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

Freeman Dyson , Julian Havil
4.4 out of 5 stars  See all reviews (7 customer reviews)
Price: 13.95 & FREE Delivery in the UK. Details
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Book Description

26 July 2009 Princeton Science Library

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.



Frequently Bought Together

Gamma: Exploring Euler's Constant (Princeton Science Library) + "e": The Story of a Number (Princeton Science Library) + An Imaginary Tale: The Story of i [the square root of minus one] (Princeton Library Science Edition) (Princeton Science Library)
Price For All Three: 33.26

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Product details

  • Paperback: 296 pages
  • Publisher: Princeton University Press (26 July 2009)
  • Language: English
  • ISBN-10: 0691141339
  • ISBN-13: 978-0691141336
  • Product Dimensions: 23.4 x 15.2 x 1.8 cm
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (7 customer reviews)
  • Amazon Bestsellers Rank: 172,392 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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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, 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

--This text refers to an out of print or unavailable edition of this title.

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Customer Reviews

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Most Helpful Customer Reviews
21 of 23 people found the following review helpful
5.0 out of 5 stars A must have for any maths enthusiast. 17 April 2003
Format:Hardcover
I had heard that this book was coming out and, having read the books by Maor and Nahin, was looking forward to the next 'constant' treatise from PUP; it' s great that the author is English this time! Well done PUP for letting the Brits in (I see that they now have an office in England). The book is (for me) the best yet of the series (if that is what it is) and having read it I can see why Gamma was the topic to be chosen (pi has of course been done several times and so has the Golden Ratio). Havil is a new author and an extremely good one-and he knows his maths. I am just an amateur enthusiast and as such I have learned so much maths from his exposition. The Harmonic Series stuff leading to the Zeta functions was some of the best for me and opened my eyes to the Prime Number Theorem and the Riemann Hypothesis; why has no-one else explained them so clearly and interestingly-and without avoiding the maths? As the author says, some parts need work to understand but it's very rewarding to get to grips with the ideas and particularly with the historical perspective that is woven into the pages. Now I have 3 great books from PUP on mathematical constants on my shelf...I await the fourth..
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3 of 3 people found the following review helpful
Format:Paperback|Verified Purchase
Although I say "accessible" , be warned this is a book for someone with say single subject A level maths, and one needs a pen & paper to work through it: the book is not a popularization, but a serious attempt to explain number theory , Gamma, and in the end the Riemann Hypothesis, to a wider audience.

The book successfully answers the question "just what is it about the the complex zeros of the Riemann zeta function that makes them relevant for the distribution of prime numbers and the Prime Number Theorem?"

Hence in some sense this book could be regarded as a follow on to John Derbyshire's book "Prime obsession".
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16 of 18 people found the following review helpful
5.0 out of 5 stars Who would have thought!? 27 Jun 2003
Format: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.
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11 of 13 people found the following review helpful
5.0 out of 5 stars Who would have thought!? 12 Aug 2003
Format: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.
Reviewer: Palle E. T. Jorgensen
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