A First Course in Discrete Mathematics

Book Synopsis: 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

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