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Gamma: Exploring Euler's Constant: 53 Paperback – 8 January 2018

by Julian Havil (Author), Freeman Dyson (Foreword)

80

Part of: Princeton Science Library (52 books)

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Among the many constants that appear in mathematics, ?, e, and i are the most familiar. Following closely behind is ?,, 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 , minus the natural logarithm of n--the numerical value being 0.5772156...But unlike its more celebrated colleagues ? 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.

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Part of series

Princeton Science Library
Print length

296 pages
Language

English
Publisher

Princeton University Press
Publication date

8 January 2018
Dimensions

13.97 x 1.91 x 21.59 cm
ISBN-10

0691178100
ISBN-13

978-0691178103
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"[Gamma] 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."-- "MAA Online"

"[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

"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"

"Mathematics is presented throughout as something connected to reality. . . . Many readers will find in [Gamma] exactly what they have been missing."---Mohammad Akbar, Plus Magazine

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

"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

"Wonderful. . . . Havil's emphasis on historical context and his conversational style make this a pleasure to read. . . .Gammais a gold mine of irresistible mathematical nuggets. Anyone with a serious interest in math will find it richly rewarding."--New Scientist"A joy from start to finish."--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 constantg, serves as the unifying motif through a wide range of mathematical adventures."-- "Notices of the American Mathematical Society"

From the Back Cover

"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

Publisher ‏ : ‎ Princeton University Press; New edition (8 January 2018)
Language ‏ : ‎ English
Paperback ‏ : ‎ 296 pages
ISBN-10 ‏ : ‎ 0691178100
ISBN-13 ‏ : ‎ 978-0691178103
Dimensions ‏ : ‎ 13.97 x 1.91 x 21.59 cm

Best Sellers Rank: 413,580 in Books (See Top 100 in Books)
- 213 in Popular & Elementary Arithmetic (Books)
- 270 in Mathematical Physics (Books)
- 487 in History of Mathematics

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Julian Havil

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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.

And so for some time I have failed to add anything useful on this page, for which I apologise. My hope is that the readers of my books will gain something of what I have gained by writing them. I do apologise for errors and omissions but have no control over Kindle versions, which seem worthy of typographical criticism. My current project is a book with working title 'Features of a Mathematical Landscape", which I hope will intrigue the intended reader... The last book, Curves for the Mathematically Curious, has met with a pretty positive response, for which I am most grateful. I am also grateful for support, as I am grateful for constructive criticism. If you have ideas for a book that would be appropriate for me to write, do say so.

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Paul A Lewicki

All about Euler

Reviewed in the United States on 19 August 2023

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Good book on Euler, it goes into a lot of detail about Euler and his theorems, hard to understand for laymen, hard to understand unless you’re a genius or close to it.

Jamil Abreu Jr

Very informative... Not always easy...

Reviewed in Brazil on 2 May 2020

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Very nice and informative reading on Euler'constant gamma but has also much material on logarithms, the harmonic series and zeta functions. As the author makes clear at the begining, you really need pencil and paper sometimes. The last two chapters on the Prime Number Theorem and Riemann Hypothesis, respectively, are particularly harder than the rest of the book. In general, the book fails sometimes at not giving explicit references for various informations but the really curious reader can find these elsewhere as he decides to go deeper.

Marco

Harmonic Series and Gamma function

Reviewed in Italy on 28 December 2015

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Excellent book dealing with Gamma constant, Gamma function, harmonic series and number Theory.
The author explains deep concepts in a simple way, nonetheless it is possible to find in this book all the useful details.
M.R. , PhD in Physics and Electronic Engineering

Gabor Ellmann

A lovely book!

Reviewed in Germany on 15 November 2013

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Havil is excellent story-teller.
It is amazing how much mathematics he can illuminate with his torch while keeping it focused on the gamma constant of Euler.

Hamptonshirewonder

The addictive delights of prime numbers made more accessible

Reviewed in the United Kingdom on 13 March 2011

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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.

From introductory calculus, the integral of 1/x is the natural logarithm of x. Imagining the graph of 1/x divided into strips of width one, the graph is bounded above and below by these strips 1/n : Gamma is the limiting number, as n gets larger, of the difference (log(n)- (1+1/2+1/3+...+1/n)). It's about 0.577,, No one knows whether it is the solution of an equation or is not, like pi or e.

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: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

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Gamma: Exploring Euler's Constant: 53 Paperback – 8 January 2018

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About the author

Julian Havil

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