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Fundamentals of Discrete Structures

ISBN: 9780558837976 | 0558837972
Edition: 1st
Format: Paperback
Publisher: Pearson Learning Solutions
Pub. Date: 1/1/2010

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Table of Contents
Introductionp. 1
Sets and Sequencesp. 9
Setsp. 10
Basic Definitionsp. 10
Naming and Describing Setsp. 14
Comparison Relations on Setsp. 17
Set Operatorsp. 19
Principle of Inclusion/Exclusionp. 29
Sequencesp. 34
Numerical Sequencesp. 35
Describing Patterns in Sequences... MORE
Summationsp. 43
Mathematical Inductionp. 45
Deductive Reasoningp. 46
First Principle of Mathematical Inductionp. 47
Examples Using Mathematical Inductionp. 48
Logicp. 63
Prepositional Logicp. 64
Logical Operationsp. 66
Prepositional Formsp. 71
Parse Trees and the Operator Hierarchy*p. 73
From English to Propositionsp. 75
Prepositional Equivalencesp. 76
Prepositional Identities and Dualityp. 79
Predicate Logicp. 81
Quantifiersp. 83
Some Rules for Using Predicatesp. 85
Relationsp. 91
Ways to Describe Relations Between Objectsp. 02
Describing a Relation Using Englishp. 93
Describing a Relation using a Picturep. 96
Describing a Relation as a Subset of the Cartesian Productp. 97
Properties of Relationsp. 100
Reflexivilyp. 100
Symmetryp. 103
Transitivityp. 106
Functionsp. 113
What is a Function?p. 114
Functions and Relationsp. 119
Properties of Functionsp. 123
Function Compositionp. 127
Identity and Inverse Functionsp. 131
An Application: Cryptographyp. 138
Caesar Rotationp. 139
Cryptography in Cyber-Commercep. 140
More About Functionsp. 141
Standard Mathematical Functionsp. 141
Growth Functionsp. 142
Functions in Program Constructionp. 144
An Application: Secure Storage of Passwordsp. 147
Countingp. 153
Counting and How to Countp. 154
Elementary Rules for Countingp. 156
The Addition Rulep. 156
The Multiplication Rulep. 157
Using the Elementary Rules for Counting Togetherp. 162
Permutations and Combinationsp. 164
Permutationsp. 165
Combinationsp. 167
Additional Examplesp. 169
Probabilityp. 177
Terminology and Backgroundp. 178
Complementp. 182
Elementary Rules for Probabilityp. 183
The Elementary Addition Rule for Probabilityp. 185
The Elementary Multiplication Rule for Probabilityp. 187
General Rules for Probabilityp. 189
The General Addition Rule for Probabilityp. 190
The General Multiplication Rule for Probabilityp. 192
Bernoulli Trials and Probability Distributionsp. 194
Expected Valuep. 196
Algorithmsp. 205
What is an Algorithm?p. 206
Applications of Algorithmsp. 206
Searching and Sorting Algorithmsp. 208
Search Algorithmsp. 208
Sorting Algorithmsp. 211
Analysis of Algorithmsp. 215
How Do We Measure Efficiency?p. 216
The Run-Time Complexity of an Algorithmp. 216
Analysis of the Linear Search Algorithmp. 219
Analysis of the Binary Search Algorithmp. 219
Analysis of the Bubblesort Algorithmp. 220
Big-O Notation*p. 222
Graphsp. 227
Graph Notationp. 229
Vertices and Edgesp. 229
Directed and Undirected Graphsp. 231
Complete Graphsp. 232
Euler Trails and Circuitsp. 233
Walks, Trails, Circuits and Cyclesp. 233
Euler Circuitsp. 235
Weighted Graphsp. 236
Minimum Spanning Treep. 238
Subgraphs and Spanning Treesp. 239
Prim's Algorithm for the Minimum Spanning Treep. 240
Matrix Notation For Graphsp. 242
Indexp. 254
Table of Contents provided by Ingram. All Rights Reserved.

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