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Supplementary sections of operations research and probability theory

ДВС.3.01

Вибіркова дисципліна для ОП

First

2023/2024

6 Semester

5

LO08. Combine mathematical and computer modeling techniques with informal expert analysis procedures to find optimal solutions. 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. PLO23.3. 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. PLO24.3. Be able to independently analyze the relevant subject area, be able to develop mathematical and structural algorithmic models.

Full-time form

To successfully learn the discipline “Supplementary sections of operations research and probability theory” 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. They should be able to (a) apply classical methods of Calculus and Probability Theory; (b) seek information in open sources and properly analyze it.

Types of paradoxes: logical, mathematical (probabilistic, statistical, related to infinity, geometrical, topological, physical, chemical, philosophical, economical and others. Birthday problem, 100 prisoners problem, three prisoners problem, two envelopes problem, Monty Hall problem, intransitive dice, Berkson's paradox, Bertrand paradox (probability), Bertrand's box paradox, Boy or Girl paradox, Parrondo's paradox, Simpson's paradox, Sleeping Beauty problem, St. Petersburg paradox. Methods for solving problems of integer linear programming. The method of branches and borders. The task of the traveling salesman problem. Examples, Applications. Exact methods of solving the traveling salesman problem. Approximate methods for solving the traveling salesman problem. Nonlinear programming problems. Gradient methods. The method of possible directions for solving problems of convex programming.

M1. 1. Gabor J. Szekely. Paradoxes in Probability Theory and Mathematical Statistics. Akademiai Kiado, 1986. 250p. 2. https://uk.wikisko.ru/wiki/List_of_paradoxes 3. Jordan M. Stoyanov Counterexamples in Probability: Third Edition. 2013, 352 p. 4. Romano J. P.; Siegel A. F. Counterexamples in probability and statistics. 1986 5.https://uk.wikipedia.org/wiki/%D0%A1%D0%BF%D0%B8%D1%81%D0%BE%D0%BA_%D0%BF%D0%B0%D1%80%D0%B0%D0%B4%D0%BE%D0%BA%D1%81%D1%96%D0%B2 M2. 1. Aho, A. Data structures and algorithms / A. Aho, J. Hopcroft, D. Ullman. - М .:Williams Publishing House, 2001. - 384 p. 2. 2. Gary, M. Computers and difficult problems / M. Gary, D.Johnson. - M .: Mir, 1982. - 419 p. 3. Goldschmidt O., Laugier A., Olinick E.V. SONET/SDH ring assignment with capacity constraints // Discrete Applied Mathematics, 2003. Vol. 129. P. 99–128 4. The traveling salesman problem and its variations / G. Gutin, A. Punnen, (eds.) // Combinatorial optimization. – Nowell: Kluwer, 2002.

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

Intermediate assesement: The maximal number of available points is 60. Personalized take-home assignment for submission Final assessment (in the form of exam): The maximal number of available points is 40. The form of exam: writing. The types of assignments are 2 writing assignments

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