Major Higher Education Programme
Field of study: 010100.62 Mathematics.
Specialty: Mathematical Analysis.
Degree: bachelor.
Course mode: full-time.
The period of study specified by the Federal State Educational Standards of Higher
Education is 4 years.
The study load of the bachelor’s programme specified by the Federal State Educational
Standards of Higher Education is 240 ECTS points.
The programme is meant to develop the students’ faculties in the fields of
to study the classical foundations of the functions theory and the idea of continuous analysis;
to introduce the theories of functions approximation and their various applications;
to master the mathematical models principles in different branches of knowledge;
to know the teaching methods and modern technologies both for elementary mathematics and mathematics, studied in higher educational institutions;
to give an idea of the modern mathematical theories (wavelet analysis, the theory of fractals, etc.);
to develop competence in using of applied mathematical packages, both for educational and scientific purposes;
to develop competence in perception of new ideas in the application of information technology in the light of their application to the teaching of Mathematics and
Automation Research;
to develop competence in the scientific analysis of various phenomena and launch of
original scientific hypotheses.
The list of courses included in the curriculum of 010100.62 Mathematics. Specialty:
Mathematical Analysis.
Fundamental humanitarian, social and economic courses.
History
Semester: 1
ECTS points: 3
Hours: 108
The course aims to understand the internal logic and content of the historical process, to give an idea about the content of major scientific concepts, and the periodization of Russian history as a part of world history.
The objectives of the course are to give students an idea of the historical methodology and chronology, to form students' historical consciousness, respect for the past and the people of their country, and for the history of other cultures, nations and states.
Philosophy
Semester: 2
ECTS points: 3
Hours: 108
The course aims to help students develop a comprehensive idea of philosophy as an independent field of spiritual culture and theoretical studies.
The objectives of the course are to introduce the features of the subject and methods of philosophy, the specifics of philosophical knowledge, to consider the basic stages of the history of philosophy, to reveal the contents of basic philosophical problems and categories, to highlight

the role of science in the development of civilization, relations between science and technology and contemporary social and ethical issues associated with them.
Foreign Language
Semester: 1-4
ECTS points:8
Hours: 288
The course aims to form the students’ ability to intercultural communication, to develop foreign language skills to succeed in the field of their choice.
The objectives of the course are to master lexical, grammatical, syntactic, phonological and orthographic components of a foreign language, and to develop a pragmatic component
(discourse competence, functional competence).
Theory of Economics
Semester: 5
ECTS points: 4
Hours: 144
The course aims to form the theoretical basis for understanding the basics of economic agents, their making economic decisions and objectives of rational behavior on the basis of systematic analysis and mathematical modeling.
The objectives of the course are to introduce the history of economic science formation and development; basic concepts of economic theory; to form the ability to analyse modern economy problems, to deepen understanding of the economy functioning through the development of economic analysis tools and in-depth studies of economic agents and economic phenomena behavior.
Compulsory humanitarian, social and economic courses.
Sociology
Semester: 5
ECTS points: 2
Hours: 72
The course aims to understand the nature of social reality; to use empirical studies in assessing social ogranisation at any level; to develop sociological thinking; to understand a variety of means and methods in analysing the effectiveness of its activities.
The objectives of the course are to form the understanding of basic problems of modern social cognition, theoretical foundations of the social science functioning, principles of correlation between methods and methodology of sociological knowledge; to transfer analysis skills of contemporary social problems in relation to a particular area of activity.
Psychology and Pedagogy
Semester: 7
ECTS points: 2
Hours: 72
The course aims to form the students’ willingness to think independently and to foresee the consequences of their own actions, to assess adequately their capabilities, to find the best way to translate the synthesis of psychological and educational opportunities in the professional sphere.
The objectives of the course are to reveal the basic concepts, phenomena and leading ideas within the content of the course, "learning", "education", "development", "person",
"communication", "cognitive processes", "educational system.
Law

