Gamma: Exploring Euler's Constant (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 (17071783), 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 nthe numerical value being 0.5772156. . .. But unlike its more celebrated colleagues p and e, the exact nature of gamma remains a mysterywe 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 todaythe 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.
"[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 aredissuaded by the dryness and formality of textbooks, 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
show more
*An electronic version of a printed book that can be read on a computer or handheld device designed specifically for this purpose.
Formats for this Ebook
Required Software  Any PDF Reader, Apple Preview 

Supported Devices  Windows PC/PocketPC, Mac OS, Linux OS, Apple iPhone/iPod Touch. 
# of Devices  Unlimited 
Flowing Text / Pages  Pages 
Printable?  Yes 
Book details
 PDF  296 pages
 Julian Havil(Author) Freeman Dyson(Foreword)
 Princeton University Press (6 April 2003)
 English
 5
 Science & Nature
Review Text
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 oneand 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 noone else explained them so clearly and interestinglyand 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..
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 subharmonic 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.
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 subharmonic 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
Freeman Dyson is not a coauthor, he merely wrote the foreword.I think the attribution on Amazon's website is therefore misleading.
A brilliant book and one you'll return to again and again!Highly recommended for anyone with an interest in maths, an impressive and illuminating work.
This books walks the line dividing serious academic mathematics and popular entertainment without either side being conscious that that is being done. A scholarly, entertaining and easily digested tour through some intriquing and mysterious basic mathematics, I find this quite the best of the plethora of popular mathematics books to appear in recent years. Havil tells you things you know, and then things you don't, with an effortless expertise. It's a pity that one sees repeatedly that this fine book is by Freeman Dyson  he contributed an introduction but this original and profound piece of work is entirely by Julian Havil  I feel like Draco Malfoy surveying his henchmen in Harry Potter because when I was at college with him, I did not realise he could write! Well, he can, and extremely well. The book is cheap, and gives you a real feel for what mathematics is and what it can be.
For someone with a limited background in pure maths, but still eager to learn and full of enthusiasm and excitement(especially after the previous 4 reviews??  and not forgetting the "Forward"!), this book left me cold. Please, teacher, do not blame the pupil and thank God my formative years managed to avoid Winchester and all who sail in her.Best wishes to all!
Name:  
The message text:  


 Log in to post comments
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 bookPrime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics