## William Feller's *Probability Theory* - Reviews 3

Below is reviews of the Third Edition of Volume I. For Reviews of the First Edition of Volume I, see THIS LINK. For Reviews of the Second Edition of Volume I, see THIS LINK. For Reviews of the First Edition of Volume II, see THIS LINK. For Reviews of the Second Edition of Volume II, see THIS LINK. |

**3. An Introduction to Probability Theory and its Applications Volume 1 (3rd edition) (1968), by William Feller.**

**3.1. Review by: S M Samuels.**

*Technometrics*

**11**(2) (1969), 405.

It should not be necessary to describe in detail the contents of this book - except insofar as it differs from that of the previous edition - since, without a doubt, virtually every reader of this review either owns or has seen a copy. Nevertheless, it seems like a good idea to be reminded of the enormous significance of Feller's book to the development and application of probability theory during the past eighteen years, and of the book's continuing usefulness - to mathematician and non-mathematician alike - even today when so many "specialized works streamlined for particular needs" (as Feller says) are available. Nowadays nearly all the formal material can be found elsewhere, often in more suitable form. But only Feller's book "operates" on so many levels simultaneously. Most of the others are more or less merely textbooks. Feller's book is really a "happening."

**3.2. Review by: H Kesten.**

*SIAM Review* **11** (1) (1969), 96.

The appearance of the third edition of this well-known book not long after the second edition became available as a paperback attests to the popularity of this book. This popularity is well deserved, since there are few other books which give the reader so clear an impression of the beauty and excitement of probability theory. The author also takes pain to show by means of examples how the theory can be applied or was stimulated by practical problems. To be sure, this first volume is an "elementary" textbook, restricted to discrete variables, which does not take the reader to present-day research, but it is ideally suited to get the students interested in the field. One should not under- estimate, however, the amount and depth of material in the book. Even though almost self-contained (e.g., Stirling's formula is proved from scratch) the book covers the author's elegant theory of recurrent events and uses it to derive the most important theorems on Markov chains (countable state space and discrete time parameter). In addition there is always Volume 2 to learn about continuous distributions (and a great deal more). The difference between this edition and the second is not great. ... The present edition has almost 50 pages more than the second edition.

**3.3. Review by: K Krickeberg.**

*Revue de l'Institut International de Statistique / Review of the International Statistical Institute* **37** (1) (1969), 106.

Feller's book is so well-known that a review of its third edition should confine itself to the changes from the second. There are many minor changes, testifying to a careful revision and adaptation to recent developments including additional references and new applications; for example, the calculation of the expectation in the problem of Banach's match boxes has been transferred to the problem section, and replaced by an elementary statistical application of the concept of expectation in biology. There are, however, many major changes as well. ... The book has gained considerably by streamlining without losing any of its original character, its charm and usefulness, its clarity and its diversity in mathematical and applied respects

**3.4. Review by: David W Miller.**

*Management Science* **14** (10, Application Series) (1968), B633-B634.

Every field has its grand masters and certainly Professor Feller is one of the grand masters of probability theory. But not every field can boast that one of its grand masters is simultaneously a master expositor. This is surely true of Professor Feller and the result is this great book, one of the classics of applied mathematics of this century. The first edition of this book in 1950 revolutionized the current conception of probability theory. That conception was that probability theory was a somewhat esoteric subject which was typified by complex combinatorial arguments applied to made-up problems of dubious interest. With this book Professor Feller opened whole new vistas and demonstrated the underlying unity of probabilistic methods in his innumerable fascinating applications. A whole generation of quantitatively oriented persons responded by spending untold hours in self-study programs with this book. Solving the problems in Feller became the hobby of a remarkably large number of people. The contemporary efflorescence of probability theory is due, in large measure, to Professor Feller's book. ... This third edition has some remarkable simplifications ... This book remains far and away the best single book on probability theory. Quantitative analysts cannot afford to be without it because they will use it all the time. But regardless of use, this masterpiece should be read for the delight of it. What comparable intellectual pleasures can the world afford?

**3.5. Review by: Charles J Stone.**

*Journal of the American Statistical Association* **64** (328) (1969), 1676.

There are a number of significant changes in Feller's excellent and unique introduction to probability theory. The character of the book, however, remains faithful to the original edition.

**3.6. Review by: J G Wendel.**

*Mathematical Reviews* MR0228020 **(37 #3604).**

All probabilists will welcome the latest edition of this classic book. While preserving the unique flavour of the former editions the author has improved the treatment of many topics. Thus, Chapter III on fluctuations in coin tossing has been completely rewritten; the treatment of the De Moivre-Laplace limit theorem, Chapter VII, has been revised; and the material on branching processes has been expanded.

JOC/EFR August 2016

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