematical methods;
ON10. Solve theoretical and applied problems of natural science;
ON11. Create applications for software packages to optimize professional activity in the studied fields of science, conduct laboratory and numerical experiments, evaluate the accuracy and reliability of simulation results;
ON12. To work in a team, to defend reasonably the correctness of the choice of solving mathematical and statistical problems; critically assess their activities, the activities of the team, and be capable of self-education and self-development.
ON2. To find methods for solving scientific problems in new and unfamiliar contexts based on mathematical methods;
ON3. Use mathematical programming methods and develop new programs to optimize computational processes and production planning;
ON4. Analyze mathematical models and substantiate the correctness of the choice of the method of solving problems (analytical, numerical, laboratory experiment);
ON5. Summarize the results of research and analytical work in relevant fields of science in the form of participation in research projects and speeches at conferences;
ON6. Classify technologies, methods and techniques of teaching mathematics based on the main achievements in the field of mathematics teaching methods.
ON7. Choose modern mathematical methods and apply them in solving problems of natural science;
ON8. To substantiate the behavior of the observed process on the basis of the theory of differential and integral calculus;
ON9. To make mathematical models of the object under study on the basis of the principles and tools of mathematical methods;
ON10. Solve theoretical and applied problems of natural science;
ON11. Create applications for software packages to optimize professional activity in the studied fields of science, conduct laboratory and numerical experiments, evaluate the accuracy and reliability of simulation results;
ON12. To work in a team, to defend reasonably the correctness of the choice of solving mathematical and statistical problems; critically assess their activities, the activities of the team, and be capable of self-education and self-development.
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The Vector Analysis
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of studying the discipline is to develop a clear understanding of the basic concepts and methods for solving problems in the theory of curvilinear and surface integrals, as well as the ability to calculate curvilinear and surface integrals. In the course of studying the course, to form students' abilities: -calculate curvilinear and surface integrals; - to have the concept of an external differential form and a piecewise smooth surface, the concept of an integral from the differential form of its properties; - deduce the abstract formula of Stokes, the formulas of Green, Ostrogradsky, the classical formula of Stokes; - to know the elements of field theory
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Kazakh (Russian) Language
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description:
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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.
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Geometry
- Number of credits: 9
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: To form the ability to use the methods of vector algebra and the method of coordinates for the study of objects of analytical geometry. The content of the discipline is aimed at studying various products of vectors, deriving and studying the equations of a straight line on a plane and in space, a plane in space, canonical equations of curves and surfaces of the second order. To develop students' geometric imagination and intuition. To form the ability to use the theory of differential calculus to study geometric objects. The content of the discipline is aimed at studying the theory of curves and surfaces, methods of differential geometry for calculating the length of a curve, curvature and torsion of curves, constructing a movable Frenet trihedron, using the first and second fundamental forms to study the internal geometry of surfaces.
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Discrete mathematics and Mathematical logic
- Number of credits: 9
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Formation of the ability to perform operations on sets, apply the apparatus of set theory to solve problems. The concept of a set. Basic concepts of graph theory, ways of setting. Elementary boolean functions, canonical ways of setting. Statements, methods for checking logical consequence. Combinatorics. To form the ability using the mathematical logic for the study of mathematical objects. In the course of studying the course to form students' abilities: - formulate and prove key statements of mathematical logic; - solve typical problems (build truth tables, find DNF and CNF formulas, prove the truth of statements and conclusions, build conclusions, find the PCNF and PDNF formulas, build logical formulas for given statements, find PNF).
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Military Training
- Number of credits: 6
- Type of control: MC
- Description: Military Training
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Differential Geometry
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: To form the ability to use the theory of differential calculus to study geometric objects. The content of the discipline is aimed at studying the theory of curves and surfaces, methods of differential geometry for calculating the length of a curve, curvature and torsion of curves, constructing a movable Frenet trihedron, using the first and second fundamental forms to study the internal geometry of surfaces.
