Measure, Topology, and Fractal Geometry

出版者:Springer

作者:Gerald Edgar

页数:272

出版时间:2007-11-26

价格:USD 54.95

装帧:Hardcover

isbn号码:9780387747484

丛书系列:Undergraduate Texts in Mathematics

图书标签:数学分形几何测度论几何UTM数学-拓扑数学-FractalGeometrycomplex

Bridges the gap between traditional books on topology/analysis and more specialized treatises on fractal geometry

Contains plenty of examples, exercises, and illustrations

Ideal for classroom use with a self-contained and careful presentation

For the Second Edition of this highly regarded textbook, Gerald Edgar has made numerous additions and changes, in an attempt to provide a clearer and more focused exposition. The most important addition is an increased emphasis on the packing measure, so that now it is often treated on a par with the Hausdorff measure. The topological dimensions were rearranged for Chapter 3, so that the covering dimension is the major one, and the inductive dimensions are the variants. A "reduced cover class" notion was introduced to help in proofs for Method I or Method II measures. Research results since 1990 that affect these elementary topics have been taken into account. Some examples have been added, including Barnsley leaf and Julia set, and most of the figures have been re-drawn.

From reviews of the First Edition:

"...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..."

- Mathematics Teaching

"The book can be recommended to students who seriously want to know about the mathematical foundation of fractals, and to lecturers who want to illustrate a standard course in metric topology by interesting examples."

- Christoph Bandt, Mathematical Reviews

"...not only intended to fit mathematics students who wish to learn fractal geometry from its beginning but also students in computer science who are interested in the subject. [For such students] the author gives the required topics from metric topology and measure theory on an elementary level. The book is written in a very clear style and contains a lot of exercises which should be worked out."

- H.Haase, Zentralblatt

Written for » Lower undergraduate

Keywords » CON_D045

Related subjects » Analysis - Geometry & Topology