Magistracy
Speciality Name:
Mathematics (URChA)
Faculty:
Mechanics and Mathematics
Qualification:
- Scientific and pedagogical direction - Master of Natural Sciences
- Model of graduating student
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Mandatory
disciplines
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Elective
disciplines
- Professional
ON1. To conduct different types of classes in mathematical disciplines, using new educational technologies and teaching methods in traditional and distance forms and to develop their methodological support, tasks for students’ independent work, recommendations for the implementation of practical tasks, action plans for educational work;
ON2. To develop model isomorphism using the transfer method for characterizing universal, existential and inductive theories;
ON3. To conduct applied research in the field of economics, financial analysis, sociology, medicine using methods of stochastic data analysis;
ON4 To work with foreign scientific publications in the field of mathematics, competently use linguistic and linguistic-cultural knowledge to summarize scientific information in the field of mathematics, including in a foreign language;
ON5. To conduct applied research in the field of mathematics and educational technologies, formulating problems and tasks, using computability theory, model theory, field theory;
ON6. To demonstrate knowledge of group theory, for further research using methods in the theory of finite groups;
ON7. To create search algorithms for various queries in databases using numbering theory and data mining tools;
ON8. To develop a curriculum for teaching mathematical disciplines in the context of modern achievements the field of mathematics and the requirements of higher education pedagogy;
ON9. To develop effective mathematical methods to solve applied problems of mathematics, physics, mechanics, economics and management;
ON10. To analyze scientific data to formulate scientific hypotheses in the framework of their own research;
ON 11. To continue independent and autonomous training for creative self-development and self-improvement, for the development of basic and subject competencies throughout all professional activity;
ON12. To make the connection between group theory and finite field theory, to study other finite fields by learning the theoretical foundations of Galois field theory.
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Psychology of management
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Formation of knowledge about the fundamental concepts of management psychology for the practical application of the most critical aspects of management in professional interaction. Basic principles of management psychology, personality in management interactions, management of personality behavior, modern ideas, psychology of managing group phenomena, motivation, and practical reflection.
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Mathematical analysis on metric spaces
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose the discipline is to develop skills and abilities for solving non-standard, atypical applied problems of modern mathematical analysis on metric spaces and stochastic analysis, as well as the formation of readiness for independent professional activity by some of their applications.
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Methods of Teaching Higher Education Mathematics
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Aim: To study the methods of proof, methods of solving problems; methods of teaching mathematics; organizational forms of teaching mathematics in high schools; aware of the contents of the mathematics in high schools; arming the future teacher with specific knowledge in teaching high school mathematics, widening the pedagogical outlook of the student, but correctly mastering general provisions on the forms and methods of organizing the high school's mathematical activity, familiarization with the peculiarities of teaching mathematics in high schools.
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Pedagogy of Higher Education
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose: To provide pedagogical theories and practical strategies for effective teaching in higher education, fostering critical thinking, and academic success. The course explores instructional methods, curriculum design, assessment techniques, and classroom management strategies preparing educators to create inclusive and stimulating learning environments.
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Foreign Language (professional)
- Number of credits: 5
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose is to acquire and improve competencies by international standards of foreign language education and to communicate in an intercultural, professional, and scientific environment. A master's student must integrate new information, understand the organization of languages, interact in society, and defend his point of view.
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History and Philosophy of Science
- Number of credits: 3
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Purpose: Understanding of modern philosophy as a system of scientific knowledge, including worldview in rational-theoretical comprehension. The discipline includes aspects of the evolution and development of scientific thinking, historical moments, the contribution of scientists and scientific schools to the formation of science, and ethical and social aspects of scientific activity.
Data for 2021-2024 years
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Additional chapter Functional Analysis and Their Applications
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main goal of the discipline is to correct the previously acquired knowledge of functional analysis, taking into account the acquired practical experience, to adapt theoretical knowledge to the specifics of research on the basis of analysis.
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Ideals and Diversity
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The goal of the discipline: to form the ability to transform the basic concepts of commutative algebra and geometry from abstract theoretical to concretely computable. to form reproductive-activity components for working with polynomials and affine space; monomial ideal; Buchberger's algorithm. to acquaint with the basic algebraic structures such as a group, a ring, a field, which have applications in various branches of modern science and technology.
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Applied analysis for Partial Differential Equations
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the course is to form the abilities
- master the basic methods, methods of various classical models of evolutionary physical phenomena and obtaining formulas for representing the corresponding solutions in simple cases.
-select and apply numerical methods for solving PDE.
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Direct and Inverse Problems for Nonclassical Equations
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The goal of the discipline is to develop the ability to:
–To master the methods of simplifying the formulation of the studied inverse problems, technologies and tools used to solve inverse problems;
-classify typical methods in the subject area using physical principles;
- Analyze and formulate typical direct and inverse problems of natural science.
