| 
|
|---|
|
|
|
|---|
Famous mathematical constants include the ratio of circular circumference to diameter, pi=3.14..., and the natural logarithmic base, e=2.718.... Students and professionals can often name a few others, but there are many more buried in the literature 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.
"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 Online
"To appreciate this kind of book, it has to be really seen. The five chapters cover
number theory & combinatorics, inequalities & approximation, real & complex analysis,
probability & stochastic processes, and geometry & topology... The number of individual
topics the book touches is really remarkable. One could read Tauberian constants one
moment and then skip over and consider Riemann zeta moments next or even Bessel function
zeroes, Dirichlet integral or Mathieu eigenvalues... It is made up of numerous individual
journeys through mathematical ideas and established results."
-- Paul F. Bracken, Mathematical Reviews
"One wonders how these two volumes were born. Published as books 94 and 169 of the Encyclopedia
of Mathematics and Its Applications, they contain a total of 269 meticulously documented essays from
all fields of mathematics... It appears astonishing to me that a single individual went through
all these topics. His achievement can only be compared to the On-Line Encyclopedia of Integer
Sequences. Could this be yet another case of obsessive collecting disorder? By no means, for we
learn that Steven Finch is also an accomplished pianist and composer, so he does have a life
beyond formulas and numbers.
Some of the most intriguing formulas of mathematics (like those of Ramanujan) adorn this treasure
trove of mathematical gems. Open problems abound. Finch generously gives credit to obscure papers
by baptizing some lesser-known constants with the names of half-forgotten authors...
[An earlier review of the first volume] asserts that "all mathematicians should own this book."
The same applies to the second volume."
-- Osmo Pekonen, Mathematical Intelligencer
Online purchase at Cambridge University Press site. Many thanks for your interest!
"The pages of Mathematical Constants abound in thousands of tales about numbers.
This book is an amazing piece of erudition destined to fascinate the novice, puzzle the
expert, and trigger the imagination of all. Every person who enjoys mathematics will find
here unexpected connections across science as well as unsuspected corners of hidden
knowledge. It will startle us, intrigue us and nurture our quest of mysterious patterns amongst
numbers and structures. Every reader will be grateful to Steven Finch for a work that is unique
in its approach, a great piece of science and a real piece of art."
-- Philippe Flajolet
"In his extremely lucid and captivating style, Steven Finch tells the stories
of 136 mathematical constants, from the super-famous (Pi) to the obscure, from the
apparently trivial Zero to the non-computable (Chaitin's) Omega, and before
we know it, we have learned a lot of new and exciting mathematics, since mathematical
constants are almost everywhere dense in math."
-- Doron Zeilberger
Famous mathematical constants include the ratio of circular circumference to diameter, pi=3.14..., and the natural logarithmic base, e=2.718.... Students and professionals usually can name at most 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 Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. Topics covered include the statistics of continued fractions, chaos in nonlinear systems, prime numbers, sum-free sets, isoperimetric problems, approximation theory, self-avoiding walks and the Ising model (from statistical physics), binary and digital search trees (from theoretical computer science), the Prouhet-Thue-Morse sequence, complex analysis, geometric probability and the traveling salesman problem. This book will be helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This is an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
"I think all mathematicians should own this book ... it is truly unusual and
abundantly exciting, whether as a desert island read or as a tool for breaking
the logjam of mathematical researcher's block ... the author conveys admirably
his excitement over some unexpected and beautiful sequence of ideas. I pay the
author the earnest compliment of stating that nearly every page in the book is
an adventure, and I am grateful that he could enlist all of us as his fellow
explorers."
-- Jet Wimp, Mathematical Intelligencer
"Finch displays a vast forest of constants, arising in a variety of specialties,
and which neither I nor most of my readers have ever met up with. Open the book
at random (I found it excellent bedtime reading), and you will learn about Favard's
constant, Schlüter's constant, Baxter's constant, the Gauss-Kuzmin-Wirsing
constant, ..., and so on into the night."
-- Philip J. Davis, SIAM News
"This is a very useful book ... it should be in each mathematical library."
-- Johann Cigler, Monatshefte für Mathematik
"What delicious browsing! The researcher who traces a newly computed number
through this book may well discover a decisive hidden connection between seemingly
unrelated problems ... Finch organizes these numbers in chapters by the mathematical
disciplines from which they arise, so individual chapters will have special interest
for students of number theory, analysis, approximation theory, combinatorics, dynamics,
complex analysis, and geometry. An excellent production, an instant classic, and a
fabulous source of open problems ... Highly recommended. All levels."
[Awarded 'Outstanding Title!']
-- D. V. Feldman, CHOICE: Current Reviews for
Academic Libraries
"For a reader with at least an undergraduate degree, the context for each constant
is described clearly and succinctly. The sections can be read independently and
each serves as an entrée to fascinating problems and results."
-- E. J. Barbeau, Mathematical Reviews
"This is an encyclopaedic feat of scholarship ... each essay is packed with results ...
there are extensive lists of references, right up-to-date, and the book is furnished
with excellent indices both of subjects and authors together with a listing of constants
in order of magnitude ... it is just right for the departmental library. Enormous fun,
and you don't even have to follow any difficult arguments; a treasure-trove for the
mathematical beachcomber."
-- Gerry Leversha, Mathematical Gazette
"The author's clear and engaging style makes the book a pleasure to read ...
this is the real strength of the book: it gives just enough information about
each of the constants to make the reader curious, and then helps them figure
out where to look to learn even more."
-- Darren Glass, MAA Online
"Mathematicians are familiar with a great many mathematical constants, but
there are more constants in this book than you could ever have imagined ..."
-- Paul J. Campbell, Mathematics Magazine
"This is an instant classic of mathematical exposition ... Mathematical Constants
shows the mysterious ubiquity and 'unreasonable effectiveness' of certain universal
constants. Anyone interested in mathematics will benefit from reading it."
-- Jonathan Sondow, BarnesandNoble.com
"There are topics that go across all fields of mathematics. Numerical constants
are one of them and they are here, for the first time, the object of a systematic
investigation ... This book is a valuable source of information and of suggestions
for further research."
-- Solomon Marcus, Zentralblatt MATH
"I consider this book to be an essential component of all mathematical libraries.
I have placed it on my 'within the grasp' shelf and have strongly recommended to
the college library that it be added to the reference collection."
-- Charles Ashbacher, Amazon.com
"This excellent book contains 136 'stories', each devoted to a mathematical constant
or a class of constants ... It is very useful and interesting for all mathematicians ..."
-- József Németh, Acta Scientiarum Mathematicarum
Online purchase at Cambridge University Press site; keyword search via Amazon and Google. Many thanks for your interest!
|
|---|