9780136020790

Discrete Mathematics With Graph Theory

by ;
  • ISBN13:

    9780136020790

  • ISBN10:

    0136020798

  • Edition: 1st
  • Format: Hardcover
  • Copyright: 11/1/1997
  • Publisher: Pearson College Div
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Summary

Adopting a user-friendly, conversationaland at times humorousstyle, these authors make the principles and practices of discrete mathematics as much fun as possible while presenting comprehensive, rigorous coverage. Starts with a chapter "Yes, There Are Proofs" and emphasizes how to do proofs throughout the text.

Table of Contents

Preface xi(6)
Suggested Lecture Schedule xvii
0 YES, THERE ARE PROOFS!
1(19)
0.1 Compound Statements
2(6)
0.2 Negation and Quantifiers
8(3)
0.3 Methods of Proof
11(9)
1 SETS AND RELATIONS
20(43)
1.1 Sets
20(8)
1.2 Operations on Sets
28(12)
1.3 Binary Relations
40(6)
1.4 Equivalence Relations
46(10)
1.5 Partial Orders
56(7)
2 FUNCTIONS
63(33)
2.1 Domain, Range, One-to-One, Onto
63(13)
2.2 Inverses and Composition
76(10)
2.3 One-to-One Correspondence; Cardinality
86(10)
3 THE INTEGERS
96(65)
3.1 The Division Algorithm
96(9)
3.2 Divisibility and the Euclidean Algorithm
105(13)
3.3 Prime Numbers
118(16)
3.4 Congruence
134(13)
3.5 Applications of Congruence
147(14)
4 INDUCTION AND RECURSION
161(50)
4.1 Mathematical Induction
161(19)
4.2 Recursively Defined Sequences
180(14)
4.3 Solving Recurrence Relations; The Characteristic Polynomial
194(8)
4.4 Solving Recurrence Relations; Generating Functions
202(9)
5 PRINCIPLES OF COUNTING
211(29)
5.1 The Principle of Inclusion-Exclusion
211(12)
5.2 The Addition and Multiplication Rules
223(10)
5.3 The Pigeon-hole Principle
233(7)
6 PERMUTATIONS AND COMBINATIONS
240(35)
6.1 Permutations
240(7)
6.2 Combinations
247(9)
6.3 Repetitions
256(7)
6.4 Derangements
263(4)
6.5 The Binomial Theorem
267(8)
7 ALGORITHMS
275(44)
7.1 What Is an Algorithm?
275(8)
7.2 Complexity
283(17)
7.3 Searching and Sorting
300(13)
7.4 Enumeration of Permutations and Combinations
313(6)
8 GRAPHS
319(30)
8.1 A Gentle Introduction
319(10)
8.2 Definitions and Basic Properties
329(12)
8.3 Isomorphism
341(8)
9 PATHS AND CIRCUITS
349(39)
9.1 Eulerian Circuits
349(10)
9.2 Hamiltonian Cycles
359(9)
9.3 The Adjacency Matrix
368(8)
9.4 Shortest Path Algorithms
376(12)
10 APPLICATIONS OF PATHS AND CIRCUITS
388(33)
10.1 The Chinese Postman Problem
388(6)
10.2 Digraphs
394(7)
10.3 RNA Chains
401(7)
10.4 Tournaments
408(5)
10.5 Scheduling Problems
413(8)
11 TREES
421(30)
11.1 What Is a Tree?
421(5)
11.2 Properties of Trees
426(7)
11.3 Spanning Trees
433(6)
11.4 Minimum Spanning Tree Algorithms
439(12)
12 DEPTH-FIRST SEARCH AND APPLICATIONS
451(15)
12.1 Depth-first Search
451(7)
12.2 The One-way Street Problem
458(8)
13 PLANAR GRAPHS AND COLORINGS
466(32)
13.1 Planar Graphs
466(10)
13.2 Coloring Graphs
476(12)
13.3 Circuit Testing and Facilities Design
488(10)
14 THE MAX FLOW--MIN CUT THEOREM
498
14.1 Flows and Cuts
498(9)
14.2 Constructing Maximal Flows
507(7)
14.3 Applications
514(6)
14.4 Matchings
520
Solutions to Selected Exercises S-1
Glossary G-1
Index I-1

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