Digital Dice: Computational Solutions to Practical Probability Problems (Princeton Puzzlers) by Paul J. Nahin (PDF)

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. In a new preface, Nahin wittily addresses some of the responses he received to the first edition.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Sosho is very difficult. This book goes a long way to teach you to master soshoHowever at least for me the task is formidable and impossible to reachThe book helps a lot but will not make you a master.

⭐A good book to practice probability theory and thinking and do experiments on a PC. Matlab is good tool for this.

⭐Excellent book! It’s full of very useful and practical information.

⭐Great book, enjoyed it.

⭐I was looking for computing problems for my teenage sons and this book proved to be a great resource. We take the problems and first discuss the theory and then work them out using Python and Sagemath. The book contains solutions in Matlab and they’re useful as pseudocode to check their programs. The book is complete with references and invaluable comments and each problem can be used as a stimulus for further investigations.BTW, when the programs output values that match the theoretical predictions it’s like magic. What better way to convince the youngsters that probability theory is not some made up stuff? Thanks to the author for having written this nice book.

⭐Very helpful book for mathematics teachers. The book requires no special background in programming in general. I highly recommend this book.

⭐著者の本を読むのは、「虚数の話」「オイラー博士の素敵な数式」「ちょっと手ごわい確率パズル」に次いで4冊目となる。この「Digital Dice」はまだ翻訳版が出ていないので辞書を引きながら読んだ。普段英語に接していない者にとっては大変だが、なんとか理解し翻訳する楽しさも味わえた。内容は確率に関する実践的な問題について理論的な解答を導くとともにMatlabを使って検証するものだが、著者によればすべての問題について理論上の解答を得ることは困難であり、こと確率に関連する問題においては乱数を用いたシュミレーションが有用であるとの考え方で、全く同感。私にとってポールJナーイン博士は神様のような存在で、今後もさらに他の著書を読むつもり。なお、Matlabのファイルは英語Amazon（あるいはプリンストン大学だったか？）のページをたどっていけばダウンロードできる。そこには「ちょっと手ごわい確率パズル（英語名Duelling Idiots …）」の ファイルもある。ちなみに、Matlabは高額なのでFreematで動かしている。（少しプログラムを変更すれば問題なく動きます）

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