Gamma: Exploring Euler's Constant

Princeton University Press, Jul 26, 2009 - Mathematics - 304 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

User Review  - 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 ... Read full review

LibraryThing Review

User Review  - sthitha_pragjna - LibraryThing

The most brilliant technical math book I have enjoyed in years. A labor of love by a teacher/mathematician. I learnt a lot about Gamma. Did you know that the chances of two randomly picked integers ... Read full review

Contents

 IV 1 VII 4 VIII 11 IX 13 X 16 XI 21 XV 22 XVI 27
 LXXXVI 134 LXXXVII 139 XC 145 XCI 155 XCII 163 XCV 164 XCVI 167 XCVII 169

 XIX 28 XX 31 XXI 33 XXII 37 XXV 42 XXVI 44 XXVII 47 XXX 49 XXXI 53 XXXIV 56 XXXV 57 XXXVI 58 XXXVII 61 XL 62 XLI 65 XLIII 69 XLVI 73 XLVII 75 XLVIII 78 XLIX 81 LII 85 LIII 86 LIV 88 LV 91 LIX 93 LX 95 LXII 98 LXIV 101 LXVII 105 LXVIII 112 LXIX 116 LXXI 119 LXXIV 121 LXXVI 123 LXXVII 125 LXXVIII 126 LXXIX 127 LXXXI 128 LXXXII 130 LXXXIII 131 LXXXIV 132 LXXXV 133
 XCVIII 171 XCIX 172 C 174 CI 179 CII 180 CIII 182 CIV 183 CV 186 CVI 189 CVII 191 CIX 193 CXII 196 CXIII 197 CXIV 200 CXV 202 CXVI 204 CXVII 206 CXVIII 207 CXIX 210 CXX 213 CXXI 217 CXXIII 219 CXXV 221 CXXIX 223 CXXX 225 CXXXII 230 CXXXIII 231 CXXXIV 232 CXXXV 235 CXXXVII 237 CXXXVIII 238 CXXXIX 239 CXL 242 CXLI 245 CXLII 247 CXLIII 249 CXLV 253 CXLVI 255 CXLVII 259 CXLVIII 263 Copyright