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E-raamat: Mathematics in Games, Sports, and Gambling: The Games People Play, Second Edition

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(Emory University, Atlanta, Georgia, USA)
  • Formaat: 378 pages
  • Sari: Textbooks in Mathematics
  • Ilmumisaeg: 28-Oct-2015
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781498719537
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Mathematics in Games, Sports, and Gambling: The Games People Play, Second EditionSuurem pilt
  • Formaat: 378 pages
  • Sari: Textbooks in Mathematics
  • Ilmumisaeg: 28-Oct-2015
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781498719537
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Mathematics in Games, Sports, and Gambling: The Games People Play, Second Edition demonstrates how discrete probability, statistics, and elementary discrete mathematics are used in games, sports, and gambling situations. With emphasis on mathematical thinking and problem solving, the text draws on numerous examples, questions, and problems to explain the application of mathematical theory to various real-life games.

This updated edition of a widely adopted textbook considers a number of popular games and diversions that are mathematically based or can be studied from a mathematical perspective. Requiring only high school algebra, the book is suitable for use as a textbook in seminars, general education courses, or as a supplement in introductory probability courses.

New in this Edition:











Many new exercises, including basic skills exercises More answers in the back of the book Expanded summary exercises, including writing exercises More detailed examples, especially in the early chapters An expansion of the discrete adjustment technique for binomial approximation problems New sections on chessboard puzzles that encourage students to develop graph theory ideas New review material on relations and functions

Exercises are included in each section to help students understand the various concepts. The text covers permutations in the two-deck matching game so derangements can be counted. It introduces graphs to find matches when looking at extensions of the five-card trick and studies lexicographic orderings and ideas of encoding for card tricks.

