Digital Dice: Computational Solutions to Practical Probability Problems
288
Digital Dice: Computational Solutions to Practical Probability Problems
288Paperback(With a New preface by the author)
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Overview
Popular-math writer Paul Nahin challenges readers to solve twenty-one difficult but fun problems, from determining the odds of coin-flipping games to figuring out the behavior of elevators. Problems build from relatively easy (deciding whether a dishwasher who breaks most of the dishes at a restaurant during a given week is clumsy or just the victim of randomness) to the very difficult (tackling branching processes of the kind that had to be solved by Manhattan Project mathematician Stanislaw Ulam). In his characteristic style, Nahin brings the problems to life with interesting and odd historical anecdotes. Readers learn, for example, not just how to determine the optimal stopping point in any selection process but that astronomer Johannes Kepler selected his second wife by interviewing eleven women.
The book shows readers how to write elementary computer codes using any common programming language, and provides solutions and line-by-line walk-throughs of a MATLAB code for each problem.
Digital Dice will appeal to anyone who enjoys popular math or computer science. In a new preface, Nahin wittily addresses some of the responses he received to the first edition.
Product Details
| ISBN-13: | 9780691158211 |
|---|---|
| Publisher: | Princeton University Press |
| Publication date: | 03/24/2013 |
| Series: | Princeton Puzzlers |
| Edition description: | With a New preface by the author |
| Pages: | 288 |
| Sales rank: | 421,722 |
| Product dimensions: | 5.50(w) x 8.40(h) x 0.90(d) |
About the Author
Table of Contents
Preface to the Paperback Edition xiii
Introduction 1
The Problems 35
1. The Clumsy Dishwasher Problem 37
2. Will Lil and Bill Meet at the Malt Shop? 38
3. A Parallel Parking Question 40
4. A Curious Coin-Flipping Game 42
5. The Gamow-Stern Elevator Puzzle 45
6. Steve's Elevator Problem 48
7. The Pipe Smoker's Discovery 51
8. A Toilet Paper Dilemma 53
9. The Forgetful Burglar Problem 59
10. The Umbrella Quandary 61
11. The Case of the Missing Senators 63
12. How Many Runners in a Marathon? 65
13. A Police Patrol Problem 69
14. Parrondo's Paradox 74
15. How Long Is the Wait to Get the Potato Salad? 77
16. The Appeals Court Paradox 81
17. Waiting for Buses 83
18. Waiting for Stoplights 85
19. Electing Emperors and Popes 87
20. An Optimal Stopping Problem 91
21. Chain Reactions, Branching Processes, and Baby Boys 96
MATLAB Solutions To The Problems 101
1. The Clumsy Dishwasher Problem 103
2. Will Lil and Bill Meet at the Malt Shop? 105
3. A Parallel Parking Question 109
4. A Curious Coin-Flipping Game 114
5. The Gamow-Stern Elevator Puzzle 120
6. Steve's Elevator Problem 124
7. The Pipe Smoker's Discovery 129
8. A Toilet Paper Dilemma 140
9. The Forgetful Burglar Problem 144
10. The Umbrella Quandary 148
11. The Case of the Missing Senators 153
12. How Many Runners in a Marathon? 157
13. A Police Patrol Problem 160
14. Parrondo's Paradox 169
15. How Long is the Wait to Get the Potato Salad? 176
16. The Appeals Court Paradox 184
17. Waiting for Buses 187
18. Waiting for Stoplights 191
19. Electing Emperors and Popes 197
20. An Optimal Stopping Problem 204
21. Chain Reactions, Branching Processes, and Baby Boys 213
Appendix 1. One Way to Guess on a Test 221
Appendix 2. An Example of Variance-Reduction in the Monte Carlo Method 223
Appendix 3. Random Harmonic Sums 229
Appendix 4. Solving Montmort's Problem by Recursion 231
Appendix 5. An Illustration of the Inclusion-Exclusion Principle 237
Appendix 6. Solutions to the Spin Game 244
Appendix 7. How to Simulate Kelvin's Fair Coin with a Biased Coin 248
Appendix 8. How to Simulate an Exponential Random Variable 252
Appendix 9. Index to Author-Created MATLAB m-Files in the Book 255
Glossary 257
Acknowledgments 259
Index 261
Also by Paul J. Nahin 265
What People are Saying About This
"Paul Nahin's Digital Dice is a marvelous book, one that is even better than his Duelling Idiots. Nahin presents twenty-one great probability problems, from George Gamow's famous elevator paradox (as corrected by Donald Knuth) to a bewildering puzzle involving two rolls of toilet paper, and he solves them all with the aid of Monte Carlo simulations and brilliant, impeccable reasoning."—Martin Gardner"Nahin's new book is a rich source of tantalizing, real-life probability puzzles that require considerable ingenuity, and in most cases computer simulation, to solve. Though written to be delved into rather than read cover-to-cover, Digital Dice has an engaging and often witty style that makes each chapter a pleasurable read."—Keith Devlin, author of The Math Gene and The Math Instinct"Open this delightful, matchless book to be sucked into a treasure trove of wonderful conundrums of everyday life. Then, persuaded by straightforward Monte Carlo simulation exercises, emerge refreshed, invigorated, and fully satisfied by the unique experience of learning from Nahin's marvelous Digital Dice."—Joseph Mazur, author of The Motion Paradox"One of the strengths of Digital Dice is its wealth of historical information. Nahin carefully notes the origin of each problem and traces its history. He also tells a number of amusing anecdotes. I found all the problems interesting, especially Parrondo's Paradox. Anyone who has not met this paradox will be amazed by it! Digital Dice is a very enjoyable read."—Nick Hobson, creator of the award-winning Web site Nick's Mathematical Puzzles"By presenting problems for which complete theoretical analysis is difficult or currently impossible, Digital Dice is a reminder that mathematics is often advanced by investigation, long before theoretical tools are brought to bear. The book's choice of problems is eclectic and interesting, and the explanations are clear and easy to read. A welcome addition to popular mathematical literature."—Julian Havil, author of Nonplussed!: Mathematical Proof of Implausible Ideas