PART 1. 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

   Projects and Papers

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

   Projects and Papers

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

   Projects and Papers

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

   Projects and Papers

PART 2. 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

   Projects and Papers

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

   Projects and Papers

   The Mathematics of Networks

7. The Cost of Being Connected

7.1 Networks and Trees

7.2 Spanning Trees, MST’s, and MaxST’s

7.3 Kruskal’s Algorithm

   Conclusion

   Key Concepts

   Exercises

   Projects and Papers

8. The Mathematics of Scheduling: Chasing the Critical Path

8.1 An Introduction to Scheduling

8.4 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

   Projects and Papers

PART 3. 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

   Projects and Papers

10. Financial Mathematics: Money Matters

10.1 Percentages

10.2 Simple Interest

10.3 Compound Interest

10.4 Consumer Debt