Semester: 1
ECTS points: 2
Hours: 72
The course aims to learn the fundamentals of jurisprudence.
The objectives of the course are to navigate both in the modern system of Russian legislation and in some specific areas of legal economic regulation, to learn methods to work with legislation, to obtain necessary knowledge for implementing professional competence, to contribute to the training of specialists with necessary skills and high qualifications.
Elective humanitarian, social and economic courses.
History of Mathematics
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The course aims to build the general context of mathematical thinking as a cultural form of activity defined both by structural features of mathematical knowledge and the place of mathematics in sciences system.
The objectives of the course are to teach to think logically, to carry the proof of the main results, to establish logical links between concepts, to apply knowledge to solve mathematical problems and problems related to the mathematical methods applications.
Philosophy of Mathematics
Semester: 2
ECTS points: 4
Hours: 144
The course aims to acquire knowledge in the field of philosophical problems of mathematics, in particular knowledge of science nature and development, the mechanisms of its formation and identity, specificity of mathematics as a science.
The objectives of the course are to learn a unique feature of mathematics as a science, the relationship between philosophy and mathematics in their historical development, analysis of philosophical problems in mathematics, such as the mode of mathematical objects being, the paradoxes in the development of mathematics and scientific revolution in mathematics.
Financial Mathematics
Semester: 7
ECTS points: 4
Hours: 144
The course aims to build knowledge and practical skills on how to use financial calculations in analysing cash flows, investment projects efficiency, interest and return of financial and credit operations in the current economic environment.
The objectives of the course are to teach students methods and practices on how to use financial and economic calculations for specific tasks, to summarise characteristics of cash flows, to carry quantitative analysis of the financial and credit operations, to evaluate the effectiveness of short-term instruments and long-term operations.
Mathematical Methods in Economics
Semester: 2
ECTS points: 4
Hours: 144
The course aims to teach students to construct mathematical models of real economic objects; systematic analysis of the economy as a complex dynamic system.

The objectives of the course are to development mathematical models of economic objects, systems and phenomena, to learn behavior of the economy participants, to study descriptive models of the economy, to analyse economic variables and statistics.
Fundamental mathematical and natural scientific courses.
Numerical Methods
Semester: 6-7
ECTS points: 7
Hours: 252
The course aims to teach students to solve applied problems by numerical methods using the computer.
The objectives of the course are to learn basic computational methods and algorithms for solving linear algebra problems; to calculate definite integrals, approximation of functions; to find numerical solutions of problems for differential equations.
Theoretical Mechanics
Semester: 6-7
ECTS points: 7
Hours: 252
The course aims to train students for solving scientific and technical problems and conducting experimental studies of physical processes.
The objectives of the course are to learn proficiently methods of analytical mechanics:
Lagrange equations and Hamilton's principle of the least action; to learn the vibrations theory foundations, rigid body dynamics, the basics of continuum mechanics.
Compulsory mathematical and natural scientific courses.
Programming Technology and Work on Computers
Semester: 1-4
ECTS points: 13
Hours: 468
The course aims to give students an idea about modern methods of information processing and phenomena studying by their numerical simulation on computers.
The objectives of the course are to learn the basics of modern information technologies; to master the techniques and methods of programming; to learn how to use software tools for processing and presentation of data obtained during a physical experiment.
Physics
Semester: 6-7
ECTS points: 6
Hours: 216
The course aims to familiarise students with the basic methods of observation, measurement and experiment, to learn how to use theoretical knowledge for practical problem solving, both in mechanics and in interdisciplinary boundaries of mechanics with other branches of physics.
The objectives of the course are to acquire knowledge about the basic principles and physical laws; to familiarise students with the basics of conducting physical experiments and analysis of measurements; to apply theoretical knowledge in practice.
Elective mathematical and natural scientific courses.
Elements of Chaotic Dynamics

