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# Mathematics Beyond the Numbers

**Author(s):** * George T Gilbert, Rhonda L Hatcher *

** Edition: ** 2

** Copyright: ** 2014

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** Mathematics Beyond the Numbers** is written in a conversational style and uses real-world data and applications to make the topics come to life for today’s students!

Designed for a one or two-semester liberal arts mathematics course, ** Mathematics Beyond the Numbers** integrates a great deal of historical background so that students can see the development of mathematics over time. In addition, some of the topics included in

**are particularly applicable to a student’s field of study. For instance, voting methods and apportionment are of interest to a political science major**

*Mathematics Beyond the Numbers*The **NEW** second edition of ** Mathematics Beyond the Numbers** by George T. Gilbert and Rhonda L. Hatcher:

**Is Flexible!**The chapters are independent of one another and can be presented in any order.**Is Interactive!**Students have access to an accompanying course website that includes online homework.**Is Practical!**Numerous exercises and examples teach students mathematical problem-solving skills so they can carry out what they have learned.**Integrates Technology!***Technology Tips*guide instructors and students to the possibilities of using technology.**Is Easy-to-Adopt!**An*Instructor’s Solutions Manual*is provided to all adopting instructors.

**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 Tilings

Regular Tilings

Semiregular Tilings

Tilings 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**

**George T Gilbert**

George Gilbert earned a B.A. in mathematics from Washington University in 1979 and a Ph.D. in mathematics from Harvard University in 1984, specializing in number theory. He has held teaching positions at the University of Texas in Austin, Saint Olaf College, and has been on the faculty at Texas Christian University for the past 20+ years. Professor Gilbert is active in the area of problem solving, having served on the William Lowell Putnam questions committee, the AIME contest committee, and as the editor of the *Problems Section of Mathematics Magazine*.

**Rhonda L Hatcher**

Rhonda Hatcher earned a B.A. in mathematics from the University of Colorado at Boulder in 1980 and a Ph.D. in mathematics from Harvard University in 1987. Her research specialty is number theory. She has taught at Saint Olaf College and is currently on the faculty of Texas Christian University. Professor Hatcher won the 1994 Deans’ Teaching Award, the 1997 Honors Professor of the Year Award, and the 2000 Chancellor’s Award for Distinguished Teaching at TCU. In 1998, the Mathematical Association of America awarded her the Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching of Mathematics. In 2000, she was awarded the Texas Professor of the Year award from The Carnegie Foundation for Advancement of Teaching and Council for Advancement and Support of Education.

#### Related ISBN's: 9781465281906, 9781465278296

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** ISBN ** 9781465281906

** Details ** eBook W/Mobius 180 days