Measure, Topology, and Fractal Geometry

by Gerald A. Edgar

Based on a course given to talented high-school students at Ohio University in 1988, this book is essentially an advanced undergraduate textbook about the mathematics of fractal geometry. It nicely bridges the gap between traditional books on topology/analysis and more specialized treatises on fractal geometry. The book treats such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. It takes into account developments in the subject matter since 1990. Sections are clear and focused. The book contains plenty of examples, exercises, and good illustrations of fractals, including 16 color plates.

Genres: Mathematics

288 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)