Measure, Topology, and Fractal Geometry

by Gerald A. Edgar

From the reviews: "In the world of mathematics, the 1980's might well be described as the "decade of the fractal". Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. However, the book also contains many good illustrations of fractals (including 16 color plates), together with Logo programs which were used to generate them. ... Here then, at last, is an answer to the question on the lips of so 'What exactly is a fractal?' I do not expect many of this book's readers to achieve a mature understanding of this answer to the question, but anyone interested in finding out about the mathematics of fractal geometry could not choose a better place to start looking." #Mathematics Teaching#1

Genres: Mathematics

230 pages, Hardcover

First published January 1, 1995

Reviews

[Robert · Rating 3 out of 5]

I can't wait to finish this—it has just gotten so tedious! My biggest peeve so far is that the author frequently refers to letters in his proofs that he has apparently (at least I hope) defined at some point in the preceding pages. This is the type of thing I try very hard to get my students away from. It is unfortunate that the author either never learned to avoid this kind of manufactured obfuscation or somehow forgot the lesson. That said, this book is vastly superior to the typical populist fractal drivel that is out there. By that I mean it has real mathematical content. I am not overly engaged by the topic, but people with a fire in the belly for point-set topology and graphics programming would find it enlightening. To help avoid confusion, keep a running list of what symbols and letters the author is using to represent what objects. Best of luck! (on page 166)