6 semester


Title of the discipline (basic disciplines)





Course of Study


3, Mathematics (economic activities)


Semester of training
(for each semester a separate table)




Amount of credits
(academic plan)




Full name of the lecturer


Leonov Nikolay Nikolaevich


Objectives of studying the discipline


To create a knowledge base and skills for students in the field of probability theory and mathematical statistics

acquaint students with the basic principles of probability theory and examples of their applications

further formation of students’ skills in abstract mathematical thinking and the ability to apply it in specific tasks, enhancing their mathematical culture

As a result of the study, the student should be able to:

be able to:

use the basic laws of random phenomena;

apply methods of probability theory and mathematical statistics in other sciences;




Algebra and number theory,

Discrete Math,

Analytic geometry,

Mathematical analysis,

Differential equations,

Functional Analysis


Contents of the discipline



Theme 1. Linear operators in normed spaces

1.1. The space of bounded linear operators

1.2. Inverse operators

Theme 2. Continuous linear functionals and adjoint operators

2.1. Continuous linear functionals

2.2. Conjugate operators.

2.3. Topologies in the original and dual spaces.

Theme 3. Compact operators

3.1. The general theory of compact operators

in Hilbert and Banach spaces.

3.2. Equations with compact operators

3.3. Integral equations of Fredholm

Theme 4. Operators in Hilbert spaces

4.1. Conjugate and self-adjoint operators in Hilbert spaces


Recommended literature



Main literature:

1. Antonevich AB, Radyno Ya.V. Functional analysis and integral equations. 2 nd ed., Revised. and additional. Minsk, Publishing house of the Belarusian State University, 2006.

2. Antonevich AB, Mazel M.Kh., Radyno Ya.V. Functional analysis and integral equations. Tutorial. Minsk, Publishing house of the Belarusian State University, 2011.

3. Kolmogorov AN, Fomin S.V. Elements of the theory of functions and functional analysis. M., Fizmatlit, 2004.

4. Lyusternik LA, Sobolev VI Short course of functional analysis. M., Higher School, 1982.

5. Trenogin V.A. Functional analysis. M., Fizmatlit, 2002.

Additional literature:

1. Berezanskii Yu.M., Us G.Yu., Sheftel Z.G. Functional analysis. Lecture course. Kiev, High school, 1990.

2. Kantorovich LV, Akilov GP Functional analysis. St. Petersburg, Nevsky Dialect, BHV-Petersburg, 2002.

3. Kirillov AA, Gvishiani AD Theorems and problems of functional analysis. M., Science, 1979.

4. Antonevich AB, Knyazev PN, Radyno Ya.V. Tasks and exercises on functional analysis. Minsk, Higher School, 1978.


Teaching Methods



interactive methods of teaching (working in small groups (team), problem training) are organized taking into account the inclusion in the learning process of all students of the group. Joint activity means that each student makes his own individual contribution, in the course of the work there is an exchange of knowledge, ideas, methods of activity. Organized individual, steam and group work. Interactive methods are based on the principles of interaction, activity of trainees, reliance on group experience, mandatory feedback


Language of instruction







Conditions (requirements), routine monitoring



– test;
– Colloquium



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