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| Introduction | p. 1 |
| Sets and Sequences | p. 9 |
| Sets | p. 10 |
| Basic Definitions | p. 10 |
| Naming and Describing Sets | p. 14 |
| Comparison Relations on Sets | p. 17 |
| Set Operators | p. 19 |
| Principle of Inclusion/Exclusion | p. 29 |
| Sequences | p. 34 |
| Numerical Sequences | p. 35 |
| Describing Patterns in Sequences | p. 36 |
| Summations | p. 43 |
| Mathematical Induction | p. 45 |
| Deductive Reasoning | p. 46 |
| First Principle of Mathematical Induction | p. 47 |
| Examples Using Mathematical Induction | p. 48 |
| Logic | p. 63 |
| Prepositional Logic | p. 64 |
| Logical Operations | p. 66 |
| Prepositional Forms | p. 71 |
| Parse Trees and the Operator Hierarchy* | p. 73 |
| From English to Propositions | p. 75 |
| Prepositional Equivalences | p. 76 |
| Prepositional Identities and Duality | p. 79 |
| Predicate Logic | p. 81 |
| Quantifiers | p. 83 |
| Some Rules for Using Predicates | p. 85 |
| Relations | p. 91 |
| Ways to Describe Relations Between Objects | p. 02 |
| Describing a Relation Using English | p. 93 |
| Describing a Relation using a Picture | p. 96 |
| Describing a Relation as a Subset of the Cartesian Product | p. 97 |
| Properties of Relations | p. 100 |
| Reflexivily | p. 100 |
| Symmetry | p. 103 |
| Transitivity | p. 106 |
| Functions | p. 113 |
| What is a Function? | p. 114 |
| Functions and Relations | p. 119 |
| Properties of Functions | p. 123 |
| Function Composition | p. 127 |
| Identity and Inverse Functions | p. 131 |
| An Application: Cryptography | p. 138 |
| Caesar Rotation | p. 139 |
| Cryptography in Cyber-Commerce | p. 140 |
| More About Functions | p. 141 |
| Standard Mathematical Functions | p. 141 |
| Growth Functions | p. 142 |
| Functions in Program Construction | p. 144 |
| An Application: Secure Storage of Passwords | p. 147 |
| Counting | p. 153 |
| Counting and How to Count | p. 154 |
| Elementary Rules for Counting | p. 156 |
| The Addition Rule | p. 156 |
| The Multiplication Rule | p. 157 |
| Using the Elementary Rules for Counting Together | p. 162 |
| Permutations and Combinations | p. 164 |
| Permutations | p. 165 |
| Combinations | p. 167 |
| Additional Examples | p. 169 |
| Probability | p. 177 |
| Terminology and Background | p. 178 |
| Complement | p. 182 |
| Elementary Rules for Probability | p. 183 |
| The Elementary Addition Rule for Probability | p. 185 |
| The Elementary Multiplication Rule for Probability | p. 187 |
| General Rules for Probability | p. 189 |
| The General Addition Rule for Probability | p. 190 |
| The General Multiplication Rule for Probability | p. 192 |
| Bernoulli Trials and Probability Distributions | p. 194 |
| Expected Value | p. 196 |
| Algorithms | p. 205 |
| What is an Algorithm? | p. 206 |
| Applications of Algorithms | p. 206 |
| Searching and Sorting Algorithms | p. 208 |
| Search Algorithms | p. 208 |
| Sorting Algorithms | p. 211 |
| Analysis of Algorithms | p. 215 |
| How Do We Measure Efficiency? | p. 216 |
| The Run-Time Complexity of an Algorithm | p. 216 |
| Analysis of the Linear Search Algorithm | p. 219 |
| Analysis of the Binary Search Algorithm | p. 219 |
| Analysis of the Bubblesort Algorithm | p. 220 |
| Big-O Notation* | p. 222 |
| Graphs | p. 227 |
| Graph Notation | p. 229 |
| Vertices and Edges | p. 229 |
| Directed and Undirected Graphs | p. 231 |
| Complete Graphs | p. 232 |
| Euler Trails and Circuits | p. 233 |
| Walks, Trails, Circuits and Cycles | p. 233 |
| Euler Circuits | p. 235 |
| Weighted Graphs | p. 236 |
| Minimum Spanning Tree | p. 238 |
| Subgraphs and Spanning Trees | p. 239 |
| Prim's Algorithm for the Minimum Spanning Tree | p. 240 |
| Matrix Notation For Graphs | p. 242 |
| Index | p. 254 |
| Table of Contents provided by Ingram. All Rights Reserved. |
Fundamentals of Discrete Structures
by Weiss, Gary M; Lyons, Damian M; Papadakis-Kanaris, Christina; Werschulz, Arthur GEdition: 1st
Format: Paperback
Pub. Date: 2010-01-01
Publisher(s): Pearson Learning Solutions
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