Mathematical Constants II

Steven R. Finch (Massachusetts Institute of Technology)

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English

Cambridge University Press
06 December 2018

Mathematical foundations; Number theory; Combinatorics & graph theory; Maths for scientists

Series: Encyclopedia of Mathematics and its Applications

Famous mathematical constants include the ratio of circular circumference to diameter, π = 3.14 …, and the natural logarithm base, e = 2.718 …. Students and professionals can often name a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here the author renews the search he began in his book Mathematical Constants, adding another 133 essays that broaden the landscape. Topics include the minimality of soap film surfaces, prime numbers, elliptic curves and modular forms, Poisson–Voronoi tessellations, random triangles, Brownian motion, uncertainty inequalities, Prandtl–Blasius flow (from fluid dynamics), Lyapunov exponents, knots and tangles, continued fractions, Galton–Watson trees, electrical capacitance (from potential theory), Zermelo's navigation problem, and the optimal control of a pendulum. Unsolved problems appear virtually everywhere as well. This volume continues an outstanding scholarly attempt to bring together all significant mathematical constants in one place.

By: Steven R. Finch (Massachusetts Institute of Technology)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 169
Dimensions: Height: 241mm, Width: 160mm, Spine: 46mm
Weight: 1.270kg
ISBN: 9781108470599
ISBN 10: 1108470599
Series: Encyclopedia of Mathematics and its Applications
Pages: 782
Publication Date: 06 December 2018
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

1. Number theory and combinatorics; 2. Inequalities and approximation; 3. Real and complex analysis; 4. Probability and stochastic processes; 5. Geometry and topology; Index.

Steven R. Finch is Research Computing Specialist at the Massachusetts Institute of Technology, Sloan School of Management. He is honoured to have received a Book Fellowship from the Clay Mathematics Institute and a Ford award for expository excellence. After the publication of the first volume of Mathematical Constants (Cambridge, 2003), he worked for three years as a statistical programmer at the Boston University School of Public Health, and then taught for ten years as a preceptor at the Harvard University Department of Statistics.

Reviews for Mathematical Constants II

'Like the best sequels, this one covers similar ground to the original but finds ways to stay fresh and interesting ... any mathematician or math student who picks it up and spends a few minutes with it is likely to find something that is new and of interest to them. ... Finch has once again written a collection of essays about a wide range of topics that I expect I will enjoy flipping through for another decade and a half until I look forward to having Volume III land on my desk.' Darren Glass, MAA reviews 'This is a remarkable book ... [which] can be thought of as a collection of essays that recount stories that are both successful and tangible.' Paul F. Bracken, MathSciNet 'Some of the most intriguing formulas of mathematics (like those of Ramanujan) adorn this treasure trove of mathematical gems ... Steven R. Finch's incredible labor of love, an encyclopedia of mathematical constants ... contain a total of 269 meticulously documented essays from all fields of mathematics.' Osmo Peokonen, The Mathematical Intelligencer 'Taken together, Mathematical Constants and Mathematical Constants II form a comprehensive and unique work that is a welcome addition to the mathematician's reference library.' Steven R. Finch, Notices of the AMS