Description

Preface Discrete mathematics is a part of mathematics that deals with discrete structures. The term "discrete" should be understood here in the sense of "not continuous" or "separated from each other" (as opposed to "discreet" meaning "unobtrusive"). In a more restrictive sense, the term "discrete" is also understood as "finite", indicating that the objects of interest in discrete mathematics are finite structures and processes. Thus, discrete mathematics is fundamentally different from calculus, theory of differential equations, or topology, which are mainly concerned with continuous concepts and infinite objects. More specifically, discrete mathematics is based on logic, set theory, and number theory, with its main branches including combinatorics and graph theory. It is applied in areas at the intersection of mathematics and computer science such as algorithms, cryptography, coding theory, and computational theory. Discrete mathematics is essential for understanding the theoretical foundations of computer science. A deep understanding of discrete mathematics allows for efficient solving of complex computing problems and the creation of effective algorithms. This textbook aims to introduce the key concepts of discrete mathematics to all those interested in this field, particularly first-year undergraduate students in computer science. By learning the fundamentals of discrete mathematics, students develop problem-solving skills applicable in various real-life scenarios. The material for the script "Discrete Mathematics for Computer Science Students" is selected to organize knowledge in this field acquired in high school and to supplement it with topics necessary for further studies in computer science. This script covers the basics of logic (Chapter 1), elements of number theory (Chapter 2), and an introduction to combinatorics (Chapter 3). Each chapter is supplemented with a set of exercises, most of which also include answers. The entire work is complemented by sample exam questions (Chapter 4).