Discrete Mathematics Through Applications

Written specifically for the high school discrete math course,Discrete Mathematics Through Applicationslets the recently revised NCTM Standards be its guide. The book focuses on the connections among mathematical topics and real-life events and situations, emphasizing problem solving, mathematical reasoning and communication.

Preface

ix

Foreword

xv

Election Theory

1

(44)

An Election Activity

2

(5)

Group-Ranking Methods and Algorithms

7

(11)

More Group-Ranking Methods and Paradoxes

18

(7)

Arrow's Conditions and Approval Voting

25

(7)

Weighted Voting and Voting Power

32

(13)

Chapter Extension Proportional Representation

38

(2)

Review

40

(5)

Fair Division

45

(58)

A Fair Division Activity

46

(4)

Estate Division

50

(10)

Apportionment Algorithms

60

(9)

More Apportionment Algorithms and Paradoxes

69

(9)

Fair Division Algorithms: The Continuous Case

78

(8)

Mathematical Induction

86

(17)

Chapter Extension Envy-Free Division

96

(3)

Review

99

(4)

Matrix Operations and Applications

103

(48)

Addition and Substraction of Matrices

104

(9)

Multiplication of Matrices, Part 1

113

(9)

Multiplication of Matrices, Part 2

122

(10)

Population Growth: The Leslie Model, Part 1

132

(5)

Population Growth: The Leslie Model, Part 2

137

(14)

Chapter Extension Harvesting Animal Populations

142

(3)

Review

145

(6)

Graphs and Their Applications

151

(62)

Modeling Projects

152

(5)

Critical Paths

157

(7)

The Vocabulary and Representations of Graphs

164

(8)

Euler Circuits and Paths

172

(12)

Hamiltonian Circuits and Paths

184

(8)

Graph Coloring

192

(21)

Chapter Extension Eulerzing Graphs

201

(3)

Review

204

(9)

More Graphs, Subgraphs, and Trees

213

(62)

Planarity and Coloring

214

(8)

The Traveling Salesperson Problem

222

(7)

Finding the Shortest Route

229

(6)

Trees and Their Properties

235

(8)

Minimum Spanning Trees

243

(12)

Binary Trees, Expression Trees, and Traversals

255

(20)

Chapter Extension Steiner Trees

266

(3)

Review

269

(6)

Counting and Probability

275

(70)

A Counting Activity

276

(6)

Counting Techniques, Part 1

282

(12)

Counting Techniques, Part 2

294

(10)

Probability, Part 1

304

(16)

Probability, Part 2

320

(25)

Chapter Extension Monte Carlo Methods

335

(3)

Review

338

(7)

Matrices Revisited

345

(62)

The Leontief Input-Output Model, Part 1

346

(8)

The Leontief Input-Output Model, Part 2

354

(9)

Markov Chains

363

(10)

Game Theory, Part 1

373

(9)

Game Theory, Part 2

382

(25)

Chapter Extension A Look at a Dominance Matrix

395

(4)

Review

399

(8)

Recursion

407

(66)

Introduction to Recursive Thinking

408

(10)

Finite Differences

418

(8)

Arithmetic and Geometric Recursion

426

(13)

Mixed Recursion, Part 1

439

(10)

Mixed Recursion, Part 2

449

(8)

Cobweb Diagrams

457

(16)

Chapter Extension Fractal Dimensions

464

(3)

Review

467

(6)

Answers to Selected Exercises

473

(68)

Illustration Credits

541

(2)

Index

543

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Discrete Mathematics Through Applications

Summary

Table of Contents

Supplemental Materials