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Written specifically for high school courses, Discrete Mathematics: Modeling Our World is a new fourth 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 fullyengaged student participation. With this text, students will see the connections among mathematical topics and reallife events and situations, while sharpening their problem solving, mathematical reasoning and communication skills. This new edition adds material on codes, logic, set notation, bin packing, and linear programming.
Chapter 1 Election Theory: Modeling the Voting Process
Lesson 1.1 An Election Activity
Lesson 1.2 GroupRanking Models
Lesson 1.3 More GroupRanking 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 EnvyFree 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 InputOutput Model, Part 1
Lesson 7.2 The Leontief InputOutput 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
New Features of the fourth edition:
• The first fullcolor edition.
• Updated data and news articles throughout.
• An increased emphasis on mathematical modeling.
• A new chapter on codes.
• The appendices of the third edition have been expanded into a tenth chapter with sections on logic, set notation, bin packing, and linear programming.
• A supplemental chapter on statistics will be available separately or as an eleventh chapter through custom publishing.
• A single electronic teacher disc that includes the student text in PDF format as well as answers, teacher notes, blackline masters, software, and test questions.
• A DVD containing all COMAP videos that are referenced in the teacher notes for each chapter.
