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Digital Dice: Computational Solutions to Practical Probability Problems (New in Paperback) (Princeton Puzzlers)by Paul J Nahin
Synopses & ReviewsPublisher Comments:"Paul Nahin's Digital Dice is a marvelous book, one that is even better than his Duelling Idiots. Nahin presents twentyone 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, reallife probability puzzles that require considerable ingenuity, and in most cases computer simulation, to solve. Though written to be delved into rather than read covertocover, 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 awardwinning 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 Synopsis:Some probability problems are so difficult that they stump the smartest mathematicians. But even the hardest of these problems can often be solved with a computer and a Monte Carlo simulation, in which a randomnumber generator simulates a physical process, such as a million rolls of a pair of dice. This is what Digital Dice is all about: how to get numerical answers to difficult probability problems without having to solve complicated mathematical equations.
Popularmath writer Paul Nahin challenges readers to solve twentyone difficult but fun problems, from determining the odds of coinflipping 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 linebyline walkthroughs 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. About the AuthorPaul J. Nahin is the author of many bestselling popularmath books, including Chases and Escapes, Dr. Euler's Fabulous Formula, When Least is Best, Duelling Idiots and Other Probability Puzzlers, and An Imaginary Tale (all Princeton). He is professor emeritus of electrical engineering at the University of New Hampshire.
Table of ContentsPreface 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 CoinFlipping Game 42 5. The GamowStern 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 CoinFlipping Game 114 5. The GamowStern 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 VarianceReduction 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 InclusionExclusion 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 AuthorCreated MATLAB mFiles in the Book 255 Glossary 257 Acknowledgments 259 Index 261 Also by Paul J. Nahin 265 What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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