Gamma Exploring Euler s Constant 1st Edition by Julian Havil, Freeman Dyson ISBN 0691099839 978-0691099835

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Product details: 

ISBN 10:  0691099839 

ISBN 13: 978-0691099835

Author: Julian Havil, Freeman Dyson

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.

Table of contents: 

Chapter 1 The Logarithmic Cradle
Chapter 2 The Harmonic Series
Chapter 3 Sub-Harmonic Series
Chapter 4 Zeta Functions
Chapter 5 Gamma’s Birthplace
Chapter 6 The Gamma Function
Chapter 7 Euler’s Wonderful Identity
Chapter 8 A Promise Fulfilled
Chapter 9 What Is Gamma Exactly
Chapter 10 Gamma as a Decimal
Chapter 11 Gamma as a Fraction
Chapter 12 Where Is Gamma
Chapter 13 It’s a Harmonic World
Chapter 14 It’s a Logarithmic World
Chapter 15 Problems with Primes
Chapter 16 The Riemann Initiative

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Tags: Julian Havil, Freeman Dyson, Gamma Exploring, Euler s Constant