Prof. Tannenbaum received Bachelors degrees in Political Science and Mathematics, and a Ph.D. in Pure Mathematics, all from the University of California, Santa Barbara. His mathematical research interests focus primarily in the interface between combinatorics, finite groups and probability, and has published papers in combinatorial designs, finite projective geometries, partitions of groups, probability, generating functions and the computation of power indexes. 

Prof. Tannenbaum has also worked on various aspects of mathematics education, including curriculum development for undergraduate general education mathematics, the preparation of secondary teachers, and Young Scholar Institutes (summer camps for talented high school students). In recognition of this work he has received many grants and awards, including a Mathematical Association of America Award for “Distinguished College or University Teaching of Mathematics.” 

Prof. Tannenbaum was born in Genoa, Italy, and at the age of four his family moved to Montevideo, Uruguay, where he spent his formative years. Beyond mathematics, his interests and hobbies include travel, languages (he speaks five), hiking, riding (bikes and horses), cooking, and most recently, painting. He and his wife Sally have three children (twin boys and a girl) and currently live in Santa Barbara, California. 

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

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