# Discrete Mathematics : Modeling Our World 5th Edition (Student Edition) (Print)

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Written specifically for high school courses, Discrete Mathematics: Modeling Our World is a new fifth edition of the formerly titled Discrete Mathematics Through Applications. It is designed to help you implement mathematical modeling in your classroom, in a way that promotes active learning, critical thinking, and fully engaged student participation. With this text, students will see the connections among mathematical topics and real-life events and situations, while sharpening their problem solving, mathematical reasoning and communication skills. **Chapter 1 Election Theory: Modeling the Voting Process**

Lesson 1.1 An Election Activity

Lesson 1.2 Group-Ranking Models

Lesson 1.3 More Group-Ranking Models 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 **Chapter 2 Fair Division**

Lesson 2.1 A Fair Division Activity

Lesson 2.2 Estate Division

Lesson 2.3 Apportionment Models

Lesson 2.4 More Apportionment Models and Paradoxes

Lesson 2.5 Fair Division Models: The Continuous Case

Lesson 2.6 Mathematical Induction

Chapter Extension Envy-Free Division

Chapter 2 Review **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 Harvesting Animal Populations

Chapter 3 Review**Chapter 4 Graphs as Models**

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**Chapter 5 Modeling with Subgraphs and Trees**

Lesson 5.1 Planarity and Coloring

Lesson 5.2 The Traveling Salesman 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**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 Models

Chapter 6 Review**Chapter 7 Matrix Models**

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**Chapter 8 Recursion**

Lesson 8.1 Introduction to Recursive Modeling

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**Chapter 9 Codes**

Lesson 9.1 A Coding Activity

Lesson 9.2 Error Detection Models

Lesson 9.3 Error Correction Models

Lesson 9.4 Privacy Codes

Chapter Extension A Public Key Model

Chapter 9 Review**Chapter 10 Additional Topics in Discrete Mathematics**

Lesson 10.1 Logic

Lesson 10.2 Set Notation

Lesson 10.3 Bin Packing

Lesson 10.4 Linear Programming

Chapter 10 Review**Features of the fifth edition:**

- Higher quality color printing and paper make the book a half inch thinner.
- Updated data, references, and news articles.
- An increased emphasis on mathematical modeling.
- Technology uses have been expanded to include Desmos in places.
- A supplemental chapter on statistics is available separately or as an eleventh chapter through custom publishing.
- A single electronic teacher USB drive that includes the answers, teacher notes, blackline masters, software, supplemental videos, and test questions.

**Teacher's USB DriveA single electronic teacher USB drive that includes the answers, teacher notes, blackline masters, software, supplemental videos (also available on the COMAP YouTube channel), and test questions.Product Number: 7673USB $88.00 each. (1 FREE with every 25 books.)Webportal: (Email for pricing.) **

Author | Nancy Crisler and Gary Froelich |

Copyright Year | ©2024 by COMAP, Inc. |

ISBN | 978-0-9971490-8-1 |

Product Number | 1513 |

Primary Level | High School |

Additional Levels | Undergraduate |

Application Areas | Discrete Mathematics, Modeling |

Pricing Options | 1-24 cost $175.00 each 25 or more $140.00 each |

Format | 654 Page Casebound Textbook |

Format Options | Print, USB, Webportal |