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Differential Equations
- Number of credits: 6
- 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
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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.
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Partial Differential Eguations
- Number of credits: 6
- 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.
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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.
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Integral Equations
- Number of credits: 6
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Aim: to introduce students with the main problems of the theory of integral equations and methods for their solving, explain the basic concepts of the theory of Volterra and Fredholm integral equations, understand the statements and proofs of the main theorems. During the study of the discipline, the following topics will be covered: Classification of integral equations. Resolvent. Fredholm determinant method. Fredholm Integral equations with degenerate kernel. Integral equations with a symmetric kernel; Riesz-Fisher theorem; expansion of a symmetric kernel in a row. Hilbert-Schmidt theorem. Volterra and Fredholm Integral equations of the first kind. Fourier and Laplace transform and their application to the solution of integral equations.
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Information-Communication Technologies
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: During the study of the discipline students will learn following aspects:ICT role in key sectors of development of society. Microsoft Office Windows Cybersafety. Internet technologies. Cloud and mobile technologies. Multimedia technologies. Smart Technology. E-technologies. Electronic business. E-learning. Electronic government. Information technologies in the professional sphere.
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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).
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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.
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Complex Analysis
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the subject of functions of a complex variable is to introduce the fundamental methods of complex analysis, these methods are based on the analysis of infinitesimal quantities and the use of properties of the field of complex numbers. When studying the subject, the following topics are considered: Cauchy's integral theory. Taylor and Laurent expansions, analytic continuation, subtraction theory and its application to the calculation of integrals, as well as mastering the basics of geometric theory and their application to an in-depth study of basic elementary functions with complex variables and conformal mappings.
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Culturology
- Number of credits: 2
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Aim of discipline is to form a bachelor's understanding of the specifics of the development of national culture in the context of world culture and civilization, need to preserve the cultural code of the Kazakh people, ability to pursue in independent professional activity a strategy of preserving the cultural heritage.
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Basics Algebraic Structures
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose: To form the ability to use the basics of algebraic structures for the study of mathematical objects. In the course of studying the course to form students' abilities: - to formulate and prove key statements of the foundations of algebraic structures; solve basic problems for groups, rings and fields; determine the equivalence and constant sign of quadratic forms, apply operator theory to solve problems with second-order surfaces; apply the theory of quadratic forms to solve problems with surfaces of second order
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Functional Analysis
- Number of credits: 6
- 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.
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Analytical Geometry
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: To form the ability to use the methods of vector algebra and the method of coordinates for the study of objects of analytical geometry. The content of the discipline is aimed at studying various products of vectors, deriving and studying the equations of a straight line on a plane and in space, a plane in space, canonical equations of curves and surfaces of the second order. To develop students' geometric imagination and intuition.
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Real 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 a real analysis as a tool for the mathematical description of the natural science picture of the world; and to form students' abilities: calculate typical tasks (determine the power of a set, check the measurability of sets, the measurability of functions, Lebesgue integrability of measurable and bounded functions) using the methods of real analysis; - to optimize the solution of applied problems using the methods of real analysis; - to classify the basic concepts of real analysis (the power of a set, open sets, closed sets, perfect sets, measurable functions on a real line, Lebesgue integral); - describe the study of real processes by the methods of real analysis; - to design the process of research of an applied problem, using the methods of real analysis
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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.
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Linear algebra and algebraic structures
- Number of credits: 9
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Objective: to introduce basic mathematical concepts based on the concept of linearity, which are necessary for training specialists in all areas of mathematics. The content of the discipline is aimed at studying the theory of polynomials, linear spaces, Euclidean spaces, unitary spaces. GCD of polynomials, basis and dimension of the sum of subspaces, transition matrix, angle between vectors, orthogonal projection of a vector onto space, orthogonalization process. To form the ability to use the basics of algebraic structures for the study of mathematical objects.
