Classics On Fractals (Studies in Nonlinearity) [Paperback]

Gerald A. Edgar (Author)

Book Description

ISBN-10: 0813341531 | ISBN-13: 978-0813341538 | Publication Date: August 7, 2003

Fractals are an important topic in such varied branches of science as mathematics, computer science, and physics. Classics on Fractals collects for the first time the historic papers on fractal geometry, dealing with such topics as non-differentiable functions, self-similarity, and fractional dimension. Of particular value are the twelve papers that have never before been translated into English. Commentaries by Professor Edgar are included to aid the student of mathematics in reading the papers, and to place them in their historical perspective. The volume contains papers from the following: Cantor, Weierstrass, von Koch, Hausdorff, Caratheodory, Menger, Bouligand, Pontrjagin and Schnirelmann, Besicovitch, Ursell, Levy, Moran, Marstrand, Taylor, de Rahm, Kolmogorov and Tihomirov, Kiesswetter, and of course, Mandelbrot.

Editorial Reviews

About the Author

Gerald A. Edgar received his B.A. degree from the University of California, Santa Barbara, and his Ph.D. from Harvard University. He has taught at Northwestern University, and is presently Professor of Mathematics at the Ohio State University. His research interests include measure theory and its application in fractal geometry, probability, and functional analysis.

Product Details

• Paperback: 384 pages
• Publisher: Westview Press (August 7, 2003)
• Language: English
• ISBN-10: 0813341531
• ISBN-13: 978-0813341538
• Product Dimensions: 9 x 6 x 0.8 inches
• Shipping Weight: 1.1 pounds
• Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,864,772 in Books (See Top 100 in Books)

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5 of 5 people found the following review helpful:

5.0 out of 5 stars The Laying of Cornerstones of Modern Math, February 1, 2005

By 

Linas Vepstas - See all my reviews
(REAL NAME)   

This review is from: Classics On Fractals (Studies in Nonlinearity) (Paperback)

The title of this book is subversive. Compared to the contents of other popular books on fractals, such as Peitgen & Saupe's "Chaos and Fractals", the reader will find almost no commonality except for the word "fractal" in the title. And this is what makes this book so wonderful and refreshing. Other pop books on fractals tend to be filled with shallow descriptions, crude phenomenology, and neither hint of the underlying theory, nor any clue of the depth and importance of it. The Peitgen-Saupe series is particularly guilty of this fault.

By contrast, in this book, "Classics on Fractals", we hear Georg Cantor explain Cantor sets in his own words, and realize how trivialized the pop-lit explanations are. We have Helge von Koch explain the Koch curve, and Felix Hausdorff explain Hausdorff measure; Besicovitch explaining fractal dimensions, Paul Levy presenting fractals that tile (now called Levy dragons), and Kolmogorov theorizing about entropy. The papers reproduced in this book are fifty to one hundred years old: we catch glimpses of the cornerstones of modern mathematics being laid.

Note, however, that you will need to have strong mathematical skills and interests to find the pleasure and entertainment in this book. This is, after all, a collection of mathematical papers written by leading mathematicians, for other mathematicians, and originally published in mathematical journals. These are not simplified expositions for the lay reader. Each non-English reprint has been translated to English, and is preceded by several paragraphs of introduction to the setting and the mathematician. Serious amateurs investigating fractals will be awed by this book, and professionals will be a bit humbled on rediscovering some of the history of fractals.

3 of 3 people found the following review helpful:

4.0 out of 5 stars Where it all began, December 26, 2000

By A Customer

This review is from: Classics On Fractals (Studies in Nonlinearity) (Hardcover)

This anthology is a collection of the classic essays on chaos, from before chaos theory was created or the word 'fractal' was coined. The math level is a little high for the general reader, but it is well worth reading once the reader has the necessary background.