Semester: 7
ECTS points: 3
Hours: 108
The course aims to familiarise students with the latest developments in the field of chaotic dynamics and its various applications.
The objectives of the course are to know about dynamic models with discrete and continuous time, about dynamic chaos of regular and chaotic attractors, bifurcation diagrams, fractal structures and their dimensions, different scenarios to chaos transition.
Mathematical Methods
Semester: 7
ECTS points: 3
Hours: 108
The course aims to know the main stages of mathematics development history, principles of construction, basic notions and concepts mathematics main branches.
The objectives of the course are to master new fundamental concepts that define the most important mathematical branches (such as a topological space, probability, graphs, etc.).
Mathematical Foundations of Computer Graphics
Semester: 8
ECTS points: 2
Hours: 72
The course aims to introduce the basic concepts of computer graphics, its function, and functionality in various fields of its application.
The objectives of the course are to form the skills how to use mathematical and algorithmic support of computer graphics for solving geometric problems; to learn mathematical and algorithmic support for the design of graphical applications; to acquire practical skills in building realistic spatial models.
Approximation of Functions
Semester: 8
ECTS points: 2
Hours: 72
The course aims to consider problems of functions approximation, theoretical and algorithmic foundations of computational mathematics; to form practical skills of solving applied mathematical problems on computers using modern instrument systems.
The objectives of the course are to study methods of functions approximation by easier, well-studied functions, methods, numerical differentiation and numerical integration.
MATLAB in Mathematical Studies
Semester: 7
ECTS points: 2
Hours: 72
The course aims to form skills how to build widely used mathematical models using the software MATLAB.
The objectives of the course are to master parameters calculation methods and basic characteristics of the models of any considered classes, practical skills for working with software packages of mathematical modeling, methodological analysis skills of scientific research and its results
Generalised Functions
Semester: 7

ECTS points: 2
Hours: 72
The course aims to study generalised functions and their application at differential equations solubility.
The objectives of the course are to develop the concept of "generalised function" and the basic operations on them, to study the Cauchy problem for a degenerate system of ordinary differential equations, to study conditions for transformation of a generalised solution to the classical one, to create a framework for understanding the modern mathematics foundations.
Fundamental field-oriented courses.
Mathematical Analysis
Semester: 1-4
ECTS points: 28
Hours: 1008
The course aims to introduce the basic techniques of differential and integral calculus.
The objectives of the course are to study theoretical foundations of mathematical analysis, to develop those parts of mathematical analysis whose apparatus is widely used in the most important economic and managerial courses; to obtain skills to apply independently mathematical tools for educational problem solving of managerial and economic content.
Algebra
Semester: 1-3
ECTS points: 15
Hours: 540
The course aims to familiarise with the concepts of algebra, to develop clear logical thinking.
The objectives of the course are to study theoretical foundations of algebra, to develop practically those parts of algebra whose apparatus is widely used in the most important economic and managerial courses; to obtain skills to apply independently mathematical tools for educational problem solving of managerial and economic content.
Analytical Geometry
Semester: 1-2
ECTS points: 8
Hours: 288
The course aims to form the mathematical culture of the students, to train students fundamentally in the field of geometry, to master modern geometry apparatus for later use in other fields of mathematical knowledge.
The objectives of the course are to form complex knowledge about the basics of analytic geometry; to obtain skills and abilities for simple problem solving in geometry.
Discrete Mathematics and Mathematical Logic
Semester: 3-4
ECTS points: 8
Hours: 288
The course aims to introduce the most important sections of discrete mathematics, to study the concepts, results and methods of mathematical logic.
The objectives of the course are to form proficiency in combinatorial formulas, recurrence equations, generating functions, and a detailed study of graph theory algorithms, algorithms for constructing a variety of disjunctive normal forms, and to grasp the possibilities of their practical application.