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Mathematical Logic
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: In the course of studying the course to form students' abilities: - formulate and prove key statements of mathematical logic; - solve typical problems (build truth tables); - apply the deduction theorem to prove the truth of the conclusions; - apply logical equivalences to simplify formulas; - use the resolution method to prove the truth of the conclusions; - determine the logical correctness for arbitrary assertions
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Multivariable Calculus
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The aim is a consideration of the concept of the limit, the continuity of functions of several variables, partial derivatives and differentiability, the application of differential calculus to finding extremums, implicit and inverse functions, the conditional extremum; the consideration of the concept of a double and triple integral and their applications.
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Linear Algebra
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose: to form the ability to use linear algebra to study mathematical objects. In the course of studying the course to form students' abilities: - to formulate and prove key statements of linear algebra; - calculate typical tasks (find the GCD of polynomials, find the basis and dimension of the sum of subspaces, the transition matrix from one basis to another, the angle between vectors, the orthogonal projection of the vector to space, complement the system of vectors to the basis of space, determine the multiplicity of the roots of the polynomial); - apply the Horner scheme for solving problems with polynomials; - apply the process of orthogonalization
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Mathematical analysis – II
- Number of credits: 9
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Objective: to develop skills in the study of integral calculus of functions depending on one variable, the application of the theory of integrals in geometry, physics, mechanics, economics, series theory. Problems: methods of integration, theorems on the mean, the use of definite integrals; convergence of numerical series, convergence and uniform convergence of functional chains, homogeneous convergence of functional series, classification of functions into power series
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Mathematical analysis – III
- Number of credits: 9
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose: to form skills of differential and integral calculus of functions of many variables, to acquaint with fundamental methods of calculation of curvilinear and superficial integrals, elements of field theory. Tasks: continuity of functions of many variables; private production; differentials of high order, extremums; Taylor's formula; multiple integrals, their applications; curvilinear, surface integrals; formulas of Stokes, Green, Ostrogradsky; elements of field theory.
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General topology
- Number of credits: 6
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: General topology, or set-theoretic topology, is a branch of topology in which students study the concept of continuity in its purest form. Here the fundamental questions of topology are explored, as well as individual issues such as connectivity and compactness.
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Basics of Algebra
- Number of credits: 6
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose: To form the ability to use the basics of algebra for the study of objects of natural science. In the course of studying the course to form students' abilities: -to formulate and prove key statements of the basis of algebra; - calculate typical tasks (calculate determinants, find the inverse matrix, find the solution of the SLAE, find the degrees and roots of complex numbers, find the rank of the matrix); -apply the algebraic properties of linearly dependent vector systems when solving problems; -find inverse matrices using the Gauss-Jordan method and by the reversibility criterion
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Programming and Numerical methods
- Number of credits: 9
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The aim of the discipline is forming the students' ability to develop programs in modern Java 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 combine various tools of Java programming language (classes, methods, packages, interfaces, etc.) to develop effective programs and software packages; justify the purpose and use of the main components of Java programming language. As a result of studying the discipline, the student must be able to make mathematical models of practical optimization problems and numerical methods for solving them, use known solution methods and draw conclusions, have an idea of the basic optimization methods and basic numerical methods, practical skills implementation of algorithms for solving optimization problems.
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Theory of real variable’s functions and functional analysis
- Number of credits: 9
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline: To form the ability to use a real analysis as a tool for the mathematical description of the natural science picture of the world. In the course of studying the course to form students' abilities: - Explain the key concepts of real analysis (concepts of set theory in the context of the corresponding theory; - Calculate typical tasks (determine the power of a set, check the measurability of sets, the measurability of functions, the summability (integrability) of functions on a real line) using the methods of real analysis. 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; explain the key concepts of functional analysis in the context of the corresponding theory; calculate typical tasks using its methods; optimize the solution of applied problems using the basic principles of functional analysis.
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Political Science
- Number of credits: 2
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The academic discipline “Political science” forms knowledge of the laws and laws of world politics and modern political processes, explaining the essence and content of the policy of national states, on the basis of ensuring national security and the realization of national interests.
