Discrete mathematics
By: Gary Chartrand and Ping Zhang
Contributors: Zhang, Ping, 1957-
Publisher: Waveland Press, Inc.
Published: 2011
Place of publication: Long Grove, Ill
Language: eng
Number of pages: 671
ISBN-13: 9781577667308
Subjects: Mathematics; Computer science
Notes: Includes index.
Table of contents: title: Preface
pagenum: ix; label: Chapter 0
title: What Is Discrete Mathematics?
pagenum: 1; label: Chapter 1
title: Logic
pagenum: 7; label: Section 1.1
title: Statements
pagenum: 7; label: Section 1.2
title: Negation, Conjunction and Disjunction
pagenum: 13; label: Section 1.3
title: Implications
pagenum: 25; label: Section 1.4
title: Biconditionals
pagenum: 36; label: Section 1.5
title: Tautologies and Contradictions
pagenum: 40; label: Section 1.6
title: Some Applications of Logic
pagenum: 43; title: Chapter Highlights and Supplementary Exercises
pagenum: 47; label: Chapter 2
title: Sets
pagenum: 53; label: Section 2.1
title: Sets and Subsets
pagenum: 53; label: Section 2.2
title: Set Operations and Their Properties
pagenum: 62; label: Section 2.3
title: Cartesian Products of Sets
pagenum: 70; label: Section 2.4
title: Partitions
pagenum: 72; title: Chapter Highlights and Supplementary Exercises
pagenum: 75; label: Chapter 3
title: Methods of Proof
pagenum: 79; label: Section 3.1
title: Quantified Statements
pagenum: 79; label: Section 3.2
title: Direct Proof
pagenum: 87; label: Section 3.3
title: Proof by Contrapositive
pagenum: 94; label: Section 3.4
title: Proof by Cases
pagenum: 98; label: Section 3.5
title: Counterexamples
pagenum: 102; label: Section 3.6
title: Existence Proofs
pagenum: 105; label: Section 3.7
title: Proof by Contradiction
pagenum: 108; title: Chapter Highlights and Supplementary Exercises
pagenum: 112; label: Chapter 4
title: Mathematical Induction
pagenum: 115; label: Section 4.1
title: The Principle of Mathematical Induction
pagenum: 115; label: Section 4.2
title: Additional Examples of Induction Proofs
pagenum: 123; label: Section 4.3
title: Sequences
pagenum: 128; label: Section 4.4
title: The Strong Principle of Mathematical Induction
pagenum: 137; title: Chapter Highlights and Supplementary Exercises
pagenum: 143; label: Chapter 5
title: Relations and Functions
pagenum: 147; label: Section 5.1
title: Relations
pagenum: 147; label: Section 5.2
title: Equivalence Relations
pagenum: 152; label: Section 5.3
title: Functions
pagenum: 159; label: Section 5.4
title: Bijective Functions
pagenum: 170; label: Section 5.5
title: Cardinalities of Sets
pagenum: 183; title: Chapter Highlights and Supplementary Exercises
pagenum: 191; label: Chapter 6
title: Algorithms and Complexity
pagenum: 197; label: Section 6.1
title: What Is an Algorithm?
pagenum: 197; label: Section 6.2
title: Growth of Functions
pagenum: 205; label: Section 6.3
title: Analysis of Algorithms
pagenum: 212; label: Section 6.4
title: Searching and Sorting
pagenum: 218; title: Chapter Highlights and Supplementary Exercises
pagenum: 228; label: Chapter 7
title: Integers
pagenum: 231; label: Section 7.1
title: Divisibility Properties
pagenum: 231; label: Section 7.2
title: Primes
pagenum: 235; label: Section 7.3
title: The Division Algorithm
pagenum: 240; label: Section 7.4
title: Congruence
pagenum: 243; label: Section 7.5
title: Introduction to Cryptography
pagenum: 246; label: Section 7.6
title: Greatest Common Divisors
pagenum: 250; label: Section 7.7
title: Integer Representations
pagenum: 262; title: Chapter Highlights and Supplementary Exercises
pagenum: 266; label: Chapter 8
title: Introduction to Counting
pagenum: 271; label: Section 8.1
title: The Multiplication and Addition Principles
pagenum: 271; label: Section 8.2
title: The Principle of Inclusion-Exclusion
pagenum: 280; label: Section 8.3
title: The Pigeonhole Principle
pagenum: 286; label: Section 8.4
title: Permutations and Combinations
pagenum: 292; label: Section 8.5
title: Applications of Permutations and Combinations
pagenum: 302; title: Chapter Highlights and Supplementary Exercises
pagenum: 308; label: Chapter 9
title: Advanced Counting Methods
pagenum: 313; label: Section 9.1
title: The Pascal Triangle and the Binomial Theorem
pagenum: 313; label: Section 9.2
title: Permutations and Combinations with Repetition
pagenum: 324; label: Section 9.3
title: Generating Functions
pagenum: 332; title: Chapter Highlights and Supplementary Exercises
pagenum: 348; label: Chapter 10
title: Discrete Probability
pagenum: 351; label: Section 10.1
title: Probability of an Event
pagenum: 351; label: Section 10.2
title: Conditional Probability and Independent Events
pagenum: 365; label: Section 10.3
title: Random Variables and Expected Values
pagenum: 375; title: Chapter Highlights and Supplementary Exercises
pagenum: 381; label: Chapter 11
title: Partially Ordered Sets and Boolean Algebras
pagenum: 387; label: Section 11.1
title: Partially Ordered Sets
pagenum: 387; label: Section 11.2
title: Lattices
pagenum: 403; label: Section 11.3
title: Boolean Algebras
pagenum: 412; title: Chapter Highlights and Supplementary Exercises
pagenum: 424; label: Chapter 12
title: Introduction to Graphs
pagenum: 431; label: Section 12.1
title: Fundamental Concepts of Graph Theory
pagenum: 432; label: Section 12.2
title: Connected Graphs
pagenum: 444; label: Section 12.3
title: Eulerian Graphs
pagenum: 457; label: Section 12.4
title: Hamiltonian Graphs
pagenum: 465; label: Section 12.5
title: Weighted Graphs
pagenum: 471; title: Chapter Highlights and Supplementary Exercises
pagenum: 480; label: Chapter 13
title: Trees
pagenum: 491; label: Section 13.1
title: Fundamental Properties of Trees
pagenum: 491; label: Section 13.2
title: Rooted and Spanning Trees
pagenum: 498; label: Section 13.3
title: The Minimum Spanning Tree Problem
pagenum: 511; title: Chapter Highlights and Supplementary Exercises
pagenum: 520; label: Chapter 14
title: Planar Graphs and Graph Colorings
pagenum: 525; label: Section 14.1
title: Planar Graphs
pagenum: 525; label: Section 14.2
title: Coloring Graphs
pagenum: 536; title: Chapter Highlights and Supplementary Exercises
pagenum: 551; label: Chapter 15
title: Directed Graphs
pagenum: 559; label: Section 15.1
title: Fundamental Concepts of Digraph Theory
pagenum: 559; label: Section 15.2
title: Tournaments
pagenum: 567; label: Section 15.3
title: Finite-State Machines
pagenum: 574; title: Chapter Highlights and Supplementary Exercises
pagenum: 590; title: Answers and Hints to Odd-Numbered Exercises
pagenum: 595; title: Index of Mathematical Terms and Names
pagenum: 659; title: List of Symbols
pagenum: 671