Anonymous
Posted September 29, 2003
This is an instant classic of mathematical exposition, a superb addition to the series Encyclopedia of Mathematics and Its Applications. Steven Finch's engaging style and lucid, self-contained essays on an amazing variety of topics will appeal to a wide audience. Beginners and experts alike will find a treasure trove of stories, unexpected appearances of numbers, connections between different subjects, and unsolved problems (e.g., if x is the square root of 2, is the tower of powers x^ x^x irrational?). From the Preface: 'Material about well- known constants appears early and carefully, for the sake of readers without much mathematical background.' The well-known constants include Pythagoras' square root of 2, the Golden Mean, Euler's e and gamma, Archimedes' pi, Apery's zeta(3), Catalan's G, Khintchine's K, Feigenbaum's delta, Madelung's M, and Chaitin's Omega. There are chapters on constants associated with the fields of number theory, real and complex analysis, approximation of functions, enumeration of discrete structures (some from physics), functional iteration (e.g., paper folding), and geometry. A Table of Constants in decimal form directs the reader to sections of the book. Many sections have extensive lists of references, and Finch indicates exactly where in the literature one should look for rigorous proofs and further elaboration. Author and Subject Indexes complement each other. More than sixty figures illuminate the text. This book shows the mysterious ubiquity and 'unreasonable effectiveness' of certain universal constants. Anyone interested in mathematics will benefit from reading it.
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More About This Textbook
Overview
Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is 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 work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
Editorial Reviews
From the Publisher
"Enormous fun, and you don't even have to follow any difficult arguments; a treasure-trove for the mathematical beachcomber."The Mathematical Gazette
"I think all mathematicians should own this book...there are sections where 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."
The Mathematical Intelligencer
"Very accessible...The author's clear and engaging style makes the book a pleasure to read."
MAA Reviews
"This is a very useful book...The emphasis is on the mathematical origin of the constants and their interrelationships. The aim is always to be clear and complete, to motivate why a particular constant or idea is important, and to indicate exactly where in the literature one should look for rigorous proofs and further elaboration. This book should be in each mathematical library."
Monatshefte für Mathematik
"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
Product Details
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Table of Contents
Preface; Notation; 1. Well-known constants; 2. Constants associated with number theory; 3. Constants associated with analytic inequalities; 4. Constants associated with the approximation of functions; 5. Constants associated with enumerating discrete structures; 6. Constants associated with functional iteration; 7. Constants associated with complex analysis; 8. Constants associated with geometry; Table; Index.