Gamma: Exploring Euler's Constant

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Princeton University Press, Jul 26, 2009 - Mathematics - 304 pages
12 Reviews

Among 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 (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 p 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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Review: Gamma: Exploring Euler's Constant

User Review  - Douglas - Goodreads

At 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 - Goodreads

I 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

All 7 reviews »

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
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XCVI
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XCVII
169

XIX
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XX
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XXI
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XXII
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XXV
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XXVI
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XXVII
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XXX
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XXXI
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XXXIV
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XXXV
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XXXVI
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XXXVII
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XL
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XLI
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XLIII
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XLVI
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XLVII
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XLVIII
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XLIX
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LII
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LIII
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LIV
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LV
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LIX
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LX
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LXII
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LXIV
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LXVII
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LXVIII
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LXIX
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LXXI
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LXXIV
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LXXVI
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LXXVII
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LXXVIII
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LXXIX
127
LXXXI
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LXXXII
130
LXXXIII
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LXXXIV
132
LXXXV
133
XCVIII
171
XCIX
172
C
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CI
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CII
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CIII
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CIV
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CV
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CVI
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CVII
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CIX
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CXII
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CXIII
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CXIV
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CXV
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CXVI
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CXVII
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CXVIII
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CXIX
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CXX
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CXXI
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CXXIII
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CXXV
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CXXIX
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CXXX
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CXXXII
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CXXXIII
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CXXXIV
232
CXXXV
235
CXXXVII
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CXXXVIII
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CXXXIX
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CXL
242
CXLI
245
CXLII
247
CXLIII
249
CXLV
253
CXLVI
255
CXLVII
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CXLVIII
263
Copyright

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About the author (2009)

Julian Havil is a 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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