Infopaket

Mathematical models of cybernetics

ВК.3.02

Вибіркова дисципліна для ОП

Second

2023/2024

4 Semester

9

PRN 1. Demonstrate knowledge and understanding of basic concepts, principles, theories of fundamental and applied mathematics and use them in practice PRN 2. Have the basic principles and methods of mathematical, complex and functional analysis, linear algebra and number theory, analytical geometry, theory of differential equations, theory of equations of mathematical physics, probability theory, mathematical statistics and random processes, numerical methods PLO21.3. Understand the fundamental areas of mathematics and computer science, to the extent necessary for learning mathematical disciplines, applied disciplines and using their methods in a chosen profession. PLO22.3. Understand the main areas of mathematical logic, theory of algorithms and computational theory, programming theory, probability theory and mathematical statistics.

Full-time form

To successfully learn the discipline the student should satisfy the following requirements. They know (a) fundamentals of mathematical methods for construction, verification and investigation of qualitative characteristics of deterministic and stochastic mathematical models; (b) classical methods of Calculus, Algebra and Probability Theory. They can (a) investigate qualitative characteristics of available mathematical models; (b) apply classical methods for solving applied problems in deterministic and stochastic models; (c) justify the possibility of changing the order of operations, such as permutation of boundary and integral symbols, etc . They should be able to (a) apply classical methods of Calculus and Probability Theory and theory of random processes; (b) seek information in open sources and properly analyze it.

Distribution of ordinal statistics. Classic representations for ordinal statistics. Moments of ordinal statistics. Extreme types theorem. Hinchin's theorem and other auxiliary results. Maximum-stable distributions and their representation. Relationship between maximum distributions in the maximum scheme and maximum stable distributions. General theory of areas of attraction. Necessary and sufficient conditions in Gnedenko's theorem. Verification of homogeneity, criteria for anomalous observations. Abnormal observations for failure-to-failure type data. The problem of extreme water consumption in rivers. Application of boundary theorems for extremums in queuing theory and reliability theory. Acquaintance with the basics of the theory of random evolution, research methods, as well as the technical apparatus inherent in this field of knowledge.

1. Resnick S.I. Extreme Values, Regular Variation and Point Processes. - Berlin: Springer, 1987. 2. Matsak Í.K., Yelementi teoríí̈ yekstremal'nikh znachen' , Kií̈v , KOMPRINT, 2014. 3. Koroliuk V.S. Stochastic systems in merging phase space / V.S. Koroliuk, N. Limnios. - Singapore:World Scientific Publishing Company, 2005. - 348 p. 4. Pinsky M. Lectures on random evolutions/M. Pinsky. - Singapore: World Scientific, 1991. - 136 p. 5. Samoylenko Í.V. Yelementi teoríí̈ vipadkovikh yevolyutsíy: Yelektronniy navchal'niy posíbnik.-2017.- 95 s. http://do.unicyb.kiev.ua/index.php/uk/2011-01-03-10-24-53/240-2017-09-07-15-21-46 docx

Lectures, seminars, consultations, test works, independent work.

Intermediate assesement: The maximal number of available points is 60. Test work no. 1: 30/18 points. Test work no. 2: 30/18 points. Final assessment (in the form of test): The maximal number of available points is 40. The form of test: writing. The types of assignments are 4 writing assignments (2 theoretical and 2 practical).

Ukrainian