Discrete mathematics with graph theory
By: Edgar G. Goodaire, Michael M. Parmenter.
Contributors: Parmenter, Michael M.
Publisher: Prentice Hall
Published: 1998
Place of publication: Upper Saddle River, NJ
Language: eng
Number of pages: 527
Subjects: Mathematics.; Computer science -- Mathematics.; Graph theory.
Notes: Includes bibliographical references and index.
Table of contents: title: Preface
pagenum: xi; title: Suggested Lecture Schedule
pagenum: xvii; label: 0
title: Yes, There Are Proofs!
pagenum: 1; label: 0.1
title: Compound Statements
pagenum: 2; label: 0.2
title: Negation and Quantifiers
pagenum: 8; label: 0.3
title: Methods of Proof
pagenum: 11; label: 1
title: Sets and Relations
pagenum: 20; label: 1.1
title: Sets
pagenum: 20; label: 1.2
title: Operations on Sets
pagenum: 28; label: 1.3
title: Binary Relations
pagenum: 40; label: 1.4
title: Equivalence Relations
pagenum: 46; label: 1.5
title: Partial Orders
pagenum: 56; label: 2
title: Functions
pagenum: 63; label: 2.1
title: Domain, Range, One-to-One, Onto
pagenum: 63; label: 2.2
title: Inverses and Composition
pagenum: 76; label: 2.3
title: One-to-One Correspondence; Cardinality
pagenum: 86; label: 3
title: The Integers
pagenum: 96; label: 3.1
title: The Division Algorithm
pagenum: 96; label: 3.2
title: Divisibility and the Euclidean Algorithm
pagenum: 105; label: 3.3
title: Prime Numbers
pagenum: 118; label: 3.4
title: Congruence
pagenum: 134; label: 3.5
title: Applications of Congruence
pagenum: 147; label: 4
title: Induction and Recursion
pagenum: 161; label: 4.1
title: Mathematical Induction
pagenum: 161; label: 4.2
title: Recursively Defined Sequences
pagenum: 180; label: 4.3
title: Solving Recurrence Relations; The Characteristic Polynomial
pagenum: 194; label: 4.4
title: Solving Recurrence Relations; Generating Functions
pagenum: 202; label: 5
title: Principles of Counting
pagenum: 211; label: 5.1
title: The Principle of Inclusion-Exclusion
pagenum: 211; label: 5.2
title: The Addition and Multiplication Rules
pagenum: 223; label: 5.3
title: The Pigeon-hole Principle
pagenum: 233; label: 6
title: Permutations and Combinations
pagenum: 240; label: 6.1
title: Permutations
pagenum: 240; label: 6.2
title: Combinations
pagenum: 247; label: 6.3
title: Repetitions
pagenum: 256; label: 6.4
title: Derangements
pagenum: 263; label: 6.5
title: The Binomial Theorem
pagenum: 267; label: 7
title: Algorithms
pagenum: 275; label: 7.1
title: What Is an Algorithm?
pagenum: 275; label: 7.2
title: Complexity
pagenum: 283; label: 7.3
title: Searching and Sorting
pagenum: 300; label: 7.4
title: Enumeration of Permutations and Combinations
pagenum: 313; label: 8
title: Graphs
pagenum: 319; label: 8.1
title: A Gentle Introduction
pagenum: 319; label: 8.2
title: Definitions and Basic Properties
pagenum: 329; label: 8.3
title: Isomorphism
pagenum: 341; label: 9
title: Paths and Circuits
pagenum: 349; label: 9.1
title: Eulerian Circuits
pagenum: 349; label: 9.2
title: Hamiltonian Cycles
pagenum: 359; label: 9.3
title: The Adjacency Matrix
pagenum: 368; label: 9.4
title: Shortest Path Algorithms
pagenum: 376; label: 10
title: Applications of Paths and Circuits
pagenum: 388; label: 10.1
title: The Chinese Postman Problem
pagenum: 388; label: 10.2
title: Digraphs
pagenum: 394; label: 10.3
title: RNA Chains
pagenum: 401; label: 10.4
title: Tournaments
pagenum: 408; label: 10.5
title: Scheduling Problems
pagenum: 413; label: 11
title: Trees
pagenum: 421; label: 11.1
title: What Is a Tree?
pagenum: 421; label: 11.2
title: Properties of Trees
pagenum: 426; label: 11.3
title: Spanning Trees
pagenum: 433; label: 11.4
title: Minimum Spanning Tree Algorithms
pagenum: 439; label: 12
title: Depth-First Search and Applications
pagenum: 451; label: 12.1
title: Depth-first Search
pagenum: 451; label: 12.2
title: The One-way Street Problem
pagenum: 458; label: 13
title: Planar Graphs and Colorings
pagenum: 466; label: 13.1
title: Planar Graphs
pagenum: 466; label: 13.2
title: Coloring Graphs
pagenum: 476; label: 13.3
title: Circuit Testing and Facilities Design
pagenum: 488; label: 14
title: The Max Flow-Min Cut Theorem
pagenum: 498; label: 14.1
title: Flows and Cuts
pagenum: 498; label: 14.2
title: Constructing Maximal Flows
pagenum: 507; label: 14.3
title: Applications
pagenum: 514; label: 14.4
title: Matchings
pagenum: 520; title: Solutions to Selected Exercises
pagenum: S-1; title: Glossary
pagenum: G-1; title: Index
pagenum: I-1