“Discrete Mathematics: An Open Introduction” is an educational text that provides readers with a comprehensive introduction to the fascinating world of discrete mathematics. The book is aimed at undergraduate students who are interested in mathematics or computer science, but it is also accessible to anyone who wants to develop their problem-solving skills or learn more about the foundations of computer science.
The book is divided into six main chapters, each covering a different area of discrete mathematics. The first chapter is an introduction to the field, providing a brief history of discrete mathematics and an overview of the topics that will be covered throughout the book. This chapter also includes a discussion of the importance of logic and proofs in mathematics.
The second chapter focuses on sets and functions. Readers will learn about set operations, the cardinality of sets, and the properties of functions. The chapter also covers relations, which are used to model a wide variety of real-world situations.
The third chapter is devoted to the study of integers and their properties. Readers will learn about divisibility, prime numbers, and the Euclidean algorithm, which is used to find the greatest common divisor of two integers. The chapter also includes a discussion of modular arithmetic, which has important applications in computer science and cryptography.
The fourth chapter covers combinatorics, which is the study of counting and arrangements. Readers will learn about permutations, combinations, and the binomial theorem. The chapter also includes a discussion of generating functions, which are used to count the number of objects with certain properties.
The fifth chapter focuses on graph theory, which is the study of networks. Readers will learn about graph terminology, connectivity, and graph algorithms. The chapter also includes a discussion of planar graphs and their properties.
The final chapter is an introduction to formal languages and automata theory. Readers will learn about regular languages, context-free languages, and Turing machines. The chapter also includes a discussion of the Church-Turing thesis, which states that any computable function can be computed by a Turing machine.
Overall, “Discrete Mathematics: An Open Introduction” is an excellent resource for anyone interested in learning more about this fascinating field. The book is well-organized and clearly written, with numerous examples and exercises that help readers develop their problem-solving skills. Whether you are a student of mathematics or computer science, or simply someone who wants to learn more about the foundations of these fields, this book is an essential read.