Differential Equations
Semester: 3-4
ECTS points: 8
Hours: 288
The course aims to understand basic concepts and principles of the economic information, and to use econometric methods in order to deal with ogranisational and administrative tasks.
The objectives of the course are to familiarise with the basics of differential equations; to form skills for mathematical research of economic problems; to get an idea how to apply differential equations in the economy.
Comprehensive Analysis
Semester: 4-5
ECTS points: 6
Hours: 216
The course aims to learn the basics of classical theory of functions for one complex variable.
The objectives of the course are to investigate functions differentiability of a complex variable, to calculate integrals, to apply complex analysis methods to compute integrals from real variable functions.
Functional Analysis
Semester: 5-6
ECTS points: 8
Hours: 288
The course aims to acquire theoretical knowledge in the field of functional analysis and skills for its use; to familiarise students with the initial skills of mathematical modeling.
The objectives of the course are to study the basic concepts and methods of linear and nonlinear functional analysis, to review their applications and to examine main spaces types’ morphology and types of functions spaces.
Differential Geometry and Topology
Semester: 4-5
ECTS points: 8
Hours: 288
The course aims to introduce the basic concepts of modern differential geometry, topology, and homological algebra and their applications.
The objectives of the course are to study foundations of geometry and topology which are necessary for developing other mathematical courses, and for developing practical skills of geometric problem solving; to form topological thinking, and the ability to distinguish between algebraic structures in geometric and analytical objects.
Probability Theory, Stochastic Processes
Semester: 5, 7
ECTS points: 8
Hours: 288
The course aims to introduce the basic concepts and methods of probability theory, to form skills how to build and examine probabilistic models of real economic processes.
The objectives of the course are to study theoretical foundations of probability theory and stochastic processes, to obtain skills to apply independently mathematical tools for educational problem solving of managerial and economic content.

Life Safety
Semester: 3
ECTS points: 2
Hours: 72
The course aims to form the idea about the unity between effective professional activity and requirements for security and human safety, to obtain skills for appropriate and safe behavior in daily life and in extreme conditions.
The objectives of the course are to give knowledge to make decisions for the protection of staff and civilians from the consequences of accidents, disasters, natural disasters; to master the methods of emergency situations forecasting and to examine natural disasters, major accidents and disasters affecting factors, to build skills of parameters control and negative impacts levels.
Compulsory field-oriented courses.
Workshop on Computer
Semester: 5-6
ECTS points: 8
Hours: 288
The course aims to familiarise students with the basic principles of programming, to teach how to use the software package Maple to solve physical problems.
The objectives of the course are to familiarise students with the basic principles of programming, with the terminology used in the numerical modeling, with different numerical methods for solving mathematical problems, to define the applicability limits of various techniques for solving numerical problems, to familiarise with the software package Maple; to form the skills of writing and debugging programs, and writing programs layout.
Elements of Field Theory
Semester: 4
ECTS points: 3
Hours: 108
The course aims to familiarise students with the elements of the field theory required for engineering and research problem solving, focused on new technologies the development.
The objectives of the course are to give information how to build differential equations systems to describe different fields, to teach calculating methods of fields characteristics from specified sources, to give an idea of mathematical formulation and the ways of problem solving for determining the characteristics of the field sources for a given physical field.
Partial Differential Equations
Semester: 5-6
ECTS points: 9
Hours: 324
The course aims to know partial differential equations, to introduce the present state of the numerical methods theory for solving various problems in differential equations and the most efficient numerical methods for solving boundary problems for partial differential equations.
The objectives of the course are to learn the basic operations with partial differential equations and their properties; to examine the generalised formulation of the Cauchy problem for ordinary differential equations and partial differential equations, to master the methodology of solving and research of boundary and initial value problems for partial differential equations.
Number Theory

Semester: 1
ECTS points: 3
Hours: 108
The course aims to study the number theory, to familiarise with the basic directions and methods of theoretical and numerical studies; to demonstrate the possibilities how to apply these methods in various fields of mathematics and its applications.
The objectives of the course are to teach students the basic theoretical and numerical methods for solving problems that arise both in number theory and the other mathematical courses and practices; to introduce the history of the number theory, and Russian scientists’ contribution to this area of mathematics.
Mathematical Statistics
Semester: 6
ECTS points: 3
Hours: 108
The course aims to introduce the basic concepts and methods of mathematical statistics used in physics, economics, biology, and other areas of practice.
The objectives of the course are to learn the theoretical foundations of modern mathematical statistics, to obtain the skills for solving mathematical problems that are models for finding managerial solutions.
Optimization Methods
Semester: 7
ECTS points: 4
Hours: 144
The course aims to master basic techniques of mathematical modeling of optimization theory, to develop skills for independent mathematical tasks analysis.
The objectives of the course are to familiarise students with the application models that are experiencing the problem of nonlinear optimization, with methods that lead application tasks to nonlinear optimization, as well as with modern algorithms for unconditional, conditional and global optimization problem solving.
The Riemann Geometry
Semester: 3
ECTS points: 4
Hours: 144
The course aims to know the theory of Riemannian manifolds for further use in other areas of mathematical knowledge.
The objectives of the course are to study the basic concepts and theorems of the Riemann geometry, the concept of linear connection, the curvature of the Riemannian metric, the
Riemannian connection, to master the methods of symbolic computation with the tensors in the
Maple computer mathematics.
Financial Markets
Semester: 7
ECTS points: 4
Hours: 144
The course aims to obtain basic knowledge in the field of financial markets.
The objectives of the course are to study the methods that will be useful in implementing of professional competence, to obtain skills for self-education in the field of financial markets.
Elective field-oriented courses.

