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Discrete Mathematics With Graph Theory,9780130920003
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Discrete Mathematics With Graph Theory

by ;
Edition:
3rd
ISBN13:

9780130920003

ISBN10:
0130920002
Format:
Hardcover
Pub. Date:
1/1/2006
Publisher(s):
PRENTICE HALL

Questions About This Book?

What version or edition is this?
This is the 3rd edition with a publication date of 1/1/2006.
What is included with this book?
  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any CDs, lab manuals, study guides, etc.

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Summary

For one or two term undergraduate courses in Discrete Mathematics for students of Mathematics and Computer Science. Adopting a user-friendly, conversationaland at times humorousstyle, these authors make the principles and practices of discrete mathematics as stimulating as possible while presenting comprehensive, rigorous coverage. Examples and exercises integrated throughout each chapter serve to pique student interest and bring clarity to even the most complex concepts. Above all, the book is designed to engage today's students in the interesting, applicable facets of modern mathematics.

Table of Contents

Preface xi
Suggested Lecture Schedule xvii
Yes, There are Proofs!
1(36)
Compound Statements
2(7)
Proofs in Mathematics
9(8)
Truth Tables
17(4)
The Algebra of Propositions
21(7)
Logical Arguments
28(9)
Review Exercises
34(3)
Sets and Relations
37(34)
Sets
37(6)
Operations on Sets
43(8)
Binary Relations
51(5)
Equivalence Relations
56(7)
Partial Orders
63(8)
Review Exercises
68(3)
Functions
71(26)
Domain, Range, One-to-One, Onto
71(8)
Inverses and Composition
79(8)
One-to-One Correspondence and the Cardinality of a Set
87(10)
Review Exercises
95(2)
The Integers
97(52)
The Division Algorithm
97(7)
Divisibility and the Euclidean Algorithm
104(10)
Prime Numbers
114(12)
Congruence
126(10)
Applications of Congruence
136(13)
Review Exercises
147(2)
Induction and Recursion
149(38)
Mathematical Induction
149(14)
Recursively Defined Sequences
163(10)
Solving Recurrence Relations; The Characteristic Polynomial
173(5)
Solving Recurrence Relations; Generating Functions
178(9)
Review Exercises
185(2)
Principles of Counting
187(24)
The Principle of Inclusion-Exclusion
187(9)
The Addition and Multiplication Rules
196(8)
The Pigeon-Hole Principle
204(7)
Review Exercises
209(2)
Permutations and Combinations
211(28)
Permutations
211(5)
Combinations
216(7)
Repetitions
223(5)
Derangements
228(3)
The Binomial Theorem
231(8)
Review Exercises
237(2)
Algorithms
239(38)
What Is an Algorithm?
239(7)
Complexity
246(13)
Searching and Sorting
259(12)
Enumeration of Permutations and Combinations
271(6)
Review Exercises
275(2)
Graphs
277(26)
A Gentle Introduction
277(9)
Definitions and Basic Properties
286(8)
Isomorphism
294(9)
Review Exercises
299(4)
Paths and Circuits
303(34)
Eulerian Circuits
303(7)
Hamiltonian Cycles
310(8)
The Adjacency Matrix
318(7)
Shortest Path Algorithms
325(12)
Review Exercises
333(4)
Applications of Paths and Circuits
337(30)
The Chinese Postman Problem
337(5)
Diagraphs
342(8)
RNA Chains
350(5)
Tournaments
355(5)
Scheduling Problems
360(7)
Review Exercises
365(2)
Trees
367(32)
What Is a Tree?
367(5)
Properties of Trees
372(5)
Spanning Trees
377(5)
Minimum Spanning Tree Algorithms
382(10)
Acyclic Digraphs and Bellman's Algorithm
392(7)
Review Exercises
397(2)
Depth-First Search and Applications
399(14)
Depth-First Search
399(6)
The One-Way Street Problem
405(8)
Review Exercises
411(2)
Planar Graphs and Colorings
413(28)
Planar Graphs
413(8)
Coloring Graphs
421(9)
Circuit Testing and Facilities Design
430(11)
Review Exercises
438(3)
The Max Flow---Min Cut Theorem
441(1)
Flows and Cuts
441(7)
Constructing Maximal Flows
448(6)
Applications
454(5)
Matchings
459(5)
Review Exercises
464
Solutions to Selected Exercises S-1
Glossary G-1
Index I-1


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