Discrete mathematics / Richard Johnsonbaugh.

Includes bibliographical references and index.

Table of contents Front Cover; List of Symbols; Title Page; Copyright Page; Contents; Preface; 1 Sets and Logic; 1.1 Sets; 1.2 Propositions; 1.3 Conditional Propositions and Logical Equivalence; 1.4 Arguments and Rules of Inference; 1.5 Quantifiers; 1.6 Nested Quantifiers; Problem-Solving Corner: Quantifiers; Chapter 1 Notes; Chapter 1 Review; Chapter 1 Self-Test; Chapter 1 Computer Exercises; 2 Proofs; 2.1 Mathematical Systems, Direct Proofs, and Counterexamples; 2.2 More Methods of Proof; Problem-Solving Corner Proving Some Properties of Real Numbers; 2.3 Resolution Proofs; 2.4 Mathematical Induction. Problem-Solving Corner Mathematical Induction2.5 Strong Form of Induction and the Well-Ordering Property; Chapter 2 Notes; Chapter 2 Review; Chapter 2 Self-Test; Chapter 2 Computer Exercises; 3 Functions, Sequences, and Relations; 3.1 Functions; Problem-Solving Corner: Functions; 3.2 Sequences and Strings; 3.3 Relations; 3.4 Equivalence Relations; Problem-Solving Corner: Equivalence Relations; 3.5 Matrices of Relations; 3.6 Relational Databases; Chapter 3 Notes; Chapter 3 Review; Chapter 3 Self-Test; Chapter 3 Computer Exercises; 4 Algorithms; 4.1 Introduction; 4.2 Examples of Algorithms. 4.3 Analysis of AlgorithmsProblem-Solving Corner Design and Analysis of an Algorithm; 4.4 Recursive Algorithms; Chapter 4 Notes; Chapter 4 Review; Chapter 4 Self-Test; Chapter 4 Computer Exercises; 5 Introduction to Number Theory; 5.1 Divisors; 5.2 Representations of Integers and Integer Algorithms; 5.3 The Euclidean Algorithm; Problem-Solving Corner Making Postage; 5.4 The RSA Public-Key Cryptosystem; Chapter 5 Notes; Chapter 5 Review; Chapter 5 Self-Test; Chapter 5 Computer Exercises; 6 Counting Methods and the PigeonholePrinciple; 6.1 Basic Principles; Problem-Solving Corner: Counting. 6.2 Permutations and CombinationsProblem-Solving Corner: Combinations; 6.3 Generalized Permutations and Combinations; 6.4 Algorithms for Generating Permutations and Combinations; 6.5 Introduction to Discrete Probability; 6.6 Discrete Probability Theory; 6.7 Binomial Coefficients and Combinatorial Identities; 6.8 The Pigeonhole Principle; Chapter 6 Notes; Chapter 6 Review; Chapter 6 Self-Test; Chapter 6 Computer Exercises; 7 Recurrence Relations; 7.1 Introduction; 7.2 Solving Recurrence Relations; Problem-Solving Corner Recurrence Relations; 7.3 Applications to the Analysis of Algorithms. 7.4 The Closest-Pair ProblemChapter 7 Notes; Chapter 7 Review; Chapter 7 Self-Test; Chapter 7 Computer Exercises; 8 Graph Theory; 8.1 Introduction; 8.2 Paths and Cycles; Problem-Solving Corner: Graphs; 8.3 Hamiltonian Cycles and the Traveling Salesperson Problem; 8.4 A Shortest-Path Algorithm; 8.5 Representations of Graphs; 8.6 Isomorphisms of Graphs; 8.7 Planar Graphs; 8.8 Instant Insanity; Chapter 8 Notes; Chapter 8 Review; Chapter 8 Self-Test; Chapter 8 Computer Exercises; 9 Trees; 9.1 Introduction; 9.2 Terminology and Characterizations of Trees; Problem-Solving Corner Trees

For one- or two-term introductory courses in discrete mathematics. An accessible introduction to the topics of discrete math, this best-selling text also works to expand students' mathematical maturity. With nearly 4,500 exercises, Discrete Mathematics provides ample opportunities for students to practice, apply, and demonstrate conceptual understanding. Exercise sets features a large number of applications, especially applications to computer science. The almost 650 worked examples provide ready reference for students as they work. A strong emphasis on the interplay among the various topic

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