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Psychology
- Number of credits: 2
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of studying the discipline is to provide scientifically grounded training of highly qualified specialists on the basis of studying the fundamental concepts of psychology management, creating the necessary prerequisites for theoretical understanding and practical application of the most important management problems related to the process of professional development.
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Sociology
- Number of credits: 2
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The course presents general questions of theory and history of sociology, methodology and methods of sociological research, special sociological theories. This course is aimed at shaping the sociological imagination of students, basic ideas about the subject and methods of sociological research, topical problems and sociology branches.
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Theoretical Mechanics and Physics
- Number of credits: 9
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose of discipline. During the course of «Theoretical mechanics» main laws of mechanical motion of given mechanical system was explained to students.The formation of scientific knowledge of the fundamental physical system laws, ideas about the system of physical theories and their evolution, about the unity of the science of physics and its role as the foundation of modern natural science, mastering the simplest methods physical experiment and theoretical apparatus.
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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.
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Mathematical modeling
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The course discusses the general principles of constructing mathematical models. The review of mathematical models of physical, chemical, biological, economic and other processes is given. An idea of the qualitative and quantitative analysis of various mathematical models is given. Specific examples describe the identification of the results of the analysis of mathematical models. Examples of solving forecasting and optimization problems based on mathematical modeling are given.
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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.
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Elementary Mathematics from a Higher Standpoint
- Number of credits: 6
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline are getting an idea of the universal nature of mathematical methods, of the close relationship between elementary mathematics and higher mathematics; about the unity of mathematics as a whole; finding the relationship between the issues of individual disciplines, developing the ability to determine the general forms and patterns in the field of mathematics; getting an opportunity to look at school mathematics from the point of view of scientific and applied interests.
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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.
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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.
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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.
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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.
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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.
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Al-Farabi and Modernity
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Aim of the discipline: 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.
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The Qualitative Theory of Differential Equations
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline is to study the basic concepts of qualitative theories of differential equations; explain the properties of solutions to a system of differential equations (singular points, classification of integral curves and trajectories, classification of singular points, etc.); – calculate typical problems (finding special points, study of types of special points, study of special points of the system of differential equations on the plane, finding the direction of points and trajectory) using the methods of qualitative theories of differential equations; – organize the solution of applied problems using geometric and mechanical meanings of singular points
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Additional chapters of Mathematical statistics
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The aim of the course is a deeper presentation of the mathematical foundations of probability theory, The objectives of studying the course are the mathematical basis of the theory of probability, based on the theory of measure; theory of mathematical expectation (Lebesgue integral with respect to probabilistic measure); the theory of conditional probabilities and conditional mathematical expectations; method of characteristic functions for proving limit theorems; calculate the simplest conditional probabilities and conditional mathematical expectations; apply theorems on passage to the limit under the sign of mathematical expectations and conditional mathematical expectations
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Classical mechanics
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline: to form the ability to demonstrate knowledge and understanding of the basic ideas of mechanics associated with solving problems, applying laws, theorems and principles of theoretical mechanics. During the study of the discipline, the following topics will be covered: Basic concepts and principles of classical mechanics; basic definitions of statics, conditions for the equilibrium of a system of forces; kinematics of a point and a rigid body, complex motion of a point and a rigid body; basic concepts, problems and theorems of dynamics
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Complex Analysis
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of studying the discipline is to obtain basic knowledge in the theory of functions of a complex variable; The ability to independently solve the problems of TFSC; Mastering the skills of using methods of complex analysis in solving physical problems.The subject of the course includes: complex numbers, analytic functions and their properties, integral over a complex variable, Cauchy integral, residues, series of analytic functions, comfort mappings, Laplace transform.
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Finite Dimensional Optimization
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline is to give an idea of the methods for study of finite-dimensional optimization problems. During the study of course, students should be competent in: -Solving applied optimization problems in the finite-dimensional space of input and output parameters; -Using the theory of necessary and sufficient optimality conditions for finding solutions to the obtained optimization models; -Using numerical minimization methods and develop new programs to find the optimal combination of design parameters -Analyzing control models and justifying the correct choice of the method of solving problems (analytical, numerical).
