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Modern problems of applied mathematics

Вибіркова дисципліна для ОП

Second

2021/2022

4 Semester

5

PLO13.3. Be able to use professional knowledge, skills and abilities in the field of fundamental sections of mathematics and computer science for research of real processes of different nature; PLO15.3. Be able to implement appropriate automated systems, operate them, performing the necessary calculations

Distance form

To successfully learn the discipline “Modern problems of applied mathematics” the student should satisfy the following requirements. Module 1 (Applied Linear Algebra) is fluent in the material of the normative courses "Algebra and Geometry", "Mathematical Analysis", "Functional Analysis". In particular, be able to perform basic operations with matrices and polynomials, know the basic concepts of the theory of linear spaces (linear dependence, basis, linear operator). The student must also have basic programming skills. Module 2 (Applications of the theory of random evolutions) must be able to use the basic apparatus of mathematical analysis, probability theory and theory of random processes, justify the possibility of changing the order of operations, such as interchanging of limits and integrals, etc .; know the basic concepts of mathematical analysis, probability theory, as well as master the methods of probability theory.

The course "Modern problems of applied mathematics" are: Module 1 (Applied linear algebra). Acquaintance with the applications of linear algebra to various fields of knowledge (physics, chemistry, economics, computer graphics, coding theory and cryptography, biology, medicine, etc.). Module 2 (Applications of the theory of random evolutions). Acquaintance with the applications of the theory of random evolution, research methods, as well as the technical apparatus inherent in this field of knowledge.

1. Rokitsʹkyy I.O. Zastosuvannya liniynoyi alhebry. – Vinnytsya: Vyd. Hlavatsʹka R.V., 2012. – 240 s. 2. Nicholson, W. Keith. Linear algebra with applications. -- 7th ed. -544p 3. Howard Anton, Chris Rorres. Elementary linear algebra : applications version. -- 11th edition 4. Koroliuk V.S. Stochastic systems in merging phase space / V.S. Koroliuk, N. Limnios. - Singapore:World Scientific Publishing Company, 2005. - 348 p. 9. Swishchuk A.V. Evolutions of Biological Systems in Random Media. Limit Theorems and Stability / A.V. Swishchuk, J. Wu. - Kluwer AP, Dordrecht, The Netherlands, 2003. - 218p. 10. Zavorotynsʹky A.V. Prykladana liniyna alhebra: Elektronnyy navchalʹnyy posibnyk.-2022.- s. http://do.unicyb.kiev.ua/index.php/uk/2011-01-03-10-24-53/ docx 11. Samoylenko I.V. Elementy teoriyi vypadkovykh evolyutsiy: Elektronnyy navchalʹnyy posibnyk.-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, consultations, test works, independent work.

Semester assessment: Maximum number of points that can be obtained by a student: 60 points: 1. Test work №1 PLO 11, PLO 15.3 - 30/18 points. 2. Test work № 2: PLO 11.3, PLO 15.3 - 30/18 points. Final assessment (in the form of an exam): Maximum number of points that can be obtained by a student: 40 points. Learning outcomes to be evaluated: , PLO 11.3, PLO 15.3. Form of conducting: written. Types of tasks: 4 written tasks (2 theoretical questions and 2 practical tasks). A student receives an overall positive grade in the discipline if his grade for the exam is not less than 24 (twenty four) points. A student is admitted to the exam if during the semester he: scored at least 36 points; performed and timely submitted at least 2 (two) independent works from the list of proposed works;

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