Wednesday, June 19, 2019

Schaum's Outline of Theory and Problems of Discrete Mathematics

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Discrete mathematics, the study of finite systems, has become increasingly important as the computer age has advanced. The digital computer is basically a finite structure, and many of its properties can be understood and interpreted within the framework of finite mathematical systems. This book, in presenting the more essential material, may be used as a textbook for a formal course in discrete mathematics or as a supplement to all current texts.

The first three chapters cover the standard material on sets, relations, and functions and algorithms. Next come chapters on logic, counting, and probability.We then have three chapters on graph theory: graphs, directed graphs, and binary trees. Finally there are individual chapters on properties of the integers, languages, machines, ordered sets and lattices, and Boolean algebra, and appendices on vectors and matrices, and algebraic systems. The chapter on functions and algorithms includes a discussion of cardinality and countable sets, and complexity. The chapters on graph theory include discussions on planarity, traversability, minimal paths, andWarshall’s and Huffman’s algorithms.We emphasize that the chapters have been written so that the order can be changed without difficulty and without loss of continuity.

Each chapter begins with a clear statement of pertinent definitions, principles, and theorems with illustrative and other descriptive material. This is followed by sets of solved and supplementary problems. The solved problems serve to illustrate and amplify the material, and also include proofs of theorems. The supplementary problems furnish a complete review of the material in the chapter. More material has been included than can be covered in most first courses. This has been done to make the book more flexible, to provide a more useful book of reference, and to stimulate further interest in the topics.

CHAPTER 1: Set Theory
CHAPTER 2: Relations
CHAPTER 3: Functions and Algorithms
CHAPTER 5: Techniques of Counting
CHAPTER 6: Advanced Counting Techniques, Recursion
CHAPTER 7: Probability
CHAPTER 8: Graph Theory
CHAPTER 9: Directed Graphs
CHAPTER 10: Binary Trees
CHAPTER 11: Properties of the Integers
CHAPTER 12: Languages, Automata, Grammars
CHAPTER 13: Finite State Machines and Turing Machines
CHAPTER 14: Ordered Sets and Lattices
CHAPTER 15: Boolean Algebra
APPENDIX A. Vectors and Matrices
APPENDIX B. Algebraic Systems

Author Details
Temple University

University of Virginia

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