Understanding Modern Mathematics

Understanding Modern Mathematics is an exceptional collection of topics meant to better acquaint students with mathematics through an exposure to its applications and an analysis of its culture. The text provides an in-depth focus on such key topics as probability, statistics, voting systems, game theory, and linear programming. Two additional chapters on geometry and symmetry can be found on the text's web site, providing students the opportunity to see the 3-dimensional geometric figures in full color. The text provides students with an understanding of how these important mathematical topics are relevant in their everyday lives while emphasizing the history of mathematics . Understanding Modern Mathematics is the perfect complement to any Liberal Arts Mathematics course. Click Here to View Chapter 6 Click Here to View Chapter 7

Preface

vii

Chapter 1 Probability

1.1 The Quantification of Likelihood

1

(9)

1.2 Galileo Galilei (A Historical Interlude)

10

(5)

1.3 Binomial Processes

15

(7)

1.4 The Normal Approximation

22

(9)

1.5 Activities/Websites

31

(2)

Chapter 2 Statistics

33

(54)

2.1 Summarizing Data

33

(10)

2.2 Totaling Measurement Errors

43

(7)

2.3 Least Squares and Regression

50

(8)

2.4 Normally Distributed Data

58

(13)

2.5 Statistical Inference

71

(11)

2.6 The Central Limit Theorem

82

(4)

2.7 Activities/Websites

86

(1)

Chapter 3 Voting Systems

87

(50)

3.1 Introduction

87

(1)

3.2 Mathematical Concepts

88

(1)

3.3 The Plurality Problem

89

(7)

3.4 Rank-Order Voting: The Borda Count

96

(11)

3.5 Sequential Pairwise Comparisons

107

(6)

3.6 Condorcet Methods: The Round Robin Tournament

113

(17)

3.7 Single Vote Systems: Cousins of Plurality and Majority Rule

130

(5)

3.8 Conclusion

135

(2)

Chapter 4 Game Theory

137

(70)

4.1 Introduction to Games

137

(11)

4.2 Formal Zero-Sum Games

148

(9)

4.3 Pure Strategies for Nonzero-Sum Games

157

(12)

4.4 Mixed Strategies for Nonzero-Sum Games

169

(19)

4.5 The Solution of Zero-Sum Games

188

(16)

4.6 Activities/Websites

204

(3)

Chapter 5 Linear Programming

207

5.1 Graphing Inequalities

207

(15)

5.2 Optimization

222

Chapters 6 and 7 are available online at the publisher's website.

Appendix

A-1

Table A

A Table of the Normal Distribution

A-1

Table B

A Table of Binomial Probabilities

A-3

References and Further Readings

R-1

Solutions to Selected Exercises

S-1

Index

I-1

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Understanding Modern Mathematics

Summary

Table of Contents

Supplemental Materials

FREE SHIPPING

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5% off 1 book, 7% off 2 books, 10% off 3+ books

Understanding Modern Mathematics

Summary

Table of Contents

Supplemental Materials

Digital License