Selected Problems in Discrete Mathematics

Contents: 1. Boolean functions: methods of defining and basic properties. 2. Closed classes and completeness. 3. K-Valved logics. 4. Graphs and networks. 5. Fundamentals of coding theory. 6. Finite automatons. 7. Fundamentals of the algorithm theory. 8. Elements of combinatorial analysis. This collection of problems is intended as an accompaniment to a course on discrete mathematics at the universities. Senior students and graduates specializing in mathematical cybernetics may also find the book useful. Lecturers can use the material for exercise during seminars. The material in this book is based on a course of lectures on discrete mathematics delivered by the authors over a number of years at the Faculty of Mechanics and Mathematics, and later at the Faculty of Computational mathematics and Cybernetics at Moscow State University. The reader can use Introduction to Discrete Mathematics by S. Yablonsky as the main text when solving the problems in this collection. The book consists of eight chapters. Hints and answers are provided for most (but not all) problems. Solutions are given in a concise form in the form of notes, and trivial conclusions are omitted. In some cases, only the outlines of solutions are presented. The exercise in the book have various origins. Most of the material is traditional and specialists on discrete mathematics are all too familiar with such problems. However, it is practically impossible to trace the origin of the problems of this kind.…