032174456X / 9780321744562 Excursions in Modern Mathematics Plus MyMathLab/MyStatLab Student Access Code Card Package consists of: 0321431308 / 9780321431301 MyMathLab/MyStatLab -- Glue-in Access Card0321568036 / 9780321568038 Excursions in Modern Mathematics0321654064 / 9780321654069 MyMathLab Inside Star Sticker

Peter Tannenbaum has bachelor's degrees in Mathematics and Political Science and a Ph. D. in Mathematics, all from the University of California, Santa Barbara. He has held faculty positions at the University of Arizona, Universidad Simon Bolivar (Venezuela), and is currently professor of mathematics at the California State University, Fresno. His current research interests are in the interface between mathematics, politics and behavioral economics. He is also 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. The Mathematics of Social Choice**

**1. The Mathematics of Voting: The Paradox of Democracy**

1.1 Preference Ballots and Preference Schedules

1.2 The Plurality Method

1.3 The Borda Count Method

1.4 The Plurality-with-Elimination Method (Instant Runoff Voting)

1.5 The Method of Piecewise Comparisons

1.6 Rankings

Profile: Kenneth J. Arrow

Key Concepts

Exercises

Projects and Papers

References and Further Readings

**2. The Mathematics of Power: Weighted Voting **

2.1 An Introduction to Weighted Voting

2.2 The Banzhaf Power Index

2.3 Applications of the Banzhaf Power Index

2.4 The Shapely-Shubik Power Index

2.5 Applications of the Shapely-Shubik Power Index

Profile: Lloyd S. Shapely

Key Concepts

Exercises

Projects and Papers

References and Further Readings

**3. The Mathematics of Sharing: Fair-Division Games**

3.1 Fair-Division Games

3.2 Two Players: The Divider-Chooser Method

3.3 The Lone-Divider Method

3.4 The Lone-Chooser Method

3.5 The Last-Diminisher Method

3.6 The Method of Sealed Bids

3.7 The Method of Markers

Profile: Hugo Steinhaus

Key Concepts

Exercises

Projects and Papers

References and Further Readings

**4. The Mathematics of Apportionment: Making the Rounds**

4.1 Apportionment Problems

4.2 Hamilton's Method and the Quota Rule

4.3 The Alabama and Other Paradoxes

4.4 Jefferson's Method

4.5 Adams's Method

4.6 Webster's Method

Historical Note: A Brief History of Apportionment in the United States

Key Concepts

Exercises

Projects and Papers

References and Further Readings

**Mini-Excursion 1: Apportionment Today**

**Part 2. Management Science**

**5. The Mathematics of Getting Around: Euler Paths and Circuits**

5.1 Euler Circuit Problems

5.2 What is a Graph?

5.3 Graph Concepts and Terminology

5.4 Graph Models

5.5 Euler's Theorems

5.6 Fleury's Algorithm

5.7 Eulerizing Graphs

Profile: Leonard Euler

Key Concepts

Exercises

Projects and Papers

References and Further Readings

**6. The Mathematics of Touring: The Traveling Salesman Problem**

6.1 Hamilton Circuits and Hamilton Paths

6.2 Complete Graphs

6.3 Traveling Salesman Problems

6.4 Simple Strategies for Solving TSPs

6.5 The Brute-Force and Nearest-Neighbor Algorithms

6.6 Approximate Algorithms

6.7 The Repetitive Nearest-Neighbor Algorithm

6.8 The Cheapest Link Algorithm

Profile: Sir William Rowan Hamilton

Key Concepts

Exercises

Projects and Papers

References and Further Readings

**7. The Mathematics of Networks: The Cost of Being Connected**

7.1 Trees

7.2 Spanning Trees

7.3 Kruskal's Algorithm

7.4 The Shortest Network Connecting Three Points

7.5 Shortest Networks for Four or More Points

Profile: Evangelista Torricelli

Key Concepts

Exercises

Projects and Papers

References and Further Readings

**8. The Mathematics of Scheduling: Chasing the Critical Path**

8.1 The Basic Elements of Scheduling

8.2 Directed Graphs (Digraphs)

8.3 Scheduling with Priority Lists

8.4 The Decreasing-Time Algorithm

8.5 Critical Paths

8.6 The Critical-Path Algorithm

8.7 Scheduling with Independent Tasks

Profile: Ronald L. Graham

Key Concepts

Exercises

Projects and Papers

References and Further Readings

**Mini-Excursion 2: A Touch of Color**

**Part 3. Growth And Symmetry**

**9. The Mathematics of Spiral Growth: Fibonacci Numbers and the Golden Ratio**

9.1 Fibonacci's Rabbits

9.2 Fibonacci Numbers

9.3 The Golden Ratio

9.4 Gnomons

9.5 Spiral Growth in Nature

Profile: Leonardo Fibonacci

Key Concepts

Exercises

Projects and Papers

References and Further Readings

**10. The Mathematics of Money: Spending it, Saving It, and Growing It**

10.1 Percentages

10.2 Simple Interest

10.3 Compound Interest

10.4 Geometric Sequences

10.5 Deferred Annuities: Planned Savings for the Future

Key Concepts

Exercises

Projects and Papers

References and Further Readings

**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 Symmetry as a Rigid Motion

11.7 Patterns

Profile: Sir Roger Penrose

Key Concepts

Exercises

Projects and Papers

References and Further Readings

**12. The Geometry of Fractal Shapes: Naturally Irregular**

12.1 The Koch Snowflake

12.2 The Sierpinski Gasket

12.3 The Chaos Game

12.4 The Twisted Sierpinski Gasket

12.5 The Mandelbrot Set

Profile: Benoit Mandelbrot

Key Concepts

Exercises

Projects and Papers

References and Further Readings

**Mini-Excursion 3: The Mathematics of Population Growth: There is Strength in Numbers**

**Part 4. Statistics**

**13. Collecting Statistical Data: Censuses, Surveys, and Clinical Studies**

13.1 The Population

13.2 Sampling

13.3 Random Sampling

13.4 Sampling: Terminology and Key Concepts

13.5 The Capture-Recapture Method

13.6 Clinical Studies

Profile: George Gallup

Key Concepts

Exercises

Projects and Papers

References and Further Readings

**14. Descriptive Statistics: Graphing and Summarizing Data**

14.1 Graphical Descriptions of Data

14.2 Variables

14.3 Numerical Summaries of Data

14.4 Measures of Spread

Profile: W. Edwards Deming

Key Concepts

Exercises

Projects and Papers

References and Further Readings

**15. Chances, Probabilities, and Odds: Measuring Uncertainty**

15.1 Random Experiments and Sample Spaces

15.2 Counting Outcomes in Sample Spaces

15.3 Permutations and Combinations

15.4 Probability Spaces

15.5 Equiprobable Spaces

15.6 Odds

Profile: Persi Diaconis

Key Concepts

Exercises

Projects and Papers

References and Further Readings

**16. The Mathematics of Normal Distributions: The Call of the Bell**

16.1 Approximately Normal Distributions of Data

16.2 Normal Curves and Normal Distributions

16.3 Standardizing Normal Data

16.4 The 68-95-99.7 Rule

16.5 Normal Curves as Models of Real-Life Data Sets

16.6 Distributions of Random Events

16.7 Statistical Inference

Profile: Carl Friedrich Gauss

Key Concepts

Exercises

Projects and Papers

References and Further Readings

**Mini-Excursion 4: The Mathematics of Managing Risk**