# Excursions in Modern Mathematics

, by Tannenbaum, Peter**Note:**Supplemental materials are not guaranteed with Rental or Used book purchases.

- ISBN: 9780321825735 | 032182573X
- Cover: Hardcover
- Copyright: 12/21/2012

**Peter Tannenbaum**earned his bachelor's degrees in Mathematics and Political Science and his PhD in Mathematics from the University of California–Santa Barbara. He has held faculty positions at the University of Arizona, Universidad Simon Bolivar (Venezuela), and is professor emeritus of mathematics at the California State University–Fresno. His research examines the interface between mathematics, politics, and behavioral economics. He has been involved in mathematics curriculum reform and teacher preparation. His hobbies are travel, foreign languages and sports. He is married to Sally Tannenbaum, a professor of communication at CSU Fresno, and is the father of three (twin sons and a daughter).

**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

Conclusion

Key Concepts

Exercises

Projects and Papers

**PART 4. 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

Projects and Papers

**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

13.4 The Mandelbrot Set

Conclusion

Key Concepts

Exercises

Projects and Papers

**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

Projects and Papers

**PART 5. 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

Projects and Papers

**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

Projects and Papers

**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

Projects and Papers

**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

Projects and Papers

Answers to Selected Exercises

Index

Photo Credits