Discrete Mathematics

Major: Computer Engineering
Code of subject: 6.123.00.O.008
Credits: 6.00
Department: Specialized Computer Systems
Lecturer: Popovych Roman Bogdanovych
Semester: 1 семестр
Mode of study: денна
Learning outcomes: Know and understand the scientific principles underlying the functioning of computer tools, systems and networks. As a result of studying the academic discipline, the student must be able to demonstrate the following learning outcomes: 1. know and apply properties of operations and basic identities of algebra of sets; 2. know and be able to investigate the mapping properties from one set to another; 3. to know and be able to investigate the properties of a relation given on one set; 4. know and be able to investigate the properties of a given algebra (sets with a given binary operation on it); 5. be able to find out the mapping properties from one algebra to another algebra; 6. be able to build for a given connected graph its skeleton tree of minimum (maximum) weight; 7. be able to apply a heuristic algorithm to obtain the correct coloring of a given connected graph.
Required prior and related subjects: Higher mathematics, part 1,2, Computer logic, Theory of information and coding, Information protection in computer systems, Algorithms and computing models
Summary of the subject: Discipline "Discrete Mathematics" aims to form in students a systematic (axiomatic) approach to the study of processes and phenomena; their acquisition of mathematical knowledge necessary, in particular, for the study of further disciplines: "Computer logic", "Theory of information and coding", "Algorithms and models of calculations", "Protection of information in computer systems". For future specialists, mathematics should become a method of thinking, a means of forming and organizing concepts. The study of the academic discipline involves lectures and practical classes and laboratory work. Lectures cover topics grouped into three sections: elements of set theory, elements of abstract algebra, elements of graph theory. Practical classes and laboratory works form the skills of researching the properties of sets, mappings, relations, algebras and graphs (routes on graphs, planarity, coloring). This discipline has no previous educational disciplines
Assessment methods and criteria: Oral survey during students' work in small groups during lectures, laboratory and practical classes. Written control and oral component of the exam, computer testing. During remote work (including during quarantine), an interview with students is planned during video conferences during lectures. Laboratory and practical work is carried out in the classroom or (in the case of distance learning) on a home computer. Individual reports from laboratory and practical works and written works are forwarded to the National Academy of Sciences, or to the teacher's e-mail via the communication channel @lpnu.ua. Remote classes are held on the MS Teams and ZOOM platforms. Current control – performance and defense of laboratory and practical works, oral and frontal examination. Final control - selective oral survey; assessment of activity, originality of submitted proposals, non-standard solutions, clarifications and definitions, etc.; interactive tests (Kahoot). Exam - test control and oral component. Completion of tasks by students within laboratory classes is estimated at 30 points. The performance of examination control by students of education is estimated at 70 points.
Recommended books: Basic 1. Baloga S.I., Discrete mathematics: Study guide. - Uzhhorod: PP "Autdorf-Shark", 2021. - 124 p. 2. Bardachov Yu.M., Sokolova N.A., Khodakov V.E. Discrete mathematics: Textbook - K.: Vyshcha shkola, 2002. - 287p. 3. Bondarenko M.F., Bilous N.V., Rutkas A.G. Computer discrete mathematics: Textbook - Kharkiv: SMIT Company, 2004. - 480 p. Auxiliary 1. Andriychuk V.I., Komarnytskyi M.Ya., Ishchuk Yu.B. Introduction to discrete mathematics - Lviv: Publishing center of LNU, 2003. - 254p. 2. Yemets V., Melnyk A., Popovych R. Modern cryptography: basic concepts - Lviv, BaK, 2003. - 144 p. 3. Zhuravchak L. M. Discrete mathematics for programmers: Study guide - Lviv: Lviv Polytechnic, 2019. – 420 p. 3. Kapitonova Yu.V., Kryviy S.L., Letychevskyi O.A., Lutskyi H.M., Pechurin M.K. Fundamentals of discrete mathematics: Textbook - K.: Naukova dumka, 2002. - 568p. 4. Nikolskyi Y.I., Pasichnyk V.A., Shcherbyna Yu.R. Discrete mathematics: Textbook - Lviv: Magnolia-2006, 2013. — 432 p. 5. Olijnyk L.O. Discrete Mathematics: A Study Guide. - Dniprodzerzhyn State Technical University, 2015. - 256 p. 6. Strelkovska I.V., Buslaev A.G., Kharsun O.M., Pashkova T.L., Baranov M.I., Grigoryeva T.I., Vishnevska V.M., Koltsova L.L. . Discrete Mathematics: A Study Guide. - Odesa: ONAZ named after O. S. Popova, 2010. -196 p.