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Functional Analysis

Code – 230100   Information and computer science; section: Software of computer equipment and automation systems

Qualification (degree) – Master

Description of course modules (sections, subjects):

  1. Concept of an infinite-dimensional linear space.
  2. Techniques for introduction of a metric and a norm in an infinite-dimensional space.
  3. Linear operator in infinite-dimensional spaces.
  4. Adjoint spaces and adjoint operators.
  5. Key principles of a linear functional analysis.
  6. Convexity and a geometrical approach to theorems on prolongation of functionals.
  7. Optimization problems, Kuhn-Tucker theorems in finite-dimensional and infinite-dimensional spaces.

Syllabus of the course:

Objective of the course: introduction of students to key concepts and results of the functional analysis, application of functional analysis methods and algorithms based on such methods to solutions of scientific and application problems.

Tasks of the course

The course is aimed at:

  • study of fundamental mathematical and applied concepts  of infinite-dimensional linear space, topological structures, operators and optimization problems in an infinite-dimensional space;
  • acquiring of skills to put problems of classical mathematical analysis into an abstract form allowing to represent and solve them in functional and analytical terms;
  • acquiring of skills to apply a geometric approach to problems of finite-dimensional and infinite-dimensional functional analysis by identification of their geometrical character;
  • introduction to application of methods of functional analysis to problems of natural science and engineering.

The course in included in optional courses of a general scientific cycle attributed to the master’s degree educational standard.

As a result of studying the course a student should:

  • know main concepts of functional analysis;
  • be able to apply in practice results of functional analysis in mathematical problems;
  • have skills of application of functional analysis methods to problems of natural science and engineering;
  • show ability and readiness to solving problems of functional analysis as applied to various subject areas.

Teaching methods:

  • lectures,
  • laboratory work,
  • students’ independent work performed according to the teacher’s task in classrooms and on an extracurricular basis, including use of technical training aids (compulsory),
  • tutorials.

Total hours – 108.

Total credits – 3.

Laboratory work – 1/36.

Form of interim assessment – pass/fail exam.

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