Discrete Mathematics Through Applications

Written specifically for the high school discrete math course, "Discrete Mathematics Through Applications" lets 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

(54)

Lesson 1.1 An Election Activity

2

(5)

Lesson 1.2 Group-Ranking Methods and Algorithms

7

(11)

Lesson 1.3 More Group-Ranking Methods and Paradoxes

18

(9)

Lesson 1.4 Arrow's Conditions and Approval Voting

27

(9)

Lesson 1.5 Weighted Voting and Voting Power

36

(19)

Chapter Extension Proportional Representation

45

(3)

Chapter 1 Review

48

(7)

Fair Division

55

(64)

Lesson 2.1 A Fair Division Activity

56

(5)

Lesson 2.2 Estate Division

61

(11)

Lesson 2.3 Apportionment Algorithms

72

(10)

Lesson 2.4 More Apportionment Algorithms and Paradoxes

82

(9)

Lesson 2.5 Fair Division Algorithms: The Continuous Case

91

(9)

Lesson 2.6 Mathematical Induction

100

(19)

Chapter Extension Envy-Free Division

111

(3)

Chapter 2 Review

114

(5)

Matrix Operations and Applications

119

(50)

Lesson 3.1 Addition and Subtraction of Matrices

120

(9)

Lesson 3.2 Multiplication of Matrices, Part 1

129

(10)

Lesson 3.3 Multiplication of Matrices, Part 2

139

(10)

Lesson 3.4 Population Growth: The Leslie Model, Part 1

149

(5)

Lesson 3.5 Population Growth: The Leslie Model, Part 2

154

(15)

Chapter Extension Keyword Matrices

159

(3)

Chapter 3 Review

162

(7)

Graphs and Their Applications

169

(62)

Lesson 4.1 Modeling Projects

170

(5)

Lesson 4.2 Critical Paths

175

(7)

Lesson 4.3 The Vocabulary and Representations of Graphs

182

(8)

Lesson 4.4 Euler Circuits and Paths

190

(11)

Lesson 4.5 Hamiltonian Circuits and Paths

201

(9)

Lesson 4.6 Graph Coloring

210

(21)

Chapter Extension Eulerizing Graphs

218

(3)

Chapter 4 Review

221

(10)

More Graphs, Subgraphs, and Trees

231

(66)

Lesson 5.1 Planarity and Coloring

232

(9)

Lesson 5.2 The Traveling Salesperson Problem

241

(6)

Lesson 5.3 Finding the Shortest Route

247

(8)

Lesson 5.4 Trees and Their Properties

255

(8)

Lesson 5.5 Minimum Spanning Trees

263

(12)

Lesson 5.6 Binary Trees, Expression Trees, and Traversals

275

(22)

Chapter Extension Steiner Trees

286

(3)

Chapter 5 Review

289

(8)

Counting and Probability

297

(80)

Lesson 6.1 A Counting Activity

298

(7)

Lesson 6.2 Counting Techniques, Part 1

305

(12)

Lesson 6.3 Counting Techniques, Part 2

317

(12)

Lesson 6.4 Probability, Part 1

329

(19)

Lesson 6.5 Probability, Part 2

348

(29)

Chapter Extension Monte Carlo Methods

364

(3)

Chapter 6 Review

367

(10)

Matrices Revisited

377

(66)

Lesson 7.1 The Leontief Input-Output Model, Part 1

378

(9)

Lesson 7.2 The Leontief Input-Output Model, Part 2

387

(11)

Lesson 7.3 Markov Chains

398

(11)

Lesson 7.4 Game Theory, Part 1

409

(9)

Lesson 7.5 Game Theory, Part 2

418

(25)

Chapter Extension A Look at a Dominance Matrix

431

(5)

Chapter 7 Review

436

(7)

Recursion

443

(74)

Lesson 8.1 Introduction to Recursive Thinking

444

(11)

Lesson 8.2 Finite Differences

455

(9)

Lesson 8.3 Arithmetic and Geometric Recursion

464

(12)

Lesson 8.4 Mixed Recursion, Part 1

476

(11)

Lesson 8.5 Mixed Recursion, Part 2

487

(9)

Lesson 8.6 Cobweb Diagrams

496

(21)

Chapter Extension Fractal Dimensions

504

(4)

Chapter 8 Review

508

(9)

Appendices

517

(18)

Answers to Selected Exercises

535

(70)

Acknowledgments

605

(1)

Illustration Credits

606

(3)

Index

609

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Discrete Mathematics Through Applications

Summary

Table of Contents

Supplemental Materials