Mathematics for Elementary Teachers with Activities, 5th edition

I. SOCIAL CHOICE

1. The Mathematics of Elections: The Paradoxes of Democracy
   • 1.1 The Basic Elements of an Election
   • 1.2 The Plurality Method
   • 1.3 The Borda Count Method
   • 1.4 The Plurality-with-Elimination Method
   • 1.5 The Method of Pairwise Comparisons
   • 1.6 Fairness Criteria and Arrow’s Impossibility Theorem
   • Conclusion
   • Key Concepts
   • Exercises
2. The Mathematics of Power: Weighted Voting
   • 2.1 An Introduction to Weighted Voting
   • 2.2 Banzhaf Power
   • 2.3 Shapley-Shubik Power
   • 2.4 Subsets and Permutations
   • Conclusion
   • Key Concepts
   • Exercises
3. The Mathematics of Sharing: Fair-Division Games
   • 3.1 Fair-Division Games
   • 3.2 The Divider-Chooser Method
   • 3.3 The Lone-Divider Method
   • 3.4 The Lone-Chooser Method
   • 3.5 The Method of Sealed Bids
   • 3.6 The Method of Markers
   • Conclusion
   • Key Concepts
   • Exercises
4. The Mathematics of Apportionment: Making the Rounds
   • 4.1 Apportionment Problems and Apportionment Methods
   • 4.2 Hamilton’s Method
   • 4.3 Jefferson’s Method
   • 4.4 Adams’s and Webster’s Methods
   • 4.5 The Huntington-Hill Method
   • 4.6 The Quota Rule and Apportionment Paradoxes
   • Conclusion
   • Key Concepts
   • Exercises

II. MANAGEMENT SCIENCE

5. The Mathematics of Getting Around: Euler Paths and Circuits
   • 5.1 Street-Routing Problems
   • 5.2 An Introduction to Graphs
   • 5.3 Euler’s Theorems and Fleury’s Algorithm
   • 5.4 Eulerizing and Semi-Eulerizing Graphs
   • Conclusion
   • Key Concepts
   • Exercises
6. The Mathematics of Touring: Traveling Salesman Problems
   • 6.1 What Is a Traveling Salesman Problem?
   • 6.2 Hamilton Paths and Circuits
   • 6.3 The Brute-Force Algorithm
   • 6.4 The Nearest-Neighbor and Repetitive Nearest-Neighbor Algorithms
   • 6.5 The Cheapest-Link Algorithm
   • Conclusion
   • Key Concepts
   • Exercises
7. The Mathematics of Networks: The Cost of Being Connected
   • 7.1 Networks and Trees
   • 7.2 Spanning Trees, MSTs, and MaxSTs
   • 7.3 Kruskal’s Algorithm
   • Conclusion
   • Key Concepts
   • Exercises
8. The Mathematics of Scheduling: Chasing the Critical Path
   • 8.1 An Introduction to Scheduling
   • 8.2 Directed Graphs
   • 8.3 Priority-List Scheduling
   • 8.4 The Decreasing-Time Algorithm
   • 8.5 Critical Paths and the Critical-Path Algorithm
   • Conclusion
   • Key Concepts
   • Exercises

III. GROWTH

9. Population Growth Models: There Is Strength in Numbers
   • 9.1 Sequences and Population Sequences
   • 9.2 The Linear Growth Model
   • 9.3 The Exponential Growth Model
   • 9.4 The Logistic Growth Model
   • Conclusion
   • Key Concepts
   • Exercises
10. Financial Mathematics: Money Matters
    • 10.1 Percentages
    • 10.2 Simple Interest
    • 10.3 Compound Interest
    • 10.4 Retirement Savings
    • 10.5 Consumer Debt
    • Conclusion
    • Key Concepts
    • Exercises

IV. SHAPE AND FORM

11. The Mathematics of Symmetry: Beyond Reflection
    • 11.1 Rigid Motions
    • 11.2 Reflections
    • 11.3 Rotations
    • 11.4 Translations
    • 11.5 Glide Reflections
    • 11.6 Symmetries and Symmetry Types
    • 11.7 Patterns
    • Conclusion
    • Key Concepts
    • Exercises
12. Fractal Geometry: The Kinky Nature of Nature
    • 12.1 The Koch Snowflake and Self-Similarity
    • 12.2 The Sierpinski Gasket and the Chaos Game
    • 12.3 The Twisted Sierpinski Gasket
    • 12.4 The Mandelbrot Set
    • Conclusion
    • Key Concepts
    • Exercises
13. Fibonacci Numbers and the Golden Ratio: Tales of Rabbits and Gnomons
    • 13.1 Fibonacci Numbers
    • 13.2 The Golden Ratio
    • 13.3 Gnomons
    • 13.4 Spiral Growth in Nature
    • Conclusion
    • Key Concepts
    • Exercises

V. STATISTICS

14. Censuses, Surveys, Polls, and Studies: The Joys of Collecting Data
    • 14.1 Enumeration
    • 14.2 Measurement
    • 14.3 Cause and Effect
    • Conclusion
    • Key Concepts
    • Exercises
15. Graphs, Charts, and Numbers: The Data Show and Tell
    • 15.1 Graphs and Charts
    • 15.2 Means, Medians, and Percentiles
    • 15.3 Ranges and Standard Deviations
    • Conclusion
    • Key Concepts
    • Exercises
16. Probabilities, Odds, and Expectations: Measuring Uncertainty and Risk
    • 16.1 Sample Spaces and Events
    • 16.2 The Multiplication Rule, Permutations, and Combinations
    • 16.3 Probabilities and Odds
    • 16.4 Expectations
    • 16.5 Measuring Risk
    • Conclusion
    • Key Concepts
    • Exercises
17. The Mathematics of Normality: The Call of the Bell
    • 17.1 Approximately Normal Data Sets
    • 17.2 Normal Curves and Normal Distributions
    • 17.3 Modeling Approximately Normal Distributions
    • 17.4 Normality in Random Events
    • Conclusion
    • Key Concepts
    • Exercises

Answers to Selected Exercises

Credits

Index

Index of Applications