Gamma: Exploring Euler's ConstantAmong 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. 
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Review: Gamma: Exploring Euler's Constant
User Review  Douglas  GoodreadsAt the time this book came out, I was going through parts of Whittaker's famous "Modern Analysis". This book was written when mathematicians still "did" mathematics. They got their hands dirty. They ... Read full review
Review: Gamma: Exploring Euler's Constant
User Review  Matt Jarvis  GoodreadsI found this book quite difficult, but it was a very engaging read none the less and exposed me to some areas of mathematics that I have not seen before, and am now eager to explore! 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 
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263  