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Linear Differential Operators
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of this course is to teach students to work with linear differential operators in finite domains. The objective of the course is to understand the basic methods of linear differential operators. Linear differential equations. Types of boundary conditions. Green's function. Boundary-value problems. The student must know the basic methods of linear differential operators. Be able to apply theorems of linear differential operators. To acquire the skills of studying linear differential operators.
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Foundations of Probability Theory
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The aim of the course is a deeper presentation of the mathematical foundations of probability theory, The objectives of studying the course are the mathematical basis of the theory of probability, based on the theory of measure; theory of mathematical expectation (Lebesgue integral with respect to probabilistic measure); the theory of conditional probabilities and conditional mathematical expectations; method of characteristic functions for proving limit theorems; calculate the simplest conditional probabilities and conditional mathematical expectations; apply theorems on passage to the limit under the sign of mathematical expectations and conditional mathematical expectations
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Minimization methods in finite space
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline is to familiarize the methods of minimization in the finite-dimensional space; Explaining the reason for choosing a particular minimization method to solve a particular problem in a finite-dimensional space; - Mathematical modeling of the system under study on the basis of the optimization goal and taking into account the limitedness of resources; - Solving applied minimization problems in finite-dimensional space; -Choosing methods of minimization and applying them in solving problems in finite-dimensional space; - Using numerical minimization techniques and developing new programs to optimize system operation and production planning
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Scientific Research Methods
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Objective - 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.
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Generalized Functions and Their Applications
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline: To form the ability to use the theory of generalized functions for solving theoretical and applied problems: - free to operate the studied abstract concepts; - independently prove the properties of operations entered according to the given definitions; - apply the studied theory when solving ordinary differential equations - apply the studied theory when solving equations of mathematical physics; - use the studied mathematical apparatus in reading modern mathematical and physical scientific literature. - free to use the obtained mathematical knowledge for solving theoretical and practical problems; - independently prove mathematical statements.
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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.
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Legal Bases of Corruption Control
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The goal 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.
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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.
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Spectral Theory of Linear Operators
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Extremal problems arise and find applications in many areas of natural science, technology and science. In mathematics, such an interesting area where extremal problems naturally arise is approximation theory. The purpose of the discipline is to acquaint students with the formulation of problems and with the basic concepts of approximation theory. To teach in various cases to build approximation aggregates for the object of interest (function, integral or operator), to estimate the errors of their approximation from above and below. To instill skills in obtaining optimal methods in terms of error or methods close to them, approximation algorithms.
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Theoretical Mechanics
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: This discipline aims to study the laws of nature; acquisition of skills in building mathematical models occurring in nature and technology processes; their analysis on the basis of the found solutions. During the study of the discipline, the following topics will be covered: Kinematics of a point and a rigid body, the complex motion of a point and a rigid body, the basic definitions and axioms of statics, the basic concepts, problems and theorems of dynamics, the oscillations of a material point.
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Theory of Random Process
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline: Familiarization of students with the basic concepts and results of the theory of random processes and their corresponding applications in mathematical science. In the course of studying the course, students should develop the ability to: - understand and be able to explain the probabilistic - mathematical foundations of the initial fundamental concepts of random processes: definition; trajectory; finite-dimensional distributions; characteristics; elements of random analysis; main classes; Wiener and Poisson processes and their properties in the context of the relevant theory; – be able to solve typical problems (finite-dimensional distribution, mathematical expectation and variance of a random process; calculation of stochastic integrals, etc.) using methods of the theory of random processes.
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Theory of functions of a complex variable
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of studying the discipline is to obtain basic knowledge in the theory of functions of a complex variable; The ability to independently solve the problems of TFSC; Mastering the skills of using methods of complex analysis in solving physical problems.The subject of the course includes: complex numbers, analytic functions and their properties, integral over a complex variable, Cauchy integral, residues, series of analytic functions, comfort mappings, Laplace transform.
