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Discrete Mathematics with Graph Theory,9780131679955
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Discrete Mathematics with Graph Theory

by ;
Edition:
3rd
ISBN13:

9780131679955

ISBN10:
0131679953
Format:
Hardcover
Pub. Date:
6/24/2005
Publisher(s):
Pearson
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Summary

Far more "user friendly" than the vast majority of similar books, this volume is truly written with the unsophisticated reader in mind. The pace is leisurely, but the authors are rigorous and maintain a serious attitude towards theorem proving throughout.Emphasizes "Active Reading" throughout, a skill vital to success in learning how to write proofs. Offers two sections on probability (2.4 and 2.5). Moves material on depth-first search, which previously comprised an entire (very short) chapter, to an earlier chapter where it fits more naturally. Rewrites section on RNA chains to include a new (and easier) algorithm for the recovery of an RNA chain from its complete enzyme digest. Provides true/false questions (with all answers in the back of the book) in every section. Features an appendix on matrices. A useful reference for mathematics enthusiasts who want to learn how to write proofs.

Table of Contents

Preface xi
To the Student xv
Suggested Lecture Schedule xix
Yes, There Are Proofs!
1(18)
Compound Statements
2(8)
Proofs in Mathematics
10(9)
Review Exercises
17(2)
Logic
19(19)
Truth Tables
19(4)
The Algebra of Propositions
23(7)
Logical Arguments
30(8)
Review Exercises
36(2)
Sets and Relations
38(34)
Sets
38(5)
Operations on Sets
43(8)
Binary Relations
51(6)
Equivalence Relations
57(7)
Partial Orders
64(8)
Review Exercises
70(2)
Functions
72(26)
Basic Terminology
72(8)
Inverses and Composition
80(8)
One-to-One Correspondence and the Cardinality of a Set
88(10)
Review Exercises
96(2)
The Integers
98(49)
The Division Algorithm
98(7)
Divisibility and the Euclidean Algorithm
105(9)
Prime Numbers
114(11)
Congruence
125(10)
Applications of Congruence
135(12)
Review Exercises
145(2)
Induction and Recursion
147(37)
Mathematical Induction
147(13)
Recursively Defined Sequences
160(10)
Solving Recurrence Relations; The Characteristic Polynomial
170(6)
Solving Recurrence Relations; Generating Functions
176(8)
Review Exercises
182(2)
Principles of Counting
184(21)
The Principle of Inclusion-Exclusion
184(8)
The Addition and Multiplication Rules
192(7)
The Pigeonhole Principle
199(6)
Review Exercises
204(1)
Permutations and Combinations
205(42)
Permutations
205(5)
Combinations
210(6)
Elementary Probability
216(8)
Probability Theory
224(7)
Repetitions
231(5)
Derangements
236(3)
The Binomial Theorem
239(8)
Review Exercises
245(2)
Algorithms
247(34)
What Is an Algorithm?
247(6)
Complexity
253(12)
Searching and Sorting
265(11)
Enumeration of Permutations and Combinations
276(5)
Review Exercises
280(1)
Graphs
281(23)
A Gentle Introduction
281(7)
Definitions and Basic Properties
288(8)
Isomorphism
296(8)
Review Exercises
301(3)
Paths and Circuits
304(35)
Eulerian Circuits
304(7)
Hamiltonian Cycles
311(8)
The Adjacency Matrix
319(7)
Shortest Path Algorithms
326(13)
Review Exercises
336(3)
Applications of Paths and Circuits
339(31)
The Chinese Postman Problem
339(5)
Digraphs
344(8)
RNA Chains
352(4)
Tournaments
356(5)
Scheduling Problems
361(9)
Review Exercises
367(3)
Trees
370(41)
Trees and their Properties
370(9)
Spanning Trees
379(5)
Minimum Spanning Tree Algorithms
384(9)
Acyclic Digraphs and Bellman's Algorithm
393(5)
Depth-First Search
398(5)
The One-Way Street Problem
403(8)
Review Exercises
409(2)
Planar Graphs and Colorings
411(27)
Planar Graphs
411(8)
Coloring Graphs
419(8)
Circuit Testing and Facilities Design
427(11)
Review Exercises
435(3)
The Max Flow---Min Cut Theorem
438
Flows and Cuts
438(7)
Constructing Maximal Flows
445(5)
Applications
450(4)
Matchings
454
Review Exercises
460
Appendix 1(1)
Solutions to True/False Questions and Selected Exercises 1(1)
Glossary 1(1)
Index 1


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