The text also explores linear and weighted equations in the section on the NFL passer rating formula and presents graphing to show how data can be compared or displayed. For each topic, the author includes exercises based on real games and actual sports data.
List of Figures xiii
List of Tables xvii
Preface xix
Author xxiii
1 Basic Probability 1(48)
1.1 Introduction
1(1)
1.2 Of Dice and Men
1(8)
1.3 Probability
9(3)
1.4 The Laws That Govern Us
12(11)
1.4.1 Dependent Events
15(8)
1.5 Poker Hands versus Batting Orders
23(5)
1.6 Let's Play for Money!
28(4)
1.7 Is That Fair?
32(7)
1.8 The Odds Are against Us
39(2)
1.9 Things Vary
41(3)
1.10 Conditional Expectation
44(5)
2 The Game's Afoot 49(40)
2.1 Applications to Games
49(1)
2.2 Counting and Probability in Poker Hands
49(5)
2.3 Roulette
54(4)
2.4 Craps
58(7)
2.4.1 Street Craps
60(1)
2.4.2 Casino Craps
61(1)
2.4.3 Other Bets
62(3)
2.5 Let's Make a Deal — The Monty Hall Problem
65(3)
2.6 Carnival Games
68(3)
2.7 Other Casino Games
71(6)
2.7.1 Caribbean Stud Poker
71(2)
2.7.2 Keno
73(1)
2.7.3 Blackjack
74(3)
2.8 Backgammon
77(12)
2.8.1 Hitting Blots
78(1)
2.8.2 Off the Bar
79(1)
2.8.3 Bearing Off
80(2)
2.8.4 Doubling
82(7)
3 Repeated Play 89(40)
3.1 Introduction
89(1)
3.2 Binomial Coefficients
89(9)
3.3 The Binomial Distribution
98(11)
3.4 The Poisson Distribution
109(6)
3.5 Streaks — Are They Real?
115(3)
3.6 Betting Strategies
118(4)
3.7 The Gambler's Ruin
122(7)
4 Card Tricks and More 129(22)
4.1 Introduction
129(1)
4.2 The Five-Card Trick
129(10)
4.2.1 Adding a Joker to the Deck
133(1)
4.2.2 More Variations of the Trick
133(6)
4.3 The Two-Deck Matching Game
139(4)
4.4 More Tricks
143(3)
4.4.1 Friends Find Each Other
144(1)
4.4.2 The Small Arithmetic Trick
144(1)
4.4.3 The Nine-Card Trick
145(1)
4.5 The Paintball Wars
146(5)
5 Dealing with Data 151(36)
5.1 Introduction
151(1)
5.2 Batting Averages and Simpson's Paradox
152(5)
5.3 NFL Passer Ratings
157(3)
5.4 Viewing Data — Simple Graphs
160(14)
5.4.1 Time Plots and Regression Lines
163(7)
5.4.2 When to Find the Regression Line
170(4)
5.5 Confidence in Our Estimates
174(4)
5.6 Measuring Differences in Performance
178(9)
5.6.1 Coefficient of Variation
181(2)
5.6.2 Relative Performance
183(4)
6 Testing and Relationships 187(28)
6.1 Introduction
187(1)
6.2 Suzuki versus Pujols
187(3)
6.3 I'll Decide if I Believe That
190(6)
6.3.1 Errors
192(1)
6.3.2 Summary of Hypothesis Testing
192(1)
6.3.3 One-Sided Tests
193(1)
6.3.4 Small Sample Sizes
194(2)
6.4 Are the Old Adages True?
196(7)
6.4.1 Home Field Advantage
196(3)
6.4.2 Lefty versus Righty
199(4)
6.5 How Good Are Certain Measurements?
203(4)
6.5.1 Batting Average and Runs Scored
205(2)
6.6 Arguing over Outstanding Performances
207(3)
6.7 A Last Look at Comparisons
210(5)
6.7.1 Small Sample Comparisons
210(5)
7 Games and Puzzles 215(58)
7.1 Introduction
215(1)
7.2 Number Arrays
215(11)
7.2.1 Magic Squares
215(6)
7.2.2 Variations on Magic Squares
221(2)
7.2.3 Sudoku
223(3)
7.3 The Tower of Hanoi
226(9)
7.3.1 Finding Solutions
228(4)
7.3.2 Bicolored Tower of Hanoi
232(1)
7.3.3 The Derangement Tower of Hanoi
233(2)
7.4 Instant Insanity
235(6)
7.5 Lights Out
241(4)
7.6 Peg Games
245(9)
7.6.1 English Board
245(4)
7.6.2 Triangular Peg Solitaire
249(5)
7.7 Puzzles on the Chessboard
254(6)
7.7.1 Chessboards and Dominoes — Tilings
254(6)
7.8 Guarini's Problem
260(2)
7.9 Martin Gardner's No 3-in-a-Line Problem
262(3)
7.10 The Knight's Tour
265(1)
7.11 Domination and Independence
266(3)
7.12 Attacking Placements and Independence
269(4)
8 Combinatorial Games 273(38)
8.1 Introduction to Combinatorial Games
273(1)
8.2 Subtraction Games
274(1)
8.3 Nim
275(10)
8.3.1 Poker Nim
281(1)
8.3.2 Moore's Nim
281(2)
8.3.3 Other Games
283(2)
8.4 Games as Digraphs
285(6)
8.4.1 Sums of Games
286(1)
8.4.2 The Sprague-Grundy Function
287(2)
8.4.3 More about Impartial Games
289(2)
8.5 Blue-Red Hackenbush
291(7)
8.6 Green Hackenbush
298(5)
8.6.1 Pruning Green Hackenbush Trees
299(4)
8.7 Games as Numbers
303(4)
8.8 More about Nimbers
307(4)
9 Appendix 311(36)
9.1 Review of Elementary Set Theory
311(6)
9.2 Relations and Functions
317(6)
9.2.1 Functions
319(4)
9.3 Standard Normal Distribution Table
323(1)
9.4 Student's t-Distribution
324(1)
9.5 Solutions to Problems
325(3)
9.6 Solutions to Selected Exercises
328(19)
Bibliography 347(4)
Index 351
Ronald J. Gould received a B.S. in Mathematics from the State University of New York at Fredonia in 1972, an M.S. in Computer Science in 1978 from Western Michigan University, and Ph.D. in Mathematics in 1979 from Western Michigan University. He joined the faculty of Emory University in 1979.Professor Gould specializes in Graph Theory with general interests in discrete mathematics and algorithms. He has written over 170 research papers and one book in this area. Professor Gould serves on the Editorial Boards of several journals in the area of discrete mathematics. Over the years he has directed over 25 master's theses and more than 25 Ph.D. dissertations.Professor Gould has received a number of honors including teaching awards from Western Michigan University (1976) and Emory University (1999), as well as the Mathematical Association of America's Southeastern Section Distinguished Teaching Award in 2008. He has also received alumni awards from both SUNY Fredonia and Western Michigan University. He was awarded the Goodrich C. White Chair from Emory University in 2001.
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