Excursions in Modern Mathematics Plus MyMathLab/MyStatLab Student Access Code Card

by Tannenbaum, Peter

• ISBN13: 9780321744562
• ISBN10: 032174456X
• Edition: 7th
• Format: Package
• Copyright: 2010-06-29
• Publisher: Pearson

Summary

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

Author Biography

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).

Table of Contents

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