Measure, Topology, and Fractal Geometry [Paperback]

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.

This is essentially an advanced undergraduate textbook about the mathematics of fractal geometry. It is based on a course given to talented high-school students at Ohio University in 1988 and contains plenty of examples, exercises, and good illustrations of fractals.

From reviews of the first edition:

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...the book also contains many good illustrations of fractals (including 16 color plates).

Mathematics Teaching

The book can be recommended to students who seriously want to know about the mathematical foundation of fractlƒ>