Catalogue


Digital dice [electronic resource] : computational solutions to practical probability problems /
Paul J. Nahin.
imprint
Princeton : Princeton University Press, c2008.
description
xi, 263 p. : ill. ; 25 cm.
ISBN
0691126984 (cloth : alk. paper), 9780691126982 (cloth : alk. paper)
format(s)
Book
More Details
imprint
Princeton : Princeton University Press, c2008.
isbn
0691126984 (cloth : alk. paper)
9780691126982 (cloth : alk. paper)
restrictions
Licensed for access by U. of T. users.
catalogue key
8839616
 
Includes bibliographical references and index.
A Look Inside
Excerpts
Flap Copy
"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 currentlyimpossible, "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"
Flap Copy
"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
Flap Copy
"Paul Nahins Digital Dice is a marvelous book, one that is even better than his Duelling Idiots . Nahin presents twenty-one great probability problems, from George Gamows 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 "Nahins 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 Nahins 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 Parrondos 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 Nicks 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 books 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
Full Text Reviews
Appeared in Choice on 2008-09-01:
Nahin (emer., Univ. of New Hampshire) has previously written a number of popular books on various mathematical topics. This book is a sequel to his earlier book of probability puzzles, Duelling Idiots and Other Probability Puzzlers (CH, Apr'01, 38-4507). Digital Dice introduces the basic ideas of Monte Carlo simulation through case studies and simple MATLAB programs. In the first half of the book, 21 probability problems are presented. In the second half of the book, the author presents MATLAB programs that can be used to compute approximate solutions to the problems. Nahin avoids discussing statistical issues, but readers will need to be comfortable with calculus and basic probability theory as well as MATLAB. Although this work might be appropriate for lower-level undergraduate students, more advanced undergraduate and graduate students would be better served by more complete monographs such as Averill Law's Simulation Modeling and Analysis (4th ed., 2006) or Sheldon Ross's Simulation (4th ed., 2006). Summing Up: Recommended. Lower-division undergraduates. B. Borchers New Mexico Institute of Mining and Technology
Reviews
Review Quotes
After the appearance of the author's earlier book on probability problems, [ Duelling Idiots And Other Probability Puzzlers ], one has high expectations for this book, and one is not disappointed. . . . The book will certainly have great appeal to all three of the targeted audiences.
After the appearance of the author's earlier book on probability problems, [Duelling Idiots And Other Probability Puzzlers], one has high expectations for this book, and one is not disappointed. . . . The book will certainly have great appeal to all three of the targeted audiences.
"After the appearance of the author's earlier book on probability problems, [ Duelling Idiots And Other Probability Puzzlers ], one has high expectations for this book, and one is not disappointed. . . . The book will certainly have great appeal to all three of the targeted audiences."-- G A. Hewer, Mathematical Reviews
After the appearance of the author's earlier book on probability problems, [ Duelling Idiots And Other Probability Puzzlers ], one has high expectations for this book, and one is not disappointed. . . . The book will certainly have great appeal to all three of the targeted audiences. -- G A. Hewer, Mathematical Reviews
After the appearance of the author's earlier book on probability problems, [Duelling Idiots And Other Probability Puzzlers], one has high expectations for this book, and one is not disappointed. . . . The book will certainly have great appeal to all three of the targeted audiences. -- G A. Hewer, Mathematical Reviews
All of the books by Nahin and Havil are worth having, including others not listed here. I particularly recommend Digital Dice for the task of teaching undergraduates in mathematics the fundamentals of computation and simulation.
"All of the books by Nahin and Havil are worth having, including others not listed here. I particularly recommend Digital Dice for the task of teaching undergraduates in mathematics the fundamentals of computation and simulation."-- James M. Cargal, The UMAP Journal
All of the books by Nahin and Havil are worth having, including others not listed here. I particularly recommend Digital Dice for the task of teaching undergraduates in mathematics the fundamentals of computation and simulation. -- James M. Cargal, The UMAP Journal
[An] enjoyable read, as [Nahin] writes clearly, with humour and is not afraid to include equations where necessary. Nahin spices the book throughout with factual and anecdotal snippets. Digital Dice will appeal to all who like recreational mathematics.
[An] enjoyable read, as [Nahin] writes clearly, with humour and is not afraid to include equations where necessary. Nahin spices the book throughout with factual and anecdotal snippets.Digital Dicewill appeal to all who like recreational mathematics.
"[An] enjoyable read, as [Nahin] writes clearly, with humour and is not afraid to include equations where necessary. Nahin spices the book throughout with factual and anecdotal snippets. Digital Dice will appeal to all who like recreational mathematics."-- Alan Stevens, Mathematics Today
[An] enjoyable read, as [Nahin] writes clearly, with humour and is not afraid to include equations where necessary. Nahin spices the book throughout with factual and anecdotal snippets. Digital Dice will appeal to all who like recreational mathematics. -- Alan Stevens, Mathematics Today
[An] enjoyable read, as [Nahin] writes clearly, with humour and is not afraid to include equations where necessary. Nahin spices the book throughout with factual and anecdotal snippets.Digital Dicewill appeal to all who like recreational mathematics. -- Alan Stevens, Mathematics Today
Digital Dice will appeal to recreational mathematicians who have even a limited knowledge of computer programming, and even nonprogrammers will find most of the problems entertaining to ponder.
Digital Dicewill appeal to recreational mathematicians who have even a limited knowledge of computer programming, and even nonprogrammers will find most of the problems entertaining to ponder.
" Digital Dice will appeal to recreational mathematicians who have even a limited knowledge of computer programming, and even nonprogrammers will find most of the problems entertaining to ponder."-- Games Magazine
