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Discrete Mathematics Through Application

Discrete Mathematics Through Application - 2nd edition

Discrete Mathematics Through Application - 2nd edition

ISBN13: 9780716736523

ISBN10: 0716736527

Discrete Mathematics Through Application by Nancy Crisler, Patience Fisher and Gary W. Froelich - ISBN 9780716736523
Edition: 2ND 00
Copyright: 2000
Publisher: W.H. Freeman
Published: 2000
International: No
Discrete Mathematics Through Application by Nancy Crisler, Patience Fisher and Gary W. Froelich - ISBN 9780716736523

ISBN13: 9780716736523

ISBN10: 0716736527


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

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