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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; measuring instruments of the teachings of Abai; the essence and meaning of Abai’s doctrine.
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Theory of extremal problems
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The objective of the discipline "Calculus of variations and methods of optimization" is to develop the students' deep knowledge of the foundations of the calculus of variations and optimization techniques; ability to apply this knowledge in the study and solution of specific problems encountered in various fields of natural science. In this course, students will learn the simplest variational problem; theory of the first and second variations; variational problems with higher derivatives; convex programming; theorem on the global minimum; linear and nonlinear programming.
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Controllability of Dynamic Systems
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline is to study the basis of the theory and methods of controllability of dynamic systems. In the course of studying the course to form students' abilities: - Compile mathematical models of the object under study based on the principles and tools of mathematical methods; - Solve theoretical and applied problems of natural science; - Select modern mathematical methods and apply them in solving problems of natural science; - Analyze mathematical models and substantiate the correctness of the choice of the method of solving problems (analytical, numerical, laboratory - Summarize the results of research and analytical work in relevant fields of science in the form of a thesis, report at student scientific conferences, participate in research projects
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Physics
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Physics can be defined as a science that explores the fundamental concepts of matter, energy and space and the relationship between them. Formation of students' understanding of the modern physical picture of the world and the scientific worldview, the main physical phenomena; mastering the fundamental concepts, laws and theories of classical and modern physics, as well as methods of physical research; methods for solving specific problems in various fields of physics; the introduction of modern scientific equipment, the behavior skills of a physical experiment, the ability to highlight specific physical content in future applications of applications.
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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 environmental management concepts that implement the principles of harmonious optimization of the conditions for human interaction with nature, including in the process of tourist and recreational activities.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.
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Extreme Problems in Approximation Theory
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Extremal problems arise and find applications in many areas of natural science, technology and science. In mathematics, such an interesting area where extremal problems naturally arise is approximation theory. The purpose of the discipline is to acquaint students with the formulation of problems and with the basic concepts of approximation theory. To teach in various cases to build approximation aggregates for the object of interest (function, integral or operator), to estimate the errors of their approximation from above and below. To instill skills in obtaining optimal methods in terms of error or methods close to them, approximation algorithms.
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Numerical methods for solving problems of mathematical physics
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose: Teaching students the basic concepts and ideas of numerical methods for solving partial differential equations, mastering the techniques for solving practical problems on a computer, and applying numerical methods necessary for mathematical formats; knowledge of the basic principles and theory of numerical methods; mastering algorithms and methods of numerical methods of mathematical physics problems, as well as questions of stability of computational algorithms; be able to analyze the approximate error of numerical calculation results; have the ability to choose optimal methods of numerical problem solving and algorithmic thinking; obtaining a numerical solution of course problems on a computer.
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Sequences and sums of independent random variables
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline is to present a number of classical and some of the latest results of the limit theorems of probability theory and mathematical statistics in one of the most important for practical applications part of the probabilistic and statistical direction of mathematics - in the section "Sequences and sums of independent random variables". The objectives of the course are: Students' understanding of the role and meanings of the limit theorems of probability theory and mathematical statistics concerning sequences and sums of independent random variables; Acquisition of skills in proving limit theorems; Ability to prove classical limit theorems by direct methods and methods of generating and characteristic functions
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Programming
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose of the discipline - is aimed at mastering by students the knowledge and skills necessary to write programs in Python; students will be introduced to the basics of the Python language, including data types, functions, loops, and conditional statements, as well as basic programming concepts such as algorithms and data structures. In addition, students will be introduced to various Python libraries and modules that will allow them to solve problems in various fields such as science, engineering, business, and others. The study of this discipline will help students develop programming skills, algorithmic thinking, logical thinking and the ability to solve complex and multifaceted problems.
