Probability: Theory and Examples

Rating:
Summary: Not user-friendly at all
Review: 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.

Rating:
Summary: Confusing ...
Review: 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.

Rating:
Summary: Poor organization spoils this book
Review: 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.

Rating:
Summary: Poor organization spoils this book
Review: 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.

Rating:
Summary: A Modern but extremely badly written book
Review: 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.