- 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: 6.5 x 1 x 9.2 inches
- Shipping Weight: 1.8 pounds
- Average Customer Review: 39 customer reviews
- Amazon Best Sellers Rank: #2,518,091 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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I remember once our professor personally graded a homework because many students were making weird mistakes over and over again. Afterwards he scolded the class because he figured out that the problem was the people were copying Durrett's solutions manual---and therefore getting the wrong answers by copying Durrett's mistakes!
The book has good content. Because I have suffered through it, and have lecture notes as a supplement, the book is my main reference. I actually like the book now. However, the book is sloppy, terribly organized, poorly written, and erroneuous at many points. This is fact and I cannot recommend this book to anyone unless you are working with somebody already ordained in the mysteries of Durrett.
If you want a good, quick, and comprehensible guide to probability theory then use Rosenthal's A First Look At Rigorous Probability Theory.
I'm not talking about average Joes here. Most of the reviewers here are graduate students. I am doctoral student in a fairly math-oriented statistics program, and many of my classmates and I have struggled with some of the confusing exposition in this book. Obviously, some struggle is necessary when tackling any difficult subject, but even some of the simpler proofs in this book take an unreasonably long amount of time to really understand. So it might be true that we're the wrong audience for this book, but if so then the intended audience for this book is quite elite.
I have met Prof. Durrett in person and I cannot deny that he's an incredible intellect and researcher. As far as probability goes, he's right at the top. But I'm not really sure that Prof. Durrett spent enough time here thinking about obstacles that people lesser than him might encounter in learning the subject.
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.
I cannot stress enough how useless this book has been. I could rant about how terrible this book is for days, but I'll give any prospective buyers the short list.
1) The author uses non-standard notation, which he introduces in odd places. In particular, he has a habit of introducing notation midway through a proof, and will never again mention what he means by it. This means you are going to be wasting a lot of time trecking backwards trying to find where he defined something or other.
2) The author will often fail to make explicit definitions or define things rigorously. When he does define things, he often does so in out of the way places that you would not expect to find them. For an example of the latter, the definition of "convergence in probability" is in the introductory note to a section. The index directs you to the correct page, but because it's at very bottom in a note, there's a good chance you will fail to notice it there. As for the former, you're going to have to do a lot of work deciding what exactly he is trying to say when he does define something.
3) The proofs are impossibly dry, and difficult to follow. In a well written book, I would expect subtle points to be explained, and tedious calculations to be glossed over. We often get the opposite here, with lengthy, uninformative calculations included to a proof but the core of the idea that produced these calculations barely explained. I've found that numerous theorems that I've seen in other contexts and whose proofs I could follow there leave me scratching my head when I try to follow the author's presentation.
4) Poorly worked out examples. I can't stress enough how frustrating this is. As I mentioned above I'm studying applied mathematics, so what I want most out this book is a body of examples that I can draw analogies to when I am trying to understand something else. This book is filled with pertinent, classical examples that it does an impossibly poor job of explaining.
I've gotten the impression that if you already have a strong grasp of probability, this book is probably a nice read. In particular, this is because you already know all the definitions and are familiar with all the examples, and have a basic idea of how the proofs should work out. In this case, you are probably just skimming, and noticing all the modern theory and examples the author has included. If you are learning this material for the first time though, it's a tragedy to have to learn out of this text. You are going to put in a lot of work for way less payoff than seems at all reasonable.
Most recent customer reviews
First, apparently this book contains a lot of examples. Important examples are necessary for building intuition.Read more
The author makes implicit definitions, sometimes we have to search for something that should be trivial, and where nothing is...Read more