A First Course in Discrete Mathematics

About this book

This highly regarded work fills the need for a treatment of elementary discrete mathematics that provides a core of mathematical terminology and concepts as well as emphasizes computer applications. Includes numerous elementary applications to computing and examples with solutions. Title of related interest by Waveland Press: Buckley-Lewinter Introductory Graph Theory with Applications (ISBN 9781478611752). 1. Number Systems The Binary System / The Octal and Haxadecimal Systems / The Integers / The Real Numbers / Case Study: Computer Arithmetic: Binary Numbers / Case Study: Computer Arithmetic: Floating-Point Numbers / Case Study: Computer Arithmetic: Floating-Point Arithmetic / Case Study: Memory Addressing and Data Encoding 2. Sets and Logic Sets and Elements / Subsets / Venn Diagrams / Intersections Unions and Complements / Conjunction Disjunction and Negation / Conditional and Biconditional Statements / Tautologies and Contradictions / Logical Implication and Decision Tables / Case Study: Searching and Sorting 3. Combinatorics Mathematical Induction / Permutations / Combinations / Binomial Coefficients / Distributions / Case Study: Correctness of Algorithms / Case Study: Introduction to Algorithm Analysis 4. Probability Finite Probability / Conditional Probability and Independence / Compound Experiments and Repeated Trials / Random Variables and Expected Value / Case Study: Random Numbers and Simulation 5. Relations and Functions Relations / Functions / Graphs of Functions / Three Classes of Functions / Operations on Functions: Inverses / Case Study: Computer Functions / Case Study: Algorithm Analysis: Orders of Magnitude / Case Study: Cryptography 6. Vectors and Matrices Matrices and Arrays / Matrix Multiplication / The Inverse of a Matrix and Determinants / Case Study: Stacks Queues and Deques / Case Study: Implementation and Comparison of Sorting Algorithms 7. Boolean Algebra Boolean Algebras and Their Properties / Boolean Functions / Karnaugh Maps and Prime Implicants / Minimizing Boolean Functions and Expressions / Case Study: Switching Theory 8. Graph Theory Graphs and Digraphs / Basic Definitions / Classes of Graphs / Matrices Associated with Graphs / Connectivity / Traversing Graphs / Case Study: Heap Sort / Case Study: The Critical Path Method