Customer Reviews

Probability: Theory and Examples (Probability: Theory & Examples)

5 star:		(4)
4 star:		(5)
3 star:		(2)
2 star:		(3)
1 star:		(10)

 

 

While attempting various homework problems or reading the text, I often find that I would like clarification on the specifics of a definition. Almost invariably, the index does not contain a reference to the material I need.

Here's an example:
Let's say I want to do exercise 6.8 on page 51, which involves the Poisson distribution. I want to have the precise definition of a Poisson distribution (this information can be found on pages 19 and 91). I look under "Poisson" in the index and find:

Poisson approximation 36
Poisson convergence 135
Poisson process 143, 147, 150

Because the exercise is on page 51, it seems that Poisson approximation on page 36 is my best bet. On page 36 I cannot find a single occurrence of "Poisson," though I do see "Polynomial approximation."

The book has a nice collection of topics, perhaps the nicest and most modern one out of the usual textbooks out there. Unfortunately, it is poorly written. The proofs of theorems are extremely unclear, even after thinking about them for some time. Furthermore, the notation is not standard and since not all of it is in the nice list at the end, I find myself often looking through the book for an explanation of some piece of notation.

My experience is with the brand new third edition. It seems that the only changes are correction of errors, cheaper price and some minor correnctions. However, I still found some errors after a short inspection and also some that I suspect, but not sure that are errors.

My advice is do not be tempted by the nice modern table of contents and by the late publication date (2005 for the third edition). I guess we have to stick to the other older texts on the topic. I strongly recommend Williams' Probability with Martingales or Ash's second edition Probability and Measure over this book.

While the book is modern, in the sense that it includes a few new proofs of standard results, I find it extremely hard to follow. While Durrett has tried to order things in a nice way, and introduce things as he goes along he has overdone it. Proofs are extremely hard to follow / except for the trivial ones/. Even some of the easy proofs, are written in such a way that a ten minute proof may turn into a 2 hour nightmare of follow-ups to other examples as well as referral to exercises which are not trivial at all to prove, but without which you cannot understand the proof completely. In general, the book is extremely painful to go through, so unless you have Feller's books and Shiryaev on the side, be prepared for quite a bit of frustration. As far as reference book, this also the wrong to buy, unless you have read and solved each exercise as you go along, you can never understand a proof. So, if you need as self-contained proof on Markov Chains, this is not the book to use. The usual mistakes and typos exist here as well, just like in any math book, but the problem is that referring to the wrong exercises to supplement you proof may discourage any reader from following through. / also at times the logic seems to be weird, like stating and if result but using it as the only if part of it, or vice versa/ In general, I would not recommend this book and considering the price of $114/ what are these people thinking?/ it is almost a stupidy to buy, unless you have to.

As someone pointed out, once you have understood the material, Durrett's Text is a good reference that collects an awful lot of material very concisely (though in an uncommon arrangement). But many proofs are just too terse. Often things are implied, but not spelled out.
This text really forces you to do your own work, which can be very rewarding, but also very frustrating.

Note that many of the positive reviews seem to come from lecturers, and note also that in many US universities the lecturer effectively chooses the text, not the students, which might explain the "success" of the book despite its flaws (not to mention the high price).

To conclude, I found myself always reading other books (eg. Williams, Billingsley) to find out what was going on, and even then sometimes had difficulties following Durrett's exposition and proofs. Would not recommend the text unless it is required, or for reference.

There aren't many graduate-level books on Probability Theory out there. Durrett's entry into the field suffers from some incomprehensible organizational choices. First, while theorems are labeled in "(Chapter.Theorem)" format, they are rarely given names, and are always referred to using "(Chapter.Theorem)" notation. For example, the second theorem in the Chapter 4 would be referred to later in the text as "(4.2)". This is fairly useless to anyone who has not memorized the entire book, as we must page back to Chapter 4 to find out what "4.2" refers to. Furthermore, Durrett adopts the convention of only numbering theorems and other important results, so referring to a past equation or calculation can be vague at times.

