Gamma: Exploring Euler's Constant (Princeton Science Library) [Paperback]

Julian Havil (Author), Freeman Dyson (Foreword)

Book Description

ISBN-10: 0691141339 | ISBN-13: 978-0691141336 | Publication Date: July 6, 2009

Among the myriad of constants that appear in mathematics, p, e, and i are the most familiar. Following closely behind is g, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery.

In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics.

Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . .. But unlike its more celebrated colleagues p and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction.

Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!).

Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.

Editorial Reviews

Review

[A] wonderful book. . . . Havil's emphasis on historical context and his conversational style make this a pleasure to read. . . . Gamma is a gold mine of irresistible mathematical nuggets. Anyone with a serious interest in maths will find it richly rewarding. -- Ben Longstaff, New Scientist



This book is a joy from start to finish. -- Gerry Leversha, Mathematical Gazette



[Gamma] is not a book about mathematics, but a book of mathematics. . . . [It] is something like a picaresque novel; the hero, Euler's constant g, serves as the unifying motif through a wide range of mathematical adventures. -- Dan Segal, Notices of the American Mathematical Society



The book is enjoyable for many reasons. Here are just two. First, the explanations are not only complete, but they have the right amount of generality. . . . Second, the pleasure Havil has in contemplating this material is infectious. -- Jeremy Gray, MAA Online



It is only fitting that someone should write a book about gamma, or Euler's constant. Havil takes on this task and does an excellent job. -- Choice



This book is accessible to a wide range of readers, and should particularly appeal to those who feel a love for mathematics and are dissuaded by the dryness and formality of text-books, but are also not satisfied by the less rigorous approach of most popular books. Mathematics is presented throughout as something connected to reality. . . . Many readers will find in this book exactly what they have been missing. -- Mohammad Akbar, Plus Magazine



This book is written in an informal, engaging, and often amusing style. The author takes pains to make the mathematics clear. He writes about the mathematical geniuses of the past with reverence and awe. It is especially nice that the mathematical topics are discussed within a historical context. -- Ward R. Stewart, Mathematics Teacher

From the Author

Gamma was my first book, written from the inspiration provided by the books by Maor and Nahin on e and i respectively.  It was a considerable suprise to me that my email to PUP suggesting the idea of a similar book on the constant gamma was replied to within days, positively and from Woodstock in England.  It took three years to write.  Now in German and Japanese translation, its paperbck form is part of Princeton Science Library.  My apologies for the typos; it seems that such are inevitable (at least for me) when writing such technical popular books! --This text refers to the Kindle Edition edition.

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Product Details

• Paperback: 304 pages
• Publisher: Princeton University Press (July 6, 2009)
• Language: English
• ISBN-10: 0691141339
• ISBN-13: 978-0691141336
• Product Dimensions: 9.2 x 6 x 0.7 inches
• Shipping Weight: 15.2 ounces (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (29 customer reviews)
• Amazon Best Sellers Rank: #368,357 in Books (See Top 100 in Books)

More About the Author

Finally I have decided to 'get a web page' and, thanks to Amazon,the procedure is very easy. I will try to add to it as time passes. Apparently, in profile I resemble Vladimir Putin; hence the choice of the lead photo!

Customer Reviews

Most Helpful Customer Reviews

40 of 41 people found the following review helpful:

5.0 out of 5 stars Who would have thought!?, June 27, 2003

By 

Palle E T Jorgensen "Palle Jorgensen" (Iowa City, Iowa United States) - See all my reviews
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This review is from: Gamma: Exploring Euler's Constant (Princeton Science Library) (Hardcover)

Who would have thought that there can be so much life in a constant? And one with a Greek name! If you have some math interests, I predict that you will get caught up in the thread of events: They are mathematical topics, but are presented like in a novel or a drama. A book that I couldn't put down. The main characters are the harmonic series, the sub-harmonic series, Riemann's Zeta function, its functional equation, its zeros, the Riemann hypothesis(it is worth a million dollars!), the prime number theorem, (..hard stuff! but it somehow seems easy in this book),Bernoulli numbers, Pell's equation, the distribution of prime numbers.... And if you forgot some of your math, you will have it reviewed in the appendices. They are attractive, well written, and to the point.

62 of 67 people found the following review helpful:

5.0 out of 5 stars This would make an excellent alternative "Calc III", February 14, 2004

By 

John P. Rickert - See all my reviews
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This review is from: Gamma: Exploring Euler's Constant (Princeton Science Library) (Hardcover)

I agree wholeheartedly with all the positive comments and enthusiasm that other reviewers have shown. This is a remarkable book, and there should be more like it. I am astounded at how much and what range of mathematics there is in a book of this length and level of accessbility. Which raises a very good point: This would be a superb book for "Calc III". It's unfortunate that many students end their study of mathematics slugging through integration by parts, partial fractions, sequences and series, the logarithm as integral, etc., the traditional hodge-podge of topics called Calculus II. And the ones who progress end up going straight into multivariable calculus with its div, grad, curl, and all that. There is never really any reward for all the work in hacking through Calc II. This book, however, would tie so much of it together, it would all suddenly seem so mysteriously connected and beautiful, and the reader (I hope) would want to go on to Complex Analysis. Thank you, Prof. Havil! I hope you find the proof to the Riemann Hypothesis.

35 of 36 people found the following review helpful:

4.0 out of 5 stars Far-reaching, but not "popular math", March 1, 2004

By 

Samer T Ismail "SF & classical music fan" (Danbury, CT) - See all my reviews
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This review is from: Gamma: Exploring Euler's Constant (Princeton Science Library) (Hardcover)

I debated for a while whether this book deserved four stars or five. There's a lot of very interesting material here: if there's one thing this book does--perhaps better than any book I've read in quite some time--is show just how interrelated far-flung mathematical concepts can be (how are the prime numbers related to pi, for example?).

My one complaint about the book--and the reason for giving it four stars instead of five--is that there are times when the formulae and notation get so dense that it's extremely difficult to follow the author's train of thought: I can think of a number of places where diagrams would have helped immensely. Likewise, since there's no list of symbols or formulae, it's not a book that you can simply browse through, in the sense that you can browse through, say, "A Brief History of Time."

Finally, let me reiterate that this book assumes that you already know a fair amount of math: if you don't know what a capital pi means, for example, you're probably going to have a hard time understanding this book. But if you *do* know what that symbol means, though, then by all means, give this book a try.