- Series: Probability: Theory & Examples
- Hardcover: 512 pages
- Publisher: Duxbury Press; 3 edition (March 16, 2004)
- Language: English
- ISBN-10: 0534424414
- ISBN-13: 978-0534424411
- Product Dimensions: 9.3 x 6.7 x 0.9 inches
- Shipping Weight: 1.8 pounds
- Average Customer Review: 2.6 out of 5 stars See all reviews (37 customer reviews)
- Amazon Best Sellers Rank: #1,058,827 in Books (See Top 100 in Books)
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Probability: Theory and Examples (Probability: Theory & Examples) 3rd 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 text refers to an alternate Hardcover edition.
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. --This text refers to an alternate Hardcover edition.
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Top Customer Reviews
More precisely, this book is comprehensive in terms of SKILLS that you will need to pass prelims/do research.
Though, it is not very good to 'tell the story of probability'. For instance, section 5.4 is called 'Doob’s Inequality, Convergence in Lp'. If you are new to this area, you might wonder why we should study convergence in Lp of martingales. Severe lack of connections between theorems/sections. If you are an undergrad trying to find your interest / grad student in other discipline but want to use some grad probability, for instance, Maybe 'A Probability Path' by Resnick, or 'A First Look at Rigorous Probability' by Rosenthal are better for this purpose.
It's a good book, but not for everyone.
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.
Let me start with a contrast: I studied undergraduate real analysis from Strichartz, and I think that was an excellent book. The proofs were useful for the homework problems, and Strichartz's discussion, while lengthy, was helpful for providing the crucial insights to actually LEARN from the text. While I felt that the textbook was quite difficult for me -- I must have spent about 20 hours a week that semester studying Strichartz -- I felt like I came out of the class with (at least) twice as strong math skills as I did when I entered the course. It is from Strichartz that I learned how to do proofs with quantifiers.
However, Durrett's textbook is the kind of textbook which teaches nothing. I do not feel like I could master the material by studying his proofs and "examples." The skills necessary to attack the (challenging) homework problems are not going to be reinforced by this textbook. I learned much more by looking at professor's online solutions to Durrett's problems. And that's what's really missing from this textbook. A good calculus textbook, like the one by James Stewart, is REPLETE with sample problems and fully-worked solutions. Most good calculus teachers know that students learn (inductively) from examples -- it is only LATER that they would care about something like a proof.
So what is the point of this textbook? I'm not sure. As far as I'm concerned, it was completely and utterly useless.
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.
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