Discrete mathematics with graph theory
By: Edgar G. Goodaire, Michael M. Parmenter.
Contributors: Parmenter, Michael M.
Edition: 3rd ed.
Publisher: Pearson Prentice Hall
Published: 2006
Place of publication: Upper Saddle River, N.J
Language: eng
Number of pages: 592
Subjects: Mathematics -- Textbooks; Computer science -- Mathematics -- Textbooks; Graph theory -- Textbooks
Genres: Textbooks.
Table of contents: title: Preface
pagenum: xi; title: To the Student
pagenum: xv; title: Suggested Lecture Schedule
pagenum: xix; label: 0
title: Yes, There Are Proofs!
pagenum: 1; label: 0.1
title: Compound Statements
pagenum: 2; label: 0.2
title: Proofs in Mathematics
pagenum: 10; title: Review Exercises
pagenum: 17; label: 1
title: Logic
pagenum: 19; label: 1.1
title: Truth Tables
pagenum: 19; label: 1.2
title: The Algebra of Propositions
pagenum: 23; label: 1.3
title: Logical Arguments
pagenum: 30; title: Review Exercises
pagenum: 36; label: 2
title: Sets and Relations
pagenum: 38; label: 2.1
title: Sets
pagenum: 38; label: 2.2
title: Operations on Sets
pagenum: 43; label: 2.3
title: Binary Relations
pagenum: 51; label: 2.4
title: Equivalence Relations
pagenum: 57; label: 2.5
title: Partial Orders
pagenum: 64; title: Review Exercises
pagenum: 70; label: 3
title: Functions
pagenum: 72; label: 3.1
title: Basic Terminology
pagenum: 72; label: 3.2
title: Inverses and Composition
pagenum: 80; label: 3.3
title: One-to-One Correspondence and the Cardinality of a Set
pagenum: 88; title: Review Exercises
pagenum: 96; label: 4
title: The Integers
pagenum: 98; label: 4.1
title: The Division Algorithm
pagenum: 98; label: 4.2
title: Divisibility and the Euclidean Algorithm
pagenum: 105; label: 4.3
title: Prime Numbers
pagenum: 114; label: 4.4
title: Congruence
pagenum: 125; label: 4.5
title: Applications of Congruence
pagenum: 135; title: Review Exercises
pagenum: 145; label: 5
title: Induction and Recursion
pagenum: 147; label: 5.1
title: Mathematical Induction
pagenum: 147; label: 5.2
title: Recursively Defined Sequences
pagenum: 160; label: 5.3
title: Solving Recurrence Relations; The Characteristic Polynomial
pagenum: 170; label: 5.4
title: Solving Recurrence Relations; Generating Functions
pagenum: 176; title: Review Exercises
pagenum: 182; label: 6
title: Principles of Counting
pagenum: 184; label: 6.1
title: The Principle of Inclusion-Exclusion
pagenum: 184; label: 6.2
title: The Addition and Multiplication Rules
pagenum: 192; label: 6.3
title: The Pigeonhole Principle
pagenum: 199; title: Review Exercises
pagenum: 204; label: 7
title: Permutations and Combinations
pagenum: 205; label: 7.1
title: Permutations
pagenum: 205; label: 7.2
title: Combinations
pagenum: 210; label: 7.3
title: Elementary Probability
pagenum: 216; label: 7.4
title: Probability Theory
pagenum: 224; label: 7.5
title: Repetitions
pagenum: 231; label: 7.6
title: Derangements
pagenum: 236; label: 7.7
title: The Binomial Theorem
pagenum: 239; title: Review Exercises
pagenum: 245; label: 8
title: Algorithms
pagenum: 247; label: 8.1
title: What Is an Algorithm?
pagenum: 247; label: 8.2
title: Complexity
pagenum: 253; label: 8.3
title: Searching and Sorting
pagenum: 265; label: 8.4
title: Enumeration of Permutations and Combinations
pagenum: 276; title: Review Exercises
pagenum: 280; label: 9
title: Graphs
pagenum: 281; label: 9.1
title: A Gentle Introduction
pagenum: 281; label: 9.2
title: Definitions and Basic Properties
pagenum: 288; label: 9.3
title: Isomorphism
pagenum: 296; title: Review Exercises
pagenum: 301; label: 10
title: Paths and Circuits
pagenum: 304; label: 10.1
title: Eulerian Circuits
pagenum: 304; label: 10.2
title: Hamiltonian Cycles
pagenum: 311; label: 10.3
title: The Adjacency Matrix
pagenum: 319; label: 10.4
title: Shortest Path Algorithms
pagenum: 326; title: Review Exercises
pagenum: 336; label: 11
title: Applications of Paths and Circuits
pagenum: 339; label: 11.1
title: The Chinese Postman Problem
pagenum: 339; label: 11.2
title: Digraphs
pagenum: 344; label: 11.3
title: RNA Chains
pagenum: 352; label: 11.4
title: Tournaments
pagenum: 356; label: 11.5
title: Scheduling Problems
pagenum: 361; title: Review Exercises
pagenum: 367; label: 12
title: Trees
pagenum: 370; label: 12.1
title: Trees and Their Properties
pagenum: 370; label: 12.2
title: Spanning Trees
pagenum: 379; label: 12.3
title: Minimum Spanning Tree Algorithms
pagenum: 384; label: 12.4
title: Acyclic Digraphs and Bellman's Algorithm
pagenum: 393; label: 12.5
title: Depth-First Search
pagenum: 398; label: 12.6
title: The One-Way Street Problem
pagenum: 403; title: Review Exercises
pagenum: 409; label: 13
title: Planar Graphs and Colorings
pagenum: 411; label: 13.1
title: Planar Graphs
pagenum: 411; label: 13.2
title: Coloring Graphs
pagenum: 419; label: 13.3
title: Circuit Testing and Facilities Design
pagenum: 427; title: Review Exercises
pagenum: 435; label: 14
title: The Max Flow-Min Cut Theorem
pagenum: 438; label: 14.1
title: Flows and Cuts
pagenum: 438; label: 14.2
title: Constructing Maximal Flows
pagenum: 445; label: 14.3
title: Applications
pagenum: 450; label: 14.4
title: Matchings
pagenum: 454; title: Review Exercises
pagenum: 460; title: Appendix
pagenum: A-1; title: Solutions to True/False Questions and Selected Exercises
pagenum: S-1; title: Glossary
pagenum: G-1; title: Index
pagenum: I-1