Discrete Mathematics Through Applications Book

Preface Foreword

1. Election Theory
Lesson 1.1 An Election Activity Lesson 1.2 Group-Ranking Methods and Algorithms Lesson 1.3 More Group-Ranking Methods and Paradoxes Lesson 1.4 Arrow's Conditions and Approval Voting Lesson 1.5 Weighted Voting and Voting Power Chapter Extension, Proportional Representation Chapter 1 Review

2. Fair Division
Lesson 2.1 A Fair Division Activity Lesson 2.2 Estate Division Lesson 2.3 Apportionment Algorithms Lesson 2.4 More Apportionment Algorithms and Paradoxes Lesson 2.5 Fair Division Algorithms: The Continuous Lesson 2.6 Mathematical Induction Chapter Extension Proportional Representation Chapter 2 Review

3. Matrix Operations and Applications
Lesson 3.1 Addition and Subtraction of Matrices Lesson 3.2 Multiplication of Matrices, Part 1
Lesson 3.3 Multiplication of Matrices, Part 2
Lesson 3.4 Population Growth: The Leslie Model, Part 1
Lesson 3.5 Population Growth: The Leslie Model, Part 2
Chapter Extension Keyword Matrices Chapter 3 Review

4. Graphs and Their Applications
Lesson 4.1 Modeling Projects Lesson 4.2 Critical Paths Lesson 4.3 The Vocabulary and Representations of Graphs Lesson 4.4 Euler Circuits and Paths Lesson 4.5 Hamiltonian Circuits and Paths Lesson 4.6 Graph Coloring Chapter Extension Eulerizing Graphs Chapter 4 Review

5. More Graphs, Subgraphs, and Trees
Lesson 5.1 Planarity and Coloring Lesson 5.2 The Traveling Salesperson Problem Lesson 5.3 Finding the Shortest Route Lesson 5.4 Trees and Their Properties Lesson 5.5 Minimum Spanning Trees Lesson 5.6 Binary Trees, Expression Trees, and Traversals Chapter Extension Steiner Trees Chapter 5 Review

6. Counting and Probability
Lesson 6.1 A Counting Activity Lesson 6.2 Counting Techniques, Part 1
Lesson 6.3 Counting Techniques, Part 2
Lesson 6.4 Probability, Part 1
Lesson 6.5 Probability, Part 2
Chapter Extension Monte Carlo Methods Chapter 6 Review

7. Matrices Revisited
Lesson 7.1 The Leontief Input-Output Model, Part 1
Lesson 7.2 The Leontief Input-Output Model, Part 2
Lesson 7.3 Markov Chains Lesson 7.4 Game Theory, Part 1
Lesson 7.5 Game Theory, Part 2
Chapter Extension A Look at a Dominance Matrix Chapter 7 Review

8. Recursion
Lesson 8.1 Introduction to Recursive Thinking Lesson 8.2 Finite Differences Lesson 8.3 Arithmetic and Geometric Recursion Lesson 8.4 Mixed Recursion, Part 1
Lesson 8.5 Mixed Recursion, Part 2
Lesson 8.6 Cobweb Diagrams Chapter Extension Fractal Dimensions Chapter 8 Review

Appendices Answers to Selected Exercises Credit Index