Gamma: Exploring Euler's Constant

Couverture
Princeton University Press, 4 janv. 2010 - 296 pages

Among the many constants that appear in mathematics, π, e, and i are the most familiar. Following closely behind is y, 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 π 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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LibraryThing Review

Avis d'utilisateur  - FPdC - LibraryThing

The constant γ (called the Euler, or the Euler-Mascheroni) constant plays a significant role in Number Theory. Being, like π or e, one of the ubiquitous mathematical constants, it is, still today ... Consulter l'avis complet

LibraryThing Review

Avis d'utilisateur  - fpagan - LibraryThing

Pickover's _Calculus and Pizza_ doesn't teach anywhere near enough calculus to be able to fully read this book, let me tell you. Euler's constant is the limit, as N approaches infinity, of 1 + 1/2 + 1/3 + ... + 1/N - ln N (approximately 0.5772156). Consulter l'avis complet

Table des matières

The Logarithmic Cradle
1
The Harmonic Series
21
SubHarmonic Series
27
Zeta Functions
37
Gammas Birthplace
47
The Gamma Function
53
Eulers Wonderful Identity
61
A Promise Fulfilled
65
Its a Logarithmic World
139
Problems with Primes
163
The Riemann Initiative
189
The Greek Alphabet
217
Big Oh Notation
219
Taylor Expansions
221
Complex Function Theory
225
Application to the Zeta Function
249

What Is Gamma Exactly?
69
Gamma as a Decimal
81
Gamma as a Fraction
91
Where Is Gamma?
101
Its a Harmonic World
119

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À propos de l'auteur (2010)

Julian Havil is a retired former master at Winchester College, England, where he taught mathematics for thirty-three years. He received a Ph.D. in mathematics from Oxford University. Freeman Dyson is professor emeritus of physics at the Institute for Advanced Study in Princeton. He is the author of several books, including Disturbing the Universe and Origins of Life.

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