Loading... Gamma: Exploring Euler's Constant (2003)by Julian Havil
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Sign up for LibraryThing to find out whether you'll like this book. No current Talk conversations about this book. 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, remarkably less well known than its famous counterparts: this lack of knowledge is ilustrated by the fact that no one knows if γ is either a rational or a irrational! This nice popular science book tells the story of γ (if one may say so...) starting with John Napier's celebrated work on logarithms, then going on to discuss the harmonic series (starting with the celebrated proof of its divergence by Nicholas Oresme, c.a. 1350), and the Zeta function, the Gamma function, and the definition of γ. It the proceeds with a digression about some properties of γ, unexpected relations of the harmonic series and the logarithm function to problems in other areas (such as the optimal choice problem, and Benford's law), and concluding with two chapters about the distribution of primes and the work of Riemann (including his famous hypothesis.) Overall, this is a very interesting book that offers a relaxed exploration of a number of important mathematical issues in an enjoyable style. ( ) Pickover's _Calculus and Pizza_ doesn't teach anywhere near enough calculus to be able to fully read this book, let me tell you. Euler's constant is the limit, as N approaches infinity, of 1 + 1/2 + 1/3 + ... + 1/N - ln N (approximately 0.5772156). 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 being co-prime is 1:pi squared divided by six ? Just one of the charming side results using "elementary methods". Go on and delve into the history and the application by Euler, and others into this weird constant that keeps popping up in unnatural physical settings and mathematical ones, including the Riemann conjecture. no reviews | add a review
References to this work on external resources. Wikipedia in English (7)Amazon.com Product Description (ISBN 0691099839, Hardcover)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. (retrieved from Amazon Mon, 30 Sep 2013 13:54:43 -0400) "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." "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."--BOOK JACKET.… (more) |
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