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Type of bind: Hardcover
Dewey Decimal Number: 519.2076
EAN num: 9780691126982
ISBN number: 0691126984
Label: Princeton University Press
Manufacturer: Princeton University Press
Quantity: 1
Page Count: 276
Printing Date: March 23, 2008
Publishing house: Princeton University Press
Sale Popularity Level: 105252
Studio: Princeton University Press
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Product 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.
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Rated by buyers -
Rather than write yet another book on probability in which the math is explained in yet another way, the author has chosen to tackle the problem of understanding probability via writing simulations and poking around a bit until you find the pattern and thus the solution. The author presents 21 problems in probability in the very first half of the book, and shows his solutions in the second half with programs written in MATLAB. The idea is that you should try writing your solutions very first before reading the second half of the book and seeing how the author solves the problem. Sometimes the author goes into detail in his reasoning, somethimes he just goes through a detailed explanation of his MATLAB code without really telling you how he arrived at his solution. Sometimes a little theory goes a long way, and this lack of theory at some points is the only real shortcoming of the book.
Of course, the problem here is, if you can't trust your intuition to solve a probability problem, how do you know that the computer program you wrote using that same intuition is also trustworthy? I found this to double as a book on helping you reason out the simulation of probability problems and also as just a good algorithm book on the solution of probability problems. You can take the approach to these specific problems and extend them to many other computational probability problems you are likely to encounter. Overall, highly recommended.
The reader should already understand fundamental probability theory and also have some experience in both Excel and MATLAB.
Rated by buyers -
This is a delightful book showing how probability can be made to come alive by using Monte Carlo simulation. Wonderful examples are given to demonstrate this. A little experience in Excel or Matlab suffices to solve by simulation interesting probability problems that are otherwise not easily amenable to an analytical solution. The book is an excellent appetizer for more mathematical books combining probability and simulation such as the highly recommended books Understanding Probability: Chance Rules in Everyday Life by Henk Tijms and Intuitive Probability and Random Processes using MATLAB by Steven Kay.
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