Second, his proofs often refer to results proved in previous exercises. Mathematical convention, as I understand it, dictates that any result you intend to refer back to later in the text should be declared in the main text in some form---as a theorem, a lemma, or a proposition. If these results are so important, Durrett should have listed them in the exposition as propositions. This way readers who are not working all the problems can still follow the proofs in the text. The proofs to the propositions in question could still be left to the exercises.

Third, on the same note as my second point, the exercises (as solved in the solutions manual) often require the use of previous exercises. Again, if you have not been working all the problems up to this point you will be sunk.

Finally, there is no way to judge the difficulty of the exercises. There are some problems in the book that you can easily spend hours racking your brain on with no progress. There is nothing in the text to distinguish such problems as extraordinarily difficult. Furthermore, when you give up and consult the solution manual, you see the solution involves (1) five exercises from previous chapters(!) and (2) an idea you would never have come up with unless you could read Durrett's mind. For such problems it would be helpful to have a hint, or at least a warning...

Overall, I would not recommend this book as a first text in Probability Theory. I've found Billingsley's text and Shorack's text much more readable. Durrett's book just isn't worth the exorbitant price Brooks/Cole/Wadsworth/Duxbury is asking. You are better off checking it out from your local library.

Apparently, the perfect text of probability has not been written yet. Durrett's textbook is as good as other good textbooks (there are not many around), but has still some flaws. Some topics (martingales, brownian motion) are given relatively more attention than in other popular textbooks, say Billingsley's "Probability and Measure". In general, the choice of the topics and their organization is what differentiates this textbook and makes it valuable. The style is somewhat terse, and sometimes the reader would appreciate some wrds of advice about the relative importance of topics and techniques (see for example the very readable "Probability with Martingales" by Williams). The problems are interesting. The book is very useful when used jointly with other, possibly more wordy, references. This edition has less typos then the first (which was an editorial scandal), but still too many to be considered decent. With less typos and a few more explanations, the third edition has good chances to become "the" reference textbook for probabilists.

I had this book for my probability class and it was just horrible. I ended up purchasing additional probability books so that I would see what is actually going on. The book is very compact and terse, horrible to read. Organization is just awful, there are lots of things all over the place.
I really would not recommend this book for probability course, especially since there are so many better ones like Bilingsley, Resnick, and Chung.

To quote professor Durrett: "Probability: Theory and Examples is written for a graduate course in probability. It is not designed for undergraduates or others who are learning the material for the first time. At the graduate level it has been very successful and is one of the mostly commonly used texts in the country. A third edition with more typos corrected and hopefully a lower price will come in roughly October 2003."

Indeed, in order to begin with chapter 1, you need a solid foundation in analysis and abstract measure theory. (You can actually read the book without this background, but then you would need to start with the material in the appendices and then go to chapter 1. However, appendices are often meant for refreshing of filling in the gaps of lost knowledge.)

For a graduate student with the proper background, there are few probability books that compare. Many journey too readily into the abstraction of sigma fields, for example. And this, I believe, is why Durrett's book is well respected. He really does stick to concrete examples, and avoids being so abstract as to become incomprehensible. In fact, to be more understandable, his statements are often short and to the point. Such writing style may take adjustment for the reader, and you will have to fill in details yourself, but such a method of reading is standard for many math textbooks.

Surely this edition is imperfect (sometimes spotty index, occasional statements which are hard to follow), but on the whole the text is very well written, insightful and understandable for the appropriate audience. The upcoming fourth edition should improve on the imperfections mentioned above.

Durrett's book would be almost the ideal text, or at least ideal reference book, on basic probability if he would just re-do the type setting, providing more space and make things easier to read, and generally more aesthetically pleasing. He also desperately needs to more clearly delineate the sections, subsections, problems, and results - maybe even use the tab key once in a while, or use bold or a different font to highlight important items! Of course this would necessitate doubling the number of pages of the book.....
Also, his notation is quite arcane at times and his proofs sometimes unnecessarily involved.
Billingsley is almost always a better learning aid.

The book features many examples and exercises. However, it is not user-friendly and would not be my first choice for an introductory course in probability. Also, most of the theory is given among exercises as you go along, and thus you never get a clear exposition. A number of results are stated as exercises, which is hardly helpful. Also, a number of exercises are used in future proofs, which is even more frustrating, if the you never got to prove the exercises.