Very well written and wide ranging
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This is a serious textbook, extremely well written, and not for the fainthearted. Buy the companion book with the solutions to the problems unless you have a tutor or are taking a course. As an engineer who uses maths as a means to an end, I'm finding it hard going, but well worth the effort. If you just want a cookbook of algorithms, look elsewhere. But if you're willing to take some time, I'd recommend this.
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This is not a quick reference book.
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I was looking for a desktop reference book to provide some background information on the probability distributions that I needed in my modelling work. This book does not provide easily accessible information, unless you are familiar with the language of set theory. The biggest complaint I have, is the fact the exercises in the book have no solutions; to get the solutions you have to purchase their other book One Thousand Exercises in Probability...
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Excellent and up-to-date.
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This book is too fast-paced for most beginning undergraduates, but is excellent for honours students in mathematics and statistics. It is also the best book I have seen for research students in mathematics or statistics and an excellent resource for anyone doing research in mathematics, statistics, economics, operational research or computing who needs a thorough, up-to-date text on probability theory. The book starts with five chapters on standard probability theory and then covers a variety of topics of interest to a wider audience. These include Markov processes and queueing theory, stationary processes, martingales and diffusion processes. It covers succinctly topics such as brownian motion, the Black-Scholes equation, Markov chain Monte Carlo and the Metropolis algorithm. Even topics such as Erdos' probabalistic method are covered in the exercises. There are lots of entertaining and helpful comments about the problems and history of probabilty. The exercises are interesting and instructive. I would have liked some more references in the text to help follow up some of the methods described.
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