Gamma Exploring Euler's Constant~tqw~ darksiderg

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    *******************************************************************************<br /> Gamma: Exploring Euler's Constant <br /> *******************************************************************************<br /> <br /> -------------------------------------------------------------------------------<br /> General Information<br /> -------------------------------------------------------------------------------<br /> Type.................: Ebook<br /> Part Size............: 8,371,793 bytes<br /> <br /> -------------------------------------------------------------------------------<br /> Post Information<br /> -------------------------------------------------------------------------------<br /> Posted by............: ~tqw~<br /> <br /> -------------------------------------------------------------------------------<br /> Release Notes<br /> -------------------------------------------------------------------------------<br /> Among the myriad of constants that appear in mathematics, p, e, and i are the <br /> most familiar. Following closely behind is g, or gamma, a constant that arises <br /> in many mathematical areas yet maintains a profound sense of mystery.<br /> <br /> In a tantalizing blend of history and mathematics, Julian Havil takes the reader <br /> on a journey through logarithms and the harmonic series, the two defining <br /> elements of gamma, toward the first account of gamma's place in mathematics.<br /> <br /> Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures <br /> prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + <br /> 1/3 + . . . up to 1/n, minus the natural logarithm of n--the numerical value <br /> being 0.5772156. . .. But unlike its more celebrated colleagues p and e, the <br /> exact nature of gamma remains a mystery--we don't even know if gamma can be <br /> expressed as a fraction.<br /> <br /> Among the numerous topics that arise during this historical odyssey into <br /> fundamental mathematical ideas are the Prime Number Theorem and the most <br /> important open problem in mathematics today--the Riemann Hypothesis (though no <br /> proof of either is offered!).<br /> <br /> Sure to be popular with not only students and instructors but all math <br /> aficionados, Gamma takes us through countries, centuries, lives, and works, <br /> unfolding along the way the stories of some remarkable mathematics from some <br /> remarkable mathematicians.<br /> <br /> Table of Contents<br /> Foreword <br /> Acknowledgements <br /> Introduction <br /> Ch. 1 The Logarithmic Cradle 1<br /> Ch. 2 The Harmonic Series 21<br /> Ch. 3 Sub-Harmonic Series 27<br /> Ch. 4 Zeta Functions 37<br /> Ch. 5 Gamma's Birthplace 47<br /> Ch. 6 The Gamma Function 53<br /> Ch. 7 Euler's Wonderful Identity 61<br /> Ch. 8 A Promise Fulfilled 65<br /> Ch. 9 What Is Gamma ... Exactly? 69<br /> Ch. 10 Gamma as a Decimal 81<br /> Ch. 11 Gamma as a Fraction 91<br /> Ch. 12 Where Is Gamma? 101<br /> Ch. 13 It's a Harmonic World 119<br /> Ch. 14 It's a Logarithmic World 139<br /> Ch. 15 Problems with Primes 163<br /> Ch. 16 The Riemann Initiative 189<br /> App. A The Greek Alphabet 217<br /> App. B Big Oh Notation 219<br /> App. C Taylor Expansions 221<br /> App. D Complex Function Theory 225<br /> App. E Application to the Zeta Function 249<br /> References 255<br /> Name Index 259<br /> Subject Index 263<br /> <br /> Product Details<br /> <br /> * ISBN: 0691099839<br /> * ISBN-13: 9780691099835<br /> * Format: Hardcover, 376pp<br /> * Publisher: Princeton University Press<br /> * Pub. Date: May 2003<br /> <br /> -------------------------------------------------------------------------------<br /> Install Notes<br /> -------------------------------------------------------------------------------<br /> PDF Reader
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