Customer Reviews

An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd Edition

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I first encountered this book in the summer after my Junior year at Indiana University. It is a two-volume work. The first volume introduces probability from the discrete viewpoint. This volume is filled with interesting applications of the theory and has hundreds of doable, informative and fun problems. Having taught several post-calculus probability courses, I often found myself looking to Feller's volumes for ideas and examples. It is a good introduction for a sophisticated undergraduate to discrete probability. The second volume looks at the measure-theoretic side of the subject. Were I to only own one reference on probability, it would be Feller's book. Feller was a significant player in the probability field in his lifetime and he is also an excellent expositor.

Although people often recommend K.L. Chung at our math department as an introduction to probability theory, i think that Feller is just another view of the problem. If you prefer a concise writing style then Chung is better. On the other hand, Feller's books are full of examples so that you cannot go through this book without having an accurate picture of the historical developments of probability theory and its many applications (even if sometimes applications are driving the need for theory...). This is anyway something you must have read if you want to get an intuitive understanding of probability theory.

Whatever your preferred writing style is, Feller is probably a "must-read" if you're involved on probability theory, just because of its importance in the literature, not because you like it. Maths are not just about formalism, they're also a matter of culture.

I came across Vol 1 as a maths student in the 1970s. Indeed, the book was suggested to me by a quantum physicist recommended for the Nobel Prize in 1965 (John Ward, now deceased)- Feynman, Schwinger and Tomonaga shared the prize.

This is a difficult book and was not widely used even in the 70s as a textbook. I can recall the word "idiosyncratic" being used by someone to describe the book. The problem is that the book seeks to address deep issues and that requires hard work. It is not the sort of book a struggling student will find helpful. As one matures as a mathematician one can appreciate the incredible depth of the material. As a practical example - about 30 years after I first touched this book a Head of Quant approached me in relation to a paper by Marsaglia on distributions of ratios of normal variates. The verification of Marsgalia's derivation (which is non-trivial) is to be found as a series of 3 problems in Vol 1.

With the development of stochastic calculus in the finance world Feller can look a bit outdated but if you can understand the core material you are doing well. Stochastic calculus would be a push over.

Vols 1 and 2 present a treasure trove for those who want to delve into the area. I still use Feller's coin tossing example from Vol 1 to demonstrate to those in the finance world that their understanding of the "law of averages" is imperfect.

The funny thing is that Vol 2 (which I could never afford as a student) is so hard to get. I think that was because Vol 2 was regarded as even more obscure than Vol 1. I got a copy from Amazon second hand and it is now united with its twin in my study.

Peter Haggstrom
BONDI BEACH AUSTRALIA

There are two ways people think about probability. The first is that probablity is a mere branch of measure theory. The second is that it is a discipline in its own right. Measure theory is only used as a mathematical tool to prove results.

This book's philosophy falls into the second category. William Feller has never thought of it, at least not that I know, as a branch of measure theory. People who have completed both of the volumes may have known this.

I'm not saying which one is more appropriate. But I know that this book is currently the best of all the books that are based on the second thought... When I need intuitive ideas, I often call for it. I believe you'll find it useful too, no matter who you are...

If you could only ever buy one book on probability, this would be the one!

Feller's elegant and lateral approach to the essential elements of probability theory and their application to many diverse and apparently unrelated contexts is head-noddingly inspiring.

Working your way through all the exercises in the book would be an excellent retirment diversion sure to stave off the onset of dementia.

I read some chapters during second year of college, and I found a bit difficult. Later, after college, I read Feller's books (Vol I,II) and I could appreciate Feller's books as excellent : a delicate mix of rigor and intuition that only the verfy gifted can write.

If you want to get an intuitive understanding of probability theory, with a lot of examples and applications, this is the book you must purchase.

It is a pleasure to read a book from one of the masters of probability. You can feel, page after page, how the author goes on and on, introducing ideas and concepts in such an intuitive way, that you want to keep on reading.

The chapter dedicated to random walks is particularly illuminating.

The more you read, the more you get into the incredible depth of the text.

Volume I is dedicated to the discrete probability and Volume II to the continuous (measure-theoretic) probability.

If you are interested in the subject, you must have both volumes. Every time you pick up one of them, you will discover a hidden treasure not unveiled in previous readings.

As many suggest Feller's book is the Bible of Discrete Probability. However, the level of the book is by no means for undergraduates, and the second volume is only suitable for post graduates. My respects to the author, but show some mercy for the unfamiliar.