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Stochastic analysis and equations
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of mastering the discipline is the formation of the following competencies: the ability to apply the methods of the theory of stochastic analysis and stochastic calculus to solve typical standard problems; the ability to analyze and freely navigate in the main directions of further development of the subjects of this discipline; the ability to investigate the relationship of diffusion processes with solutions of stochastic differential equations.
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The Theory of Finite Fields
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline: to form the ability to use the elements of the theory of finite fields in mathematics and technology. The content of the discipline is aimed at studying the theory of groups and fields, finite and infinite groups
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Theory the Models
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline: to form the ability to apply the methods of model theory to problems arising in various areas of mathematics; analyze, generalize and systematize scientific information about isomorphisms of models, the method of transferring and characterizing universal, existential and inductive theories.
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Elements of theory of numberings
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline is to form the ability to build different numbering for different families of sets and functions. mastering category-theoretic approaches in numbering theory, learning how to work with sub-objects and main sub-objects in the category of numbered sets.
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Effective computability
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: TThe goal of the discipline is to form motivation to gain knowledge of the theory of effective computability, to develop the necessary practical skills for modern research in mathematical logic by formulating and discussing open topical problems.
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Computable Ordinals
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline: the formation of skills and abilities for solving non-standard, atypical applied problems with modern problems and research trends in the theory of computability in infinite levels of various hierarchies, the formation of readiness for independent professional activity for modern research in mathematical logic by formulating and discussing open topical problems.
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Computable Functions
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The goal of the discipline: to form the ability to determine the computability of various functions. The content of the discipline is aimed at studying the computability of a function, primitive and partially recursive functions, computability on a Turing machine, computability with respect to oracles, numbering of computable functions, as well as stopping problems, recursion theorems and Rice's theorem.
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Analysis Fourier
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline is to develop the necessary practical skills for working with the apparatus of harmonic analysis, to gain personal experience in solving standard, typical industrial applied problems by Fourier series and integrals, continuous and discrete Fourier transforms, to illustrate the applications of Fourier analysis methods to solving specific problems.
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Analytical methods in spectral theory of differential operators
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The objectives of mastering the discipline are: to form the ability of undergraduates to work with the studied spectral properties of solutions to a problem with a normal derivative in the boundary condition for the Lavrentiev-Bitsadze operator and to be able to show their application in constructing a solution to this problem.
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Harmonic Analysis on Lie groups and Representation Theory
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the course is to develop the ability to analyze the various connections of harmonic analysis with general questions of the theory of functions and functional analysis; get a clear understanding of the Lie group and applications in the field of non-commutative Fourier analysis, spectral theory and mathematical physics.
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Geometric control theory
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The goal of the discipline is to develop the ability to:
-explore management functions;
- to analyze the methods of checking the criteria for the existence of the solution of boundary value problems of optimal control with various kinds of constraints;
- to master the methods of constructing the solution of boundary value problems of optimal control with linear and quadratic criteria of efficiency;
- to apply constructive theory of optimal control in solving applied problems.
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The Qualitative and asymptotic Theory of Differential Equations
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: Discipline Objective: To Form Abilities
- Calculate typical problems using methods of qualitative theories of differential equations;
- To arrange the solution of applied problems using the geometric and mechanical meanings of singular points;
- Classify singular points on the plane by methods of qualitative theories of differential equations;
- Describe the study of singular points of a linear autonomous system of differential equations on a plane by methods of qualitative theories of differential equations.
- Design the process of researching an applied problem using the methods of methods of qualitative theories of differential equations;
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Multidimensional Complex Analysis
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The purpose of the discipline is to further develop the competence of multivariate complex analysis by deepening the knowledge and skills gained in complex analysis; generalization of the accumulated information theories of holomorphic functions of several variables and holomorphic mappings of complex manifolds.
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General algebra
- Type of control: [RK1+MT+RK2+Exam] (100)
- Description: The main goal of this discipline is the formation of skills and abilities to solve applied problems of an algebraic structure, to use the basic laws of algebraic construction, which allow this structure to create a new object of the same type, to apply the methods of algebraic structures in the field of Mathematics.
Data for 2021-2024 years
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Pedagogical
- Type of control: Защита практики
- Description: Aim оf discipline: formation of the ability to carry out educational activities in universities, to design the educational process and conduct certain types of training sessions using innovative educational technologies.
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Research
- Type of control: Защита практики
- Description: The purpose of the practice: gaining experience in the study of an actual scientific problem, expand the professional knowledge gained in the learning process, and developing practical skills for conducting independent scientific work. The practice is aimed at developing the skills of research, analysis and application of economic knowledge.
Data for 2021-2024 years