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The Calculus of Variations and Optimization Technigues
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The objective of the discipline "Calculus of variations and methods of optimization" is to develop the students' deep knowledge of the foundations of the calculus of variations and optimization techniques; ability to apply this knowledge in the study and solution of specific problems encountered in various fields of natural science. In this course, students will learn the simplest variational problem; theory of the first and second variations; variational problems with higher derivatives; convex programming; theorem on the global minimum; linear and nonlinear programming.
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Probability and statistics
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The content of the discipline is aimed at studying such concepts and definitions as the space of elementary events; probabilistic space; basic probability formulas; independent trials; random variables and their numerical characteristics; characteristic functions; laws of large numbers and limit theorems; basic concepts of sampling theory; point estimators and their properties; methods for finding point estimators; interval estimators; testing statistical hypotheses.
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Introduction to the Theory of Extremal Problems
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline is to teach students – Introduction to the general theory of extremal problems in a Banach space; – Solve optimal control problems, study the functional on boundedness, find the minimizing sequence, investigate the convergence of a sequence to a set; – Order the solution of applied problems using the geometric and physical meanings of the derivative; – Classify methods of extremal problems; – Describe the derivations of nonlinear operators and nonlinear functionals; – Design an application research process using methods of extremal problems
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Differential Equations With A Small Parameter
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The aim of the discipline is to introduce students with the role of differential equations with a small parameter in problems of natural science, the main problems and methods for solving such equations. During the course, students must have following abilities: - explain the basic concepts and theorems of the theory of differential equations with a small parameter, the proofs of the basic statements; - to possess the main asymptotic methods for solving differential equations with a small parameter; - correctly choose a method for solving differential equations with a small parameter
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General physics
- 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.
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Object-Oriented C++ Programming
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The aim of the discipline is forming the students' ability to develop programs in С++ programming language with its further use in various fields of professional activity; explain the main principles underlying the creation of various applications in С++ programming language; combine various tools of С++ programming language (classes, methods, packages, interfaces, etc.) to develop effective programs and software packages; justify the purpose and use of the main components of С++ programming language; synthesize, interpret and evaluate the learning outcomes of the discipline for their further application in professional activities.
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Optimal Control
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Study of the theoretical foundations of optimal control and methods for solving problems of optimal control by constructing minimizing sequences in function spaces. In the course of studying the discipline, students have the ability to: compose mathematical problems of choosing an object model based on principes of optimal control and justify the correct choice of the solution method, generalize the results of research and analytical work.
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Basics of Groups and Rings Theories
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: In the course, groups and their subgroups, group constructions, normal subgroups, coset classes, abelian groups are studied; expansions of fields, finite fields, algebraically closed and real closed fields; Ideals, radicals, semisimple and simple rings. As applications, we consider connections of linear groups with quaternion algebras, parametrization of rotation groups of three-dimensional and four-dimensional Euclidean spaces.
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Psevdoparabolic equations
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the course "Pseudoparabolic equations": to acquaint students with the theory and topical problems of the pseudo-parabolic equation and modern methods for solving them. In the course of studying the course, to form students' abilities: - demonstrate and develop mathematical literacy; - has knowledge of the basic concepts of the theory of pseudo-prabolic equations; - be able to formulate problem statements for a pseudo-prabolic equation and determine the class of solution; -to form the ability to abstract thinking, analysis, synthesis; -be able to and perform independent scientific research new sections of fundamental and applied mathematics.
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Advanced Cryptosystems
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The goal of the course is to fully acquaint students with the boundaries of the application of elliptical cryptography and examples of the application of this cryptosystem in cryptology and their algebraic fundamentals. As a result of studying the course, students receive the necessary skills in the application of the elliptical cryptosystem in practice. This course explores modern cryptography systems. The course begins with a review of the necessary material from modern algebra and number theory, cryptosystems with a secret and public key and basic schemes of electronic signatures. Most of the course will be devoted to the results of number theory and the foundations of the theory of Galois fields used in cryptography; the history of algorithms for recognizing the simplicity of numbers and polynomial-time simplicity tests; as well as sections of cryptosystems based on the properties of discrete logarithms, including those based on elliptic curves; interactive protocols, authentication issues.
