*PREFACE*

**CHAPTER 1 VOTING METHODS **

1.1 Plurality and Runoff Methods

*Runoff Elections *

*Preference Rankings*

1.2 Borda’s Method: A Scoring System

1.3 Head-to-Head Comparisons

*Single-Peaked Preference Rankings *

1.4 Approval Voting

1.5 The Search for an Ideal Voting System

1.6 Weighted Voting Systems

*Dictators, Dummies, and Veto Power*

*The Banzhaf Power Index *

*The Shapley-Shubik Power Index *

*Writing Exercises *

*Projects*

*Key Terms *

*Review Test*

*Suggested Readings*

**CHAPTER 2 APPORTIONMENT: SHARING WHAT CANNOT BE DIVIDED ARBITRARILY**

2.1 Quota Methods

*Hamilton’s Method*

*Lowndes’ Method *

2.2 Early Divisor Methods

*Jefferson’s Method*

*Webster’s Method*

2.3 Apportionment in Today’s House of Representatives

*The Hill–Huntington Method*

*Other Apportionment Methods*

2.4 The Search for an Ideal Apportionment Method

*Writing Exercises *

*Projects *

*Key Terms *

*Review Test*

*Suggested Readings *

**CHAPTER 3 THE MATHEMATICS OF MONEY **

3.1 Powers, Roots, and Logarithms

3.2 Simple Interest

3.3 Compound Interest

*Inflation*

3.4 The Rewards of Systematic Savings

3.5 Amortized Loans

*Finding a Loan Balance *

*Amortization Schedules *

*Writing Exercises *

*Projects *

*Key Terms *

*Review Test*

*Suggested Readings *

**CHAPTER 4 PROBABILITY **

4.1 Elementary Probability

4.2 Odds

*House Odds and Fair Bets *

4.3 The Addition Rule

4.4 Conditional Probability and the Multiplication Rule

*The Multiplication Rule *

*Independence and the Multiplication Rule *

4.5 Counting Techniques

*Permutations *

*Combinations *

4.6 Probability Problems Using Counting Techniques

*The Birthday Problem *

4.7 Expected Value

4.8 Genetics

*Writing Exercises *

*Projects *

*Key Terms *

*Review Test*

*Suggested Readings*

**CHAPTER 5 STATISTICS **

5.1 Organizing and Presenting Data

*Bar Graphs *

*Histograms *

*Pie Charts *

5.2 Typical and Central Values

*The Mode *

*The Median *

*The Mean *

*Estimating the Mean of Grouped Data *

5.3 Measures of Spread

*The Range *

*The Standard Deviation *

*Estimating the Standard Deviation of Grouped Data *

5.4 The Normal Distribution

*Percentiles *

5.5 Estimating the Mean

*Confidence Intervals *

*Sample Standard Deviation and Confidence Intervals *

5.6 Polls and Margin of Error

5.7 Garbage In, Garbage Out: A Look at Misleading Uses of Statistics and at Sampling Techniques

*The Source of the Data *

*The Data: Questions and Answers *

*The Conclusions Drawn from the Data *

*Writing Exercises *

*Projects *

*Key Terms *

*Review Test*

*Suggested Readings *

**CHAPTER 6 PATHS AND NETWORKS **

6.1 Eulerian Paths and Circuits on Graphs

*Eulerization *

6.2 The Traveling Salesman Problem

*The Nearest Neighbor Algorithm *

*The Greedy Algorithm *

6.3 Efficient Networking: Minimal Spanning Trees

*Prim’s Algorithm *

*Writing Exercises *

*Projects *

*Key Terms *

*Review Test*

*Suggested Readings*

**CHAPTER 7 TILINGS AND POLYHEDRA **

7.1 Polygons

7.2 Tiling’s

*Regular Tilings *

*Semiregular Tiling’s *

*Tiling’s with Nonregular Polygons *

*Tilings with Other Shapes *

7.3 Polyhedra

*Regular Polyhedra *

*Semiregular Polyhedra *

*Writing Exercises *

*Projects *

*Key Terms *

*Review Test*

*Suggested Readings *

**CHAPTER 8 NUMBER THEORY **

8.1 Divisibility and Primes

*Prime Numbers *

*The Division Algorithm *

*The Greatest Common Divisor *

8.2 Modular Arithmetic

8.3 Divisibility Tests

8.4 Check Digits

8.5 Tournament Scheduling

8.6 Introduction to Cryptology

*The Caesar Cipher *

*Affine Ciphers *

8.7 Advanced Encryption Methods

*The Hill Cipher *

*The RSA Public Key System *

*Writing Exercises *

*Projects *

*Key Terms *

*Review Test*

*Suggested Readings *

*APPENDIX A *

*ANSWERS TO SELECTED EXERCISES*