evelopment and analysis of a statistical model of the Kollatz algorithm
Students Name: Shymanskyi Denys Adamovych
Qualification Level: magister
Speciality: System Design
Institute: Institute of Computer Science and Information Technologies
Mode of Study: full
Academic Year: 2021-2022 н.р.
Language of Defence: ukrainian
Abstract: Shymanskyi D.A., Kosobutskyi P.S. (head). Development and analysis of a statistical model of the Kollatz algorithm. Master’s thesis. - National University "Lviv Polytechnic", Lviv, 2021. Extended annotation. Topicality: The study of such problems is not just to solve the problem, but to develop methods that can be used to solve similar problems. This particular problem may have applications outside of mathematics, but research may not be relevant at this time, but may be needed in the near future. Mathematics in general has ceased to be just a subject that is being studied for direct application. Often the methods or ideas used in proving a theorem can be applied to other problems. This hypothesis must be tested using mathematical methods of statistical modeling. Along with the study of the theoretical foundations and methods of mathematical statistics, the skills of practical use of statistical software are important. After all, modern statistical data processing is almost impossible without certain computer programs. The purpose of the thesis: Development and analysis of the statistical model of the Kollatz algorithm. Task: • Analyze the theoretical part concerning the history of the hypothesis, the algorithm, the possibilities of implementation and methods of calculating the proof of the hypothesis; • Investigate the tools that will be used to develop a statistical model of the Kollatz algorithm and conduct a comparative analysis; • Develop a statistical model that will become the basis of the study; Object of study: • Sequence Kollatz. • Ways to implement modeling of the Kollatz algorithm. • Methods of processing and evaluation of statistical characteristics. Subject of study: The subject of research is the methods of practical implementation for the development of a statistical model of the Kollatz algorithm, methods for modeling a statistical model. This note contains the following material: In the first section of the thesis were considered and analyzed what is Kollatz’s hypothesis. Examples of attempts to solve this hypothesis are given. Some of the sequences and graphs of Kollatz are considered, the dependences in this problem are given. The second section considered the tools and methods that can be used as a basis for building a statistical model, analyzed and selected the system, which will be the basis for the development of the program. A list of modeling methods was compiled, from which the most optimal for work was chosen. The description of the systems considered for use in the development of the program, their functionality and characteristics and a comparative analysis with analogues. The third section presented the progress of the work. Developed block diagram of the program. Also in the third section the program code in the system of mathematical calculations - Matlab was developed and the course of work in the development of the statistical model is given. Subsequently, a number of calculations and checks on the type of distribution were performed. Master’s thesis contains 80 pages, 11 tables, 31 figures, a list of used sources of 65 items, 2 appendix. Key words: Matlab, Kollatz, Kollatz hypothesis, statistical model, statistical characteristics, distribution, system, modeling, mathematical, hypothesis, problem, probability, indicators, experiment. 1 Wentzel E.S. Probability theory [Text]. E.S. Wentzel M: Nauka., 1969.- 576 p. 2. Storm R. Probability theory. Mathematical statistics [Text]. Statistical quality control. R. Storm - M .: Izd-vo "Mir", 1970.- 368 p. 3. Gmurman VE Probability theory and mathematical statistics [Text]: A textbook for universities. V.E. Gmurman - 8th edition, Moscow: Higher School, 2003. - 479 p. 4. Gmurman VE Guide to solving problems in probability theory and statistics [Text]: A textbook for universities. V.E. Gmurman - M .: Higher School, 2002. - 405 p.