- Series: Cambridge Series in Statistical and Probabilistic Mathematics
- Hardcover: 440 pages
- Publisher: Cambridge University Press; 4 edition (August 30, 2010)
- Language: English
- ISBN-10: 0521765390
- ISBN-13: 978-0521765398
- Product Dimensions: 8.5 x 1.2 x 10 inches
- Shipping Weight: 2.1 pounds (View shipping rates and policies)
- Average Customer Review: 40 customer reviews
- Amazon Best Sellers Rank: #134,635 in Books (See Top 100 in Books)
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Probability: Theory and Examples (Cambridge Series in Statistical and Probabilistic Mathematics) 4th Edition
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"This book is also an excellent resource. Several interesting and concrete examples are presented throughout the textbook, which will help novices obtain a better understanding of the fundamentals of probability theory."
Ramesh Garimella, Computing Reviews
"The best feature of the book is its selection of examples. The author has done an extraordinary job in showing not simply what the presented theorems can be used for, but also what they cannot be used for."
Miklos Bona, SIGACT News
This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The new edition begins with a short chapter on measure theory to orient readers new to the subject.
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Top customer reviews
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Being done with the class, I now find the book an excellent reference - it is a very concise presentation of the material.
I recommend this book if you're a student in a graduate-level class or if you're already familiar with the material. But if you want to teach yourself, this book is too difficult a starting point.
As a textbook, it also fails because it never really explains the purpose of the theory he is discussing. This is probably the worst mathematics book I have ever read. (I am currently a 2nd year PhD student and my undergraduate degree is in Mathematics).
The only upside of this book is that it contains some recently developed theory.
First, apparently this book contains a lot of examples. Important examples are necessary for building intuition. However, many of the examples in this book are not essential. So if you work though the examples, it's likely you will not be able to follow the flow of theorems uninterruptedly (being able to see structure of the theory is very important for me); if you skip some of the examples, it's bad because they are referenced in the some of the proofs of theorems.
Second, this book does not differentiate propositions, lemmas, corollaries, and theorems. The names of some theorems help, but they are insufficient for me to tell which ones are the main nontrivial results, i.e. the cornerstones of the theory.
Third, some of the important intuitions pop up in the middle of nowhere. For example, an important intuition (or conceptional foundation) is that sigma algebras encode information, and measurable functions (random variables) represent outcomes that are knowable based on the available information. Nowhere in this book I see this, but when discussing conditional expectation, this intuition suddenly becomes indispensable.
I don't agree with the author.
His book is only good as a reference book for those who have mastered the contents( for example, the professors who have taught probability for their entire lives and take for granted that every line in the book is trivial. If it is indeed trivial, why bother to write a book! what is a textbook for?)
For my own experience, to follow this book, I have to read everything from Billingsley's textbook!
Most recent customer reviews
The author makes implicit definitions, sometimes we have to search for something that should be trivial, and where nothing is...Read more