|
Digital Dice: Computational Solutions to Practical Probability Problems
Binding: Hardcover
Author: Paul J. Nahin
Manufacturer: Princeton University Press
Availability: Usually ships in 24 hours
Features:
Average Rating: 4.0
Total Customer Reviews: 5
List Price: $27.95
Our Price: $18.45
Sales Rank: 274886
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.
|
Users Product Reviews: |
Product Review Summary: Good concept-poor execution I have liked Nahin's other books so I bought this one since I wanted to learn more about simulating probability problems. All seemed well, the examples were written in Nahin's literate style and seemed mathematically sound. Then I got interested in a particular problem, No. 12, "How many runners in a marathon" where you try to estimate the total size of a population from samples. I ran into major problems in many areas of the discussion.
First, in the theory, Nahin does not show the derivation of the key formula that E{Xmax} = n*(N+1)/(n+1) even though he obviously had a simplified derivation available in a reference. I found the reference "Estimating the Size of a Population" by R. W. Johnson on google scholar but to get online access to the article cost more than the price of the book! Not all of us have access to the online subscriptions through a university library like he does. This formula is intrinsic to his implementation but we don't know why it works since he made no attempt to explain it.
The implementation is quite poor both in style and in accuracy. In style, Nahin uses names of builtin Matlab function names, like size() and error(), as array names. Matlab's compiler is smart enough to do the right thing but this causes major confusion for anyone trying to read the code.
There are several other major problems. First, in trying to generate samples without replacement, Nahin first uses matlab's randperm function. That's good; this is a great function. But then he inexplicably generates random samples from the randperm output using a clumsy implementation of an obscure algorithm by Bebbington, which he does not explain either. But since randperm randomizes the sample, a random sample without replacement of length n of x = randperm(N) is simply x(1:n). There is no need to randomize what is random already.
The final straw is that there is a typo in his code listing of estimate.m at line 21. Matlab complained about unbalanced parentheses right away so there is no way he ran this code. Since he uses Latex based tools, this is inexcusable since you can insert the code directly into the text. If his publisher insisted on re-typing his text (I don't know whether Princeton is that backward but maybe they are), he could have done what I did, which is to scan the book text and OCR it and try it out.
Another problem is that Nahin says he wrote his code in a non-Matlab style resembling BASIC so readers without Matlab can use the code. But then he uses functions like randperm without explanation and this is not available in any version of BASIC that I have ever seen. Nahin does not mention that there is a free Matlab compatible program called Octave . He could have written his code in better and more understandable Matlab style and his readers could still run it without paying for the very expensive Matlab program.
So, I wish I could recommend this book but I cannot. For his next book, I suggest Nahin get it reviewed by someone who understands math and Matlab programming and maybe find a publisher that can transcribe his manuscript accurately
BTW, I would be willing to bet that the other reviewers have not tried to run his code. Nahin does not make this easy. The code should be available online so we don't have to type it or OCR it.
Product Review Summary: An Excellent Bet! Over the last few years, Paul Nahin has written a variety of books such as An Imaginary Tale, Dueling Idiots, When Least is Best, and Chases and Escapes. I've read most of his books and enjoyed each one. Anyone reading his writing will find it detailed, well-presented, and there is always a hint of humor and a bit of story telling that make the prose bubble along. Digital Dice is no exception to this and it has the added advantage of being participatory by definition---the reader is expected to work on the problems and not just read the book.
My favorite problem is "The toilet paper dilemma." It is a cute problem of a toilet stall with two fresh rolls of paper. Folks enter the stall at random and independently. Some folks are "big choosers" who always take paper from the big roll, and likewise some folks are "little choosers." If the rolls are even in size the each chooses to take from nearest roll. Now, let p be the probability of a big chooser entering a stall and q=1-p the probability of a little chooser entering the stall. Each enters independently and at random. Let n be the starting length of the roll and let M_n(p) be average number of portions of paper left on a roll when the other roll empties. The problem is to explore the nature of M_200(p) as p varies from 0 to 1.
Nahin tells the story of how Donald Knuth first wrote about this problem and he shows you a lovely recursion for M_n(p) with a simple, illustrative diagram. Only after Nahin thoroughly explains the problem is the reader sent to find her own solution.
Note that the problems are not new so you may well find some quite familiar. Even then, there should be a few to interest you and enjoy. If you have seen all the problems, well, the stories that pepper the text are fun, too.
Product Review Summary: Superlative Overview of Computational Methods for Probablity This book is exactly what it purports to be; a computational guide to solving real world probability problems. The essence of the book is to take very complex probability examples and show how to solve them using the Monte Carlo system; writing a program to run thousands or millions of computations with random number generators to see how the probability unfolds.
Digital Dice is only for those with an extensive understanding of probability and an inclination towards complex mathematical models. If your mission is to write coding to answer complex probability problems, this book will prove to be invaluable.
Product Review Summary: A practical and fun approach to solving probability problems 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 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 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.
Product Review Summary: Delightful book 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.
|
Similar Products with reviews:
Impossible?: Surprising Solutions to Counterintuitive Conundrums
Group Theory in the Bedroom, and Other Mathematical Diversions
Chases and Escapes: The Mathematics of Pursuit and Evasion
How Round Is Your Circle?: Where Engineering and Mathematics Meet
When Least Is Best: How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible
|
Wireless Products Store
Disclaimer: All product data on this page belongs to Amazon.com. No
guarantees are made as to accuracy of prices and information.
|
