Digital Dice

by Nahin, Paul J.

• ISBN13: 9780691126982
• ISBN10: 0691126984
• Format: Hardcover
• Copyright: 2008-03-03
• Publisher: Princeton Univ Pr

Summary

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 random-number generator simulates a physical process, such as a million rolls of a pair of dice. This is whatDigital Diceis all about: how to get numerical answers to difficult probability problems without having to solve complicated mathematical equations. 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 Dicewill appeal to anyone who enjoys popular math or computer science.

Table of Contents

Introduction	p. 1
The Problems	p. 35
The Clumsy Dishwasher Problem	p. 37
Will Lil and Bill Meet at the Malt Shop?	p. 38
A Parallel Parking Question	p. 40
A Curious Coin-Flipping Game	p. 42
The Gamow-Stern Elevator Puzzle	p. 45
Steve's Elevator Problem	p. 48
The Pipe Smoker's Discovery	p. 51
A Toilet Paper Dilemma	p. 53
The Forgetful Burglar Problem	p. 59
The Umbrella Quandary	p. 61
The Case of the Missing Senators	p. 63
How Many Runners in a Marathon?	p. 65
A Police Patrol Problem	p. 69
Parrondo's Paradox	p. 74
How Long Is the Wait to Get the Potato Salad?	p. 77
The Appeals Court Paradox	p. 81
Waiting for Buses	p. 83
Waiting for Stoplights	p. 85
Electing Emperors and Popes	p. 87
An Optimal Stopping Problem	p. 91
Chain Reactions, Branching Processes, and Baby Boys	p. 96
MATLAB Solutions To The Problems	p. 101
The Clumsy Dishwasher Problem	p. 103
Will Lil and Bill Meet at the Malt Shop?	p. 105
A Parallel Parking Question	p. 109
A Curious Coin-Flipping Game	p. 114
The Gamow-Stern Elevator Puzzle	p. 120
Steve's Elevator Problem	p. 124
The Pipe Smoker's Discovery	p. 129
A Toilet Paper Dilemma	p. 140
The Forgetful Burglar Problem	p. 144
The Umbrella Quandary	p. 148
The Case of the Missing Senators	p. 153
How Many Runners in a Marathon?	p. 157
A Police Patrol Problem	p. 160
Parrondo's Paradox	p. 169
How Long is the Wait to Get the Potato Salad?	p. 176
The Appeals Court Paradox	p. 184
Waiting for Buses	p. 187
Waiting for Stoplights	p. 191
Electing Emperors and Popes	p. 197
An Optimal Stopping Problem	p. 204
Chain Reactions, Branching Processes, and Baby Boys	p. 213
One Way to Guess on a Test	p. 221
An Example of Variance-Reduction in the Monte Carlo Method	p. 223
Random Harmonic Sums	p. 229
Solving Montmort's Problem by Recursion	p. 231
An Illustration of the Inclusion-Exclusion Principle	p. 237
Solutions to the Spin Game	p. 244
How to Simulate Kelvin's Fair Coin with a Biased Coin	p. 248
How to Simulate an Exponential Random Variable	p. 252
Index to Author-Created MATLAB m-Files in the Book	p. 255
Glossary	p. 257
Acknowledgments	p. 259
Index	p. 261
Table of Contents provided by Ingram. All Rights Reserved.