Digital Dice will appeal to recreational mathematicians who have even a limited knowledge of computer programming, and even nonprogrammers will find most of the problems entertaining to ponder. -- Games Magazine
Digital Dicewill appeal to recreational mathematicians who have even a limited knowledge of computer programming, and even nonprogrammers will find most of the problems entertaining to ponder. -- Games Magazine
[T]he book is targeted at teachers and students of probability theory or computer science, as well as aficionados of recreational mathematics, but anyone who is familiar with the basics of probability and is capable of writing simple computer programs will have no problem working their way through this interesting and rewarding book.
"[T]he book is targeted at teachers and students of probability theory or computer science, as well as aficionados of recreational mathematics, but anyone who is familiar with the basics of probability and is capable of writing simple computer programs will have no problem working their way through this interesting and rewarding book."-- Physics World
[T]he book is targeted at teachers and students of probability theory or computer science, as well as aficionados of recreational mathematics, but anyone who is familiar with the basics of probability and is capable of writing simple computer programs will have no problem working their way through this interesting and rewarding book. -- Physics World
The problems are accessible but still realistic enough to be engaging, and the solutions in the back of the book will get you through any sticky spots. Writing your own versions of a few of these programs will acquaint you with a useful approach to problem solving and a novel style of thinking.
"The problems are accessible but still realistic enough to be engaging, and the solutions in the back of the book will get you through any sticky spots. Writing your own versions of a few of these programs will acquaint you with a useful approach to problem solving and a novel style of thinking."-- Brian Hayes, American Scientist
The problems are accessible but still realistic enough to be engaging, and the solutions in the back of the book will get you through any sticky spots. Writing your own versions of a few of these programs will acquaint you with a useful approach to problem solving and a novel style of thinking. -- Brian Hayes, American Scientist
This well-written entertaining collection of twenty-one probability problems presents their origin and history as well as their computer solutions. . . . These problems could be used in a computer programming course or a probability course that includes Monte Carlo simulations.
"This well-written entertaining collection of twenty-one probability problems presents their origin and history as well as their computer solutions. . . . These problems could be used in a computer programming course or a probability course that includes Monte Carlo simulations."-- Thomas Sonnabend, Mathematics Teacher
This well-written entertaining collection of twenty-one probability problems presents their origin and history as well as their computer solutions. . . . These problems could be used in a computer programming course or a probability course that includes Monte Carlo simulations. -- Thomas Sonnabend, Mathematics Teacher
By presenting problems for which complete theoretical analysis is difficult or currently impossible,Digital Diceis 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.
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 Dicehas an engaging and often witty style that makes each chapter a pleasurable read.
One of the strengths ofDigital Diceis 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 Diceis a very enjoyable read.
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 marvelousDigital Dice.
Paul Nahin'sDigital Diceis a marvelous book, one that is even better than hisDuelling 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.
This item was reviewed in:
Choice, September 2008
To find out how to look for other reviews, please see our guides to finding book reviews in the Sciences or Social Sciences and Humanities.
Summaries
Main Description
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.
Main Description
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 what Digital Dice is 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 Dice will appeal to anyone who enjoys popular math or computer science.
Table of Contents
Introductionp. 1
The Problemsp. 35
The Clumsy Dishwasher Problemp. 37
Will Lil and Bill Meet at the Malt Shop?p. 38
A Parallel Parking Questionp. 40
A Curious Coin-Flipping Gamep. 42
The Gamow-Stern Elevator Puzzlep. 45
Steve's Elevator Problemp. 48
The Pipe Smoker's Discoveryp. 51
A Toilet Paper Dilemmap. 53
The Forgetful Burglar Problemp. 59
The Umbrella Quandaryp. 61
The Case of the Missing Senatorsp. 63
How Many Runners in a Marathon?p. 65
A Police Patrol Problemp. 69
Parrondo's Paradoxp. 74
How Long Is the Wait to Get the Potato Salad?p. 77
The Appeals Court Paradoxp. 81
Waiting for Busesp. 83
Waiting for Stoplightsp. 85
Electing Emperors and Popesp. 87
An Optimal Stopping Problemp. 91
Chain Reactions, Branching Processes, and Baby Boysp. 96
MATLAB Solutions To The Problemsp. 101
The Clumsy Dishwasher Problemp. 103
Will Lil and Bill Meet at the Malt Shop?p. 105
A Parallel Parking Questionp. 109
A Curious Coin-Flipping Gamep. 114
The Gamow-Stern Elevator Puzzlep. 120
Steve's Elevator Problemp. 124
The Pipe Smoker's Discoveryp. 129
A Toilet Paper Dilemmap. 140
The Forgetful Burglar Problemp. 144
The Umbrella Quandaryp. 148
The Case of the Missing Senatorsp. 153
How Many Runners in a Marathon?p. 157
A Police Patrol Problemp. 160
Parrondo's Paradoxp. 169
How Long is the Wait to Get the Potato Salad?p. 176
The Appeals Court Paradoxp. 184
Waiting for Busesp. 187
Waiting for Stoplightsp. 191
Electing Emperors and Popesp. 197
An Optimal Stopping Problemp. 204
Chain Reactions, Branching Processes, and Baby Boysp. 213
One Way to Guess on a Testp. 221
An Example of Variance-Reduction in the Monte Carlo Methodp. 223
Random Harmonic Sumsp. 229
Solving Montmort's Problem by Recursionp. 231
An Illustration of the Inclusion-Exclusion Principlep. 237
Solutions to the Spin Gamep. 244
How to Simulate Kelvin's Fair Coin with a Biased Coinp. 248
How to Simulate an Exponential Random Variablep. 252
Index to Author-Created MATLAB m-Files in the Bookp. 255
Glossaryp. 257
Acknowledgmentsp. 259
Indexp. 261
Table of Contents provided by Ingram. All Rights Reserved.

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