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# Mathematics Beyond the Numbers

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

** Edition: ** 3

** Copyright: ** 2022

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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*** 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 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*

**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: 9781792432927, 9798765729748

### Print Package

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** ISBN ** 9781792432927

** Details ** Print Prod w/Maple TA 180 days