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

4.3 out of 5 stars 38 customer reviews
ISBN-13: 978-0691099835
ISBN-10: 0691099839
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Editorial Reviews


"[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, Millennium Mathematics Project, University of Cambridge

"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 Inside Flap

"I like this book very much. So much, in fact, that I found myself muttering 'neat stuff!' all the way through. While it is about an important topic, there isn't a single competitor. This amazing oversight by past authors is presumably the result of the topic requiring an author with a pretty sophisticated mathematical personality. Havil clearly has that. His skillful weaving of mathematics and history makes the book a 'fun' read. Many instructors will surely find the book attractive."--Paul J. Nahin, author of Duelling Idiots and Other Probability Puzzlers and An Imaginary Tale

"This is an excellent book, mathematically as well as historically. It represents a significant contribution to the literature on mathematics and its history at the upper undergraduate and graduate levels. Julian Havil injects genuine excitement into the topic."--Eli Maor, author of e: The Story of a Number


Product Details

  • Series: Princeton Science Library
  • Hardcover: 266 pages
  • Publisher: Princeton University Press (April 6, 2003)
  • Language: English
  • ISBN-10: 0691099839
  • ISBN-13: 978-0691099835
  • Product Dimensions: 9.5 x 6.4 x 1 inches
  • Shipping Weight: 13.6 ounces
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (38 customer reviews)
  • Amazon Best Sellers Rank: #1,510,784 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: Hardcover
After reading Paul Nahin's lovely book on i, "An Imaginary Tale" (also published by Princeton University Press), I could not believe it when the same publisher produced a book on gamma. Gamma seems to always have been one of the neglected constants in mathematics (by the general public). e, pi, and i seem to capture the imagination more, my guess is because the mathematics required to understand them are more elementary (I use the word "elementary" completely tongue in cheek), and you can quickly see the dazzling results they are associated with.
Gamma is different. While you can understand the theory presented in Julian Havil's book if you stayed awake during second semester calculus, you definitely have to work at it. The requisite analytic number theory presented may turn away the average reader if they are not prepared to make the commitment to stay on the roller coaster for the full ride.
You will be rewarded if you can break through the initial 2 or 3 chapters introducing us to the logarithm and the harmonic series. To be fair, as a previous reviewer has noted, the material on Napier and the logarithm has been done in a more satisfactory manner by Eli Maor in his book on e. But this is only a minor drawback. As long as you are comfortable with the natural logarithm, you can omit Chapter 1 with no loss.
Chapter 4 starts off with the zeta function, arguably the most enticing and mysterious function in all of mathematics, despite approximately 150 years of analysis by the world's best mathematicians. This one function alone could arguably be said to be the genesis of analytic number theory (even though Dirichlet's work on primes in arithmetic progressions has typically been given credit for that role).
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Format: Hardcover Verified Purchase
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.
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Format: 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.
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Format: 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.
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Per the foreword, this book is "aimed at students of mathematics, be they eager high school students or undergraduates". As a summa cum laude graduate math major (of some years ago) I expected to enjoy an romp thru some beautiful mathematical ideas. Well, the ideas are there, and Havil is to be commended for gathering some unusual and interesting topics. And much of the extensive mathematical notation is supported with nice numeric examples. However, much of it is not. All too often there are pages of integrals, sums, and products that go happily on without a clue to some of the beautiful things that are happening. The most frustrating example is the "proof" of Euler's zeta function formula, one of the prettiest pieces of mathematics. I still cannot understand Havil's presentation. (It was thrilling to read the same proof in "Prime Obsession" by Derbyshire so I know it can be explained with simple algebra.) Also, "Gamma" appears to be intended to be read in one sitting since it is rarely possible to begin at an advanced chapter. It is assumed that you remember definitions and notations which have appeared long before. To the author's credit, there are occasional backward references by page number, but then, about half of these are frustratingly wrong. Finally, it would be nice to see a copy of the errata for this book. I hope this book appears in a 2nd edition where the level of its presentation is made much more consistent.
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