Approximation Theory of Functions
Semester: 7
ECTS points: 3
Hours: 108
The course aims to introduce the classical and modern methods of problem solving in approximation theory: interpolation, best approximation, splines, and wavelets.
The objectives of the course are to introduce the classical results of approximation theory, to study and develop the methods and approaches to solving mathematical problems by means of approximation theory.
Introduction to r-adic Analysis
Semester: 7
ECTS points: 3
Hours: 108
The course aims to introduce the theory of p-adic numbers, and non-Archimedean geometry.
The objectives of the course are to introduce the results of the integral calculus, the theory of generalised functions and pseudo differential operators over the r-adic numbers field, to describe the application of r-adic analysis to the quantum field theory, the string theory, the quantum groups, and the theory of stochastic processes.
Whitney Topology
Semester: 8
ECTS points: 5
Hours: 180
The course aims to study algebraic and differential topology, the Whitney-Graustein theorem about the classification of smooth closed curves, the Whitney's theorems on embedding, vector bundles and singularity theory.
The objectives of the course are to study attachments and immersions, to familiarise with
Whitney theorem, calculus jets; Whitney topology in the space of smooth maps; transversality theorem; Thom transversality theorem and its consequences: Morse lemma, weak Whitney's theorem.
Mathematical Bioecology
Semester: 8
ECTS points: 5
Hours: 180
The course aims to give basic knowledge and understanding of mathematical modeling possibilities, classification of mathematical models and their applicability to the bio-ecology.
The objectives of the course are to construct a mathematical model of ecological processes, to study methods of mathematical models investigation, the concept of the model adequacy and solutions analysis from the practical point of view.
Introduction to Analytic Number Theory
Semester: 8
ECTS points: 4
Hours: 144
The course aims to state how to apply methods computer algebra systems for implementing number-theoretic algorithms, to study methods for implementing algebra and number theory algorithms, to introduce applications of number theory and the theory of elliptic curves in modern cryptography.

The objectives of the course are to learn the techniques of the number-theoretic algorithms, computational algorithms in finite fields, to present basic calculation algorithms on elliptic curves, and to teach students techniques of implementing open key cryptosystems on elliptic curves.
Mathematics of Fractals
Semester: 8
ECTS points: 4
Hours: 144
The course aims to familiarise students with the fractals and fractal structures and their role in the mathematical knowledge.
The objectives of the course are to give an idea of geometrical and physical fractal objects, fractal sets and their functions; to examine the fractal dimensions, fragmentation, and the hierarchical ogranisation of fractals; to familiarise with the peculiarities of fractals physical properties.
Use of Information Technology for Teaching Mathematics
Semester: 8
ECTS points: 4
Hours: 144
The course aims to study the theory and practice of various software products (generic and specialised) in teaching of mathematics.
The objectives of the course are to familiarise students with various kinds of applied software for the education sector, to form an expanded system of knowledge about information modeling.
Wavelets
Semester: 8
ECTS points: 4
Hours: 144
The course aims to present the fundamentals of the wavelet transforms theory, to introduce modern methods of approximation and functional recovery, signal and image compression and processing.
The objectives of the course are to study the basic concepts, definitions and propositions of the wavelet transforms theory, multiresolution analysis, to obtain skills for constructing the classical wavelets, to study how to apply wavelet transforms for approximation and functional recovery, signal and image compression and processing.