» Measure, Topology, and Fractal Geometry (Undergraduate Texts in Mathematics)
Rating: 4.5 / 5.00 (3 reviews)
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Measure, Topology, and Fractal Geometry (Undergraduate Texts in Mathematics) Details
Binding: HardcoverDewey Decimal Number: 511
EAN: 9780387747484
ISBN: 0387747486
Label: Springer
Manufacturer: Springer
Number Of Items: 1
Number Of Pages: 272
Publication Date: 2007-11-26
Publisher: Springer
Studio: Springer
Measure, Topology, and Fractal Geometry (Undergraduate Texts in Mathematics) Reviews
Customer Rating:
Summary: A nice book
Comment: I liked this book because it provided me with a new perspective on metric spaces, in using them as a basis learning about fractals. I think it serves as a nice book for an undergraduate to read and get enthused about studying fractals at a higher level.
Customer Rating:
Summary: Good starting point to study fractal geometry.
Comment: This book could be used as a bridge between traditional books on topology-analysis and the speciallized treatises on fractal geometry. More a catalog of definitions, methods, and references than a course text, it covers the fundamental topological and measure-theoretic concepts needed to understand the principles of some of the different dimension theories that exist. But warning: the book is far away of being a complete exposition on any of the subjects it includes.
Suitable for 3rd-year undergrads. Interesting examples and exercises. Extensive bibliography.
Please check my other reviews in my member page (just click on my name above).
Customer Rating:
Summary: A difficult but worthy book!
Comment: The programs are in LOGO: don't let the turtles fool you, this is the real stuff by a master teacher. It is hard and the examples are even harder. The problem sets are at times impossible, but in the end Dr. Edgar delivers: understanding! Your unique Associates ID is: thefractaltransl.
Editorial Review for Measure, Topology, and Fractal Geometry (Undergraduate Texts in Mathematics):
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 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. Especially, for the last 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
About the second edition: Changes throughout the text, taking into account developments in the subject matter since 1990; Major changes in chapter 6. Since 1990 it has become clear that there are two notions of dimension that play complementary roles, so the emphasis on Hausdorff dimension will be replaced by the two: Hausdorff dimension and packing dimension. 6.1 will remain, but a new section on packing dimension will follow it, then the old sections 6.2--6.4 will be re-written to show both types of dimension; Substantial change in chapter 7: new examples along with recent developments; Sections rewritten to be made clearer and more focused.
