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A Modern Approach to Probability Theory (Probability and Its Applications), by Bert E. Fristedt, Lawrence F. Gray
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Students and teachers of mathematics and related fields will find this book a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra. A variety of applications―Bayesian statistics, financial mathematics, information theory, tomography, and signal processing―appear as threads to both enhance the understanding of the relevant mathematics and motivate students whose main interests are outside of pure areas.
- Sales Rank: #1394407 in Books
- Brand: Brand: Birkhäuser
- Published on: 1996-12-23
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x 1.69" w x 6.14" l, 2.74 pounds
- Binding: Hardcover
- 758 pages
- Used Book in Good Condition
Review
"Covers the essentials in a clear and readable fashion… A must for professionals and an attractive text for a graduate course." ―American Mathematical Monthly (review of the first edition)
"This ambitious book is intended as ‘a textbook in probability for graduate students in mathematics and related areas such as economics, statistics, physics and operations research’…The coverage is careful and thorough…Quite a lot of fairly recent material is incorporated, and this is certainly one of the book’s strengths. The selection of material is sensible, and the quality of exposition is good…In sum: the book contains a lot of good mathematics, nicely done, and should prove useful to students and teachers, and to specialists in probability theory." ―Mathematical Reviews (review of the first edition)
"The book takes the reader from a relatively low level.... To the point where he or she can specialize in research topics of current interest. ...an outstanding basis for teaching a graduate course in probability theory. The exhaustive compilation of results and detailed index also make it a very useful reference text for the more advanced probabilist... a good buy for anyone looking for a very accessible and complete mathematical account of modern probability theory." ―Journal of the American Statistical Association (review of the first edition)
Most helpful customer reviews
24 of 25 people found the following review helpful.
Finally, a readable one!
By A Customer
Targeted clientele: Grad students doing research in the engineering or applied sciences who discover that they need to know detailed probability and measure theory - at an intuitive yet rigorous depth which books like Papoulis' or Stark/Woods' just cannot provide.
Pros: A very readable book, unlike most of the other books on this subject, which are either too concise and dense and written primarily for mathematicians, or not detailed enough to show all the nuances of the topic. The book has a good set of examples, and web-based solutions to some of the problems. It also does not ignore routine undergrad-type computational problems to highlight practical aspects of the subject. The book is encyclopedic in nature (which is good and bad depending on what your objectives are) and covers some cutting-edge topics. Very good for self-study. If you have some time, it will 'hand-hold' your way to a solid understanding of the subject.
Cons: The book is encyclopedic (see above). Unlike Resnick's text which is very focused and designed to give you the minimum tools necessary to quickly come up to speed, this text has a lot of detail which is not ideal if you need to know the topics NOW. It is designed for a three quarter sequence. The measure theory section is nicely presented, but forces the readers to prove many of the results as exercises. This may foster better learning but, once again, if you're in a hurry.....Lacks a chapter ending set of comprehensive problems which tests the overall understanding of the material in the chapter (since the problem sets immediately follow the individual sections and are geared only for that specific section).
14 of 16 people found the following review helpful.
Intentions were good, but result is murder for students
By StudyA'lot
I studied probability theory from this book under the tutelage of both its authors.
Results: Pitiful. I went to graduate school mostly to study probability theory, in the end it was to prove my least favorite course. It was the only course I did not get an A.
The idea behind the book is simply great, the coverage is almost universal and there is a lot of good mathematics in it.
The problem, and it is a huge problem, is that too many proofs are left to the readers. Sometimes even difficult ones. Proofs are supposed to teach how to use the theory, they are the best applications of previous results and mathematical techniques. What am I supposed to learn if, as a student, I am going to be deprived of those opportunities?
Solutions to selected problems. Do not be fooled by the fact that there are solutions to selected problems. While there are a lot of them, they are often a few lines or just a number or a partial hint. Hence do not expect too much help there.
How did most of us cope with this fact? Very simple: we all bought other books that provided more proofs and details.
Most disappointing feature: conditional probabilities: I could not understand a thing. Then, after studying them from other books, I got them.
Best feature? The Borel Cantelli Lemmas. I think I will never forget them. So many applications and so much to fight with them.
What did my schoolmates say? I took this class at the U. of Minnesota and the hate for this book was almost as universal as its coverage of the subject.
Final Comment: Excellent book if you already know the subject and want to cover it from a deeper or new point of view. But, for students this book is murder.
About the authors. Bert Fristedt is a gentleman the like of whom I have seldomly encountered and even Lawrence Gray, although less patient than Fristedt, is an excellent person and very knowledgeble in his field. But in this book the two combined to kill students and their desire to learn the subject. How that could happen is beyond my comprehension.
Anecdote: There was a student in my class who mastered pretty much all this book (with Billingsley's text on the side). It took him 3 years, he never got his Ph.D and now makes a living doing something else. Many students who went on to academic positions did not get an A in this class.
My roomate taught the book how to fly! In several occasions I saw the book flying across the living room. He went on to a career in academia.
Other books. Sure. Billingsley's, Chung's, Kallenberg's (almost as difficult but wih all the proofs at least), and a few more..... but not Fristedt's and Grey's! The book is murder!
0 of 0 people found the following review helpful.
Poor printing copy
By drjps
This text is not really a great introductory text for a student who is not already very advanced in mathematics. However, it is a great reference and a good text for the highly motivated student who is comfortable with advanced math. This was the text which served as my main reference as a graduate student. It was a difficult read for me, but persistence paid off.
However, the copy I received when ordering this was a very poor print for the following reasons:
1) cheap, rough, flat/matte, and thick feeling paper
2) ink variability, some text thin, other text thick and somewhat blurry.
3) the binding is very tight, but maybe it loosens over time.
The copy I used in grad school has thinner somewhat glossier paper and a high quality printed text being clean, thin, easily legible ink. It's not a $65 book, so it makes me wonder if the "seconds" are being offered at a discounted rate. I'd rather pay twice the price for a high quality print! Afterall, that's why I'm buying the physical book and not an e-book!!!
I will either return this and wait for a higher quality, or try an exchange for a different copy. I'll update my review if the new copy is higher quality.
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