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Automata and formal languages theory
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: This course explores formal languages, regular languages, and regular expressions. The main part of the course is devoted to the study of deterministic finite automata and non-deterministic finite automata. An algorithm for minimizing the state of deterministic finite automata is also considered. And research push-down automata and Turing machines.
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The Theory of Algorithms
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline is to form the ability to use the theory of algorithms for the study of objects of natural science: – Explain key concepts of algorithm theory (such as computable functions, recursive and recursively enumerable sets, and computable reducibility of sets); – Use modern methods of step-by-step constructions to solve some typical problems; – Use the acquired knowledge to solve problems in diploma or other scientific papers. When studying the discipline, students will study the following aspects: primitive recursive functions, partially recursive functions, computable functions on a Turing machine, Church's Thesis, Gödel numbering of recursive functions, s-m-n theorem, basic concepts of numbering theory.
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Computing Methods for solving differential equations
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose of the discipline is teaching students the ability to use basic numerical methods; - mastering the construction of algorithms for solving mathematical problems with a computer; - knowledge of algorithms and methods of numerical methods of Algebra and analysis, as well as questions of stability of computational algorithms; -ability to analyze the approximate error of numerical calculation results; - be able to conduct research on the presentation of types of problems of Algebra, Analysis and elementary differential equations and their numerical methods; - have the ability to choose optimal methods of numerical problem solving and algorithmic thinking
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Probability Theory and Mathematical statistics
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of studying the discipline is to master the basic probabilistic and mathematical-statistical concepts; mastering the main methods for solving probabilistic and mathematical statistical problems; 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
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Boundary value problems of mathematical physics
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: In the course the following questions will be considered: The statements of boundary and initial-boundary problems for equations of mathematical physics, parabolic, hyperbolic and elliptic equations, strong and weak generalized solution and class of solutions, the method of obtaining a priori estimates, energy methods, functional methods, existence, uniqueness and stability of solutions; applications to solving applied problems of natural science.
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Linear integro-differential equations
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Solving of initial and boundary value problems for linear integro-differential equations of higher orders in cases where the order of the external differential operator is greater than or equal and less than the order of derivatives under the integral term. Solving linear integro-differential equations with and without the fundamental system of solutions of external and internal differential operators
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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.
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The Theory of Generalized Function
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: In the course of studying the course to form students' abilities: - Calculate typical tasks (Completeness of the space of generalized functions. Change of variables in generalized functions. Differentiation of generalized functions) 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 differential equation problem by the methods of the theory of generalized functions and the theory of function spaces. - Design the process of studying an applied problem using the methods of the theory of generalized functions
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The Theory of Sobolev Spaces
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The course covers the following issues: the basic properties of Lebesgue spaces, the basic integral inequalities in the theory of functional spaces (Holder, Jensen, Minkowski, Hardy and their generalization for series and integrals), compactness criteria for sets in Lebesgue spaces, definitions and basic properties of Sobolev averagings and their application for approximating functions from of Lebesgue spaces by means of smooth functions To be able: to apply the basic integral inequalities for solving problems about estimating norms in function spaces, the norms of Hardy operators and averaging operators, to establish the accuracy of the corresponding estimates, to apply the compactness criteria. To master: various modern methods of estimating sums and integrals, methods of working with mixed norms and norms of integral operators of Lebesgue spaces. - The study of the main integral inequalities and their application. - To form the ability to abstract thinking, analysis, synthesis; - carry out independently scientific research in new sections of fundamental and applied mathematics. - Compile mathematical models of the object under study based on the principles and tools of mathematical methods; - Solve theoretical and applied problems of natural science; - Analyze mathematical models and justify the correct choice of problem solving method.
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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.
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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.
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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;