**Mathematical World**

Volume: 3;
1993;
152 pp;
Softcover

MSC: Primary 92;
Secondary 90

Print ISBN: 978-0-8218-9500-9

Product Code: MAWRLD/3

List Price: $25.00

AMS Member Price: $20.00

MAA Member Price: $22.50

**Electronic ISBN: 978-1-4704-2471-8
Product Code: MAWRLD/3.E**

List Price: $25.00

AMS Member Price: $20.00

MAA Member Price: $22.50

# Mathematics and Sports

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*L. E. Sadovskiĭ; A. L. Sadovskiĭ*

This unique book presents simple mathematical models of various aspects of sports with applications to sports training and competitions. Requiring only a background in precalculus, it would be suitable as a textbook for courses in mathematical modeling and operations research at the high school or college level. Coaches and those who participate in sports will find it interesting as well. The lively writing style and wide range of topics make this book especially appealing.

#### Readership

Advanced high school and undergraduate mathematics students. Coaches and sportsmen with elementary (pre-calculus) mathematics knowledge.

#### Reviews & Endorsements

Some of the … mathematical applications—particularly in areas related to operations research—are more intriguing. The authors have made a good effort to draw illustrations from many different sports … They also demonstrate a wide variety of mathematical techniques with relatively simple examples … a student might find something here to spark an interest in further investigation.

-- Journal of the American Statistical Association

A nice survey of applications of mathematics in sporting events.

-- Mathematical Reviews

Treatment is concise and insightful.

-- Zentralblatt MATH

#### Table of Contents

# Table of Contents

## Mathematics and Sports

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Table of Contents v6 free
- Preface ix10 free
- Chapter 1. Mathematics and Sports (in Place of a Foreword) 112 free
- Chapter 2. What is Applied Mathematics? 516
- Chapter 3. Why Five Sets? (Mathematical Modeling of Tennis) 1324
- Section 3.1 A little history 1324
- Section 3.2 The arithmetic of tennis 1425
- Section 3.3 How long should one play? 1526
- Section 3.4 Elementary concepts of probability theory 1627
- Section 3.5 The model of a game is a Markov chain 1829
- Section 3.6 Play! 1930
- Section 3.7 Finishing the game 2031
- Section 3.8 Vector operations 2132
- Section 3.9 Now let us go on to complete the set 2233
- Section 3.10 Let's have it out 2435
- Section 3.11 Practice makes perfect 2536
- Section 3.12 Model of a tiebreaker 2637
- Section 3.13 Markov chains and basketball 2738

- Chapter 4. Those Judges! 3546
- Section 4.1 What is an examination by experts? 3546
- Section 4.2 Rankings 3647
- Section 4.3 Shortcomings of the majority principle 3748
- Section 4.4 Judging figure skating 4051
- Section 4.5 Multiround examinations by experts and their modeling 4556
- Section 4.6 Hierarchic examination (judging competitive gymnastics) 4758
- Section 4.7 Examination by experts. An overview 4960

- Chapter 5. Records! Records! 5364
- Chapter 6. Linear Programming and Sports 7182
- Section 6.1 Positioning players on a basketball team 7182
- Section 6.2 Soccer clubs and players 7586
- Section 6.3 Some basic concepts and facts 7889
- Section 6.4 The problem of an athlete's diet 8495
- Section 6.5 Linear programming problems 8697
- Section 6.6 Corner points and convex combinations 90101
- Section 6.7 Corner points and feasible solutions 93104
- Section 6.8 The simplex method 95106
- Section 6.9 Indoors or out? 96107
- Section 6.10 Some general inferences 99110

- Chapter 7. Game Models 103114
- Section 7.1 Meteors vs. Pennants (on a soccer theme) 103114
- Section 7.2 Matrix games 107118
- Section 7.3 Problem of the final spurt 114125
- Section 7.4 Games against nature 118129
- Section 7.5 How to wax skis 118129
- Section 7.6 The iron game 121132
- Section 7.7 Matrix games and linear programming 126137
- Section 7.8 Zany Zebras at Mayapple Leafs (on a hockey theme) 127138
- Section 7.9 How to form a swimming team 129140

- Chapter 8. Organizing Competitions is an Operations Planning Problem 131142
- Chapter 9. Classifications in Sports 139150
- Chapter 10. Conclusion 147158
- References 151162
- Back Cover Back Cover1164