Infopaket

Additional sections of mathematical analysis

ВК.1.03

Вибіркова дисципліна для ОП

Short

2024/2025

6 Semester

4

RN1. Demonstrate knowledge and understanding of the basic concepts, principles, theories of fundamental and applied mathematics and use them in practice. RN2. Possess the basic principles and methods of mathematical, complex and functional analysis ... RN14. Demonstrate the ability for self-study and continued professional development. RN15. Be able to organize one's own activities and obtain results within a limited time. RN16. Demonstrate skills in interacting with other people, the ability to work in teams. RN18. Effectively communicate information, ideas, problems and solutions with specialists and society in general. RN20. Demonstrate professional communication skills, including oral and written communication in Ukrainian and at least one other common European language.

1) Know the material of the courses "Mathematical Analysis 1", "Mathematical Analysis 2" and "Topology of the Real Line and Measure Theory", "Integral Theory", "Harmonic Analysis". 2) Be able to solve problems within the basic university courses "Mathematical Analysis 1", "Mathematical Analysis 2", "Topology of the Real Line and Measure Theory", "Integral Theory", "Harmonic Analysis".

Examples and counterexamples for functions of one variable 1 Real line 2 Continuity and limit 3 Derivative 4 Riemann integrability 5 Sequences and series 6 Uniform convergence 7 Sets and measure on the real line Examples and counterexamples for functions of many variables 1 Functions of two variables 2 Sets on the plane 3 Area 4 Metric and topological spaces 5 Function spaces

Main 1. Gelbaum Bernard R., Olmsted John M. H. Counterexamples in Analysis. – Courier Corporation, 2003. – 195 p. 3. Rajwade A. R., Bhandari A. K. Surprises and Counterexamples in Real Function Theory. – HINDUSTAN, 2007. – 301 p. 4. Wise Gary L., Hall Eric B. Counterexamples in Probability and Real Analysis. – Oxford University Press, 1993. – 224 p. 5. Schilling René L., Kühn Franziska Counterexamples in Measure and Integration. – Cambridge University Press, 2021. – 431 p.

Lectures. Consultations. Practical (modular work). Independent work.

Forms of student assessment: Semester assessment: 1) modular test paper I – 30 points 2) modular test paper II – 30 points 3) additional points – up to 15 points Summary assessment in the form of a credit: – 40 points

Ukrainian