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by Nancy Crisler, Patience Fisher and Gary W. Froelich

Edition: 2ND 00Copyright: 2000

Publisher: W.H. Freeman

Published: 2000

International: No

Nancy Crisler, Patience Fisher and Gary W. Froelich

Edition: 2ND 00
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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. The new edition adds a wealth of new features and content, including pedagogical tools aimed at fostering the participatory spirit. Current applications are highlighted through hundreds of real-world examples and a new art program.

- Treatment of a topic usually begins with an exploration activity. We believe that exploration of a problem is critical to understanding it and its solution.
- Lessons are written in an informal style that is designed to be read easily by the student. Users of the book report that students who are absent usually have little trouble reading material they missed.
- Exercises often contain new ideas. Students learn by doing. In most cases, students are expected to do all the exercises.
- The themes of mathematical modeling, appropriate use of technology, and decision making are consistently emphasized
- The strands of algorithmic thinking, recursive thinking, and mathematical induction are woven throughout the book
- New chapter extensions at the end of each chapter (before the exercises) which can serve as starting points for additional explorations, activities and projects related to the chapter
- New sample calculator screens in the text and blackline masters that show detailed instruction for the TI-83
- New biographical captions for photos of individuals important to the development of discrete mathematics
- New coverage of fractals in Chapter 8
- New real-world applications, plus many more examples and projects
- New newspaper clippings highlighting recent applications

**Crisler, Nancy : Pattonville School District, St. Louis**

**Fisher, Patience : University of Nebraska**

**Froelich, Gary : Consortium for Mathematics and Its Applications, Inc.**

**Chapter 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 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 Case

Lesson 2.6 Mathematical Induction

Chapter Extension: Envy-Free Division

**Chapter 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: Applications of the Leslie Matrix

**Chapter 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 5. More Graphs, Subgraphs and Trees**

Lesson 5.1 Planarity and Coloring

Lesson 5.2 The Traveling Salesperson Problem

Lesson 5.3 Shortest Route Problems

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 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 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 8. Recursion**

Lesson 8. 1 An Introduction to Recursive Thinking

Lesson 8. 1 Finite Differences

Lesson 8. 1 Arithmetic and Geometric Recursion

Lesson 8. 1 Mixed Recursion, Part 1

Lesson 8. 1 Mixed Recursion, Part 2

Lesson 8. 1 Cobweb Diagrams

Chapter Extension: Fractal Dimensions--NEW!

Answers to Selected Exercises

Sources of Illustrations

Index

Summary

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. The new edition adds a wealth of new features and content, including pedagogical tools aimed at fostering the participatory spirit. Current applications are highlighted through hundreds of real-world examples and a new art program.

- Treatment of a topic usually begins with an exploration activity. We believe that exploration of a problem is critical to understanding it and its solution.
- Lessons are written in an informal style that is designed to be read easily by the student. Users of the book report that students who are absent usually have little trouble reading material they missed.
- Exercises often contain new ideas. Students learn by doing. In most cases, students are expected to do all the exercises.
- The themes of mathematical modeling, appropriate use of technology, and decision making are consistently emphasized
- The strands of algorithmic thinking, recursive thinking, and mathematical induction are woven throughout the book
- New chapter extensions at the end of each chapter (before the exercises) which can serve as starting points for additional explorations, activities and projects related to the chapter
- New sample calculator screens in the text and blackline masters that show detailed instruction for the TI-83
- New biographical captions for photos of individuals important to the development of discrete mathematics
- New coverage of fractals in Chapter 8
- New real-world applications, plus many more examples and projects
- New newspaper clippings highlighting recent applications

Author Bio

**Crisler, Nancy : Pattonville School District, St. Louis**

**Fisher, Patience : University of Nebraska**

**Froelich, Gary : Consortium for Mathematics and Its Applications, Inc.**

Table of Contents

**Chapter 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 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 Case

Lesson 2.6 Mathematical Induction

Chapter Extension: Envy-Free Division

**Chapter 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: Applications of the Leslie Matrix

**Chapter 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 5. More Graphs, Subgraphs and Trees**

Lesson 5.1 Planarity and Coloring

Lesson 5.2 The Traveling Salesperson Problem

Lesson 5.3 Shortest Route Problems

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 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 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 8. Recursion**

Lesson 8. 1 An Introduction to Recursive Thinking

Lesson 8. 1 Finite Differences

Lesson 8. 1 Arithmetic and Geometric Recursion

Lesson 8. 1 Mixed Recursion, Part 1

Lesson 8. 1 Mixed Recursion, Part 2

Lesson 8. 1 Cobweb Diagrams

Chapter Extension: Fractal Dimensions--NEW!

Answers to Selected Exercises

Sources of Illustrations

Index

Publisher Info

Publisher: W.H. Freeman

Published: 2000

International: No

Published: 2000

International: No

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. The new edition adds a wealth of new features and content, including pedagogical tools aimed at fostering the participatory spirit. Current applications are highlighted through hundreds of real-world examples and a new art program.

- Treatment of a topic usually begins with an exploration activity. We believe that exploration of a problem is critical to understanding it and its solution.
- Lessons are written in an informal style that is designed to be read easily by the student. Users of the book report that students who are absent usually have little trouble reading material they missed.
- Exercises often contain new ideas. Students learn by doing. In most cases, students are expected to do all the exercises.
- The themes of mathematical modeling, appropriate use of technology, and decision making are consistently emphasized
- The strands of algorithmic thinking, recursive thinking, and mathematical induction are woven throughout the book
- New chapter extensions at the end of each chapter (before the exercises) which can serve as starting points for additional explorations, activities and projects related to the chapter
- New sample calculator screens in the text and blackline masters that show detailed instruction for the TI-83
- New biographical captions for photos of individuals important to the development of discrete mathematics
- New coverage of fractals in Chapter 8
- New real-world applications, plus many more examples and projects
- New newspaper clippings highlighting recent applications

**Crisler, Nancy : Pattonville School District, St. Louis**

**Fisher, Patience : University of Nebraska**

**Froelich, Gary : Consortium for Mathematics and Its Applications, Inc.**

**Chapter 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 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 Case

Lesson 2.6 Mathematical Induction

Chapter Extension: Envy-Free Division

**Chapter 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: Applications of the Leslie Matrix

**Chapter 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 5. More Graphs, Subgraphs and Trees**

Lesson 5.1 Planarity and Coloring

Lesson 5.2 The Traveling Salesperson Problem

Lesson 5.3 Shortest Route Problems

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 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 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 8. Recursion**

Lesson 8. 1 An Introduction to Recursive Thinking

Lesson 8. 1 Finite Differences

Lesson 8. 1 Arithmetic and Geometric Recursion

Lesson 8. 1 Mixed Recursion, Part 1

Lesson 8. 1 Mixed Recursion, Part 2

Lesson 8. 1 Cobweb Diagrams

Chapter Extension: Fractal Dimensions--NEW!

Answers to Selected Exercises

Sources of Illustrations

Index