Measure, Topology, and Fractal Geometry (Undergraduate Texts in Mathematics)

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9780387747484: Measure, Topology, and Fractal Geometry (Undergraduate Texts in Mathematics)

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.

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From the Back Cover:

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

Review:

From the reviews of the second edition:

"As a non-specialist, I found this book very helpful. It gave me a better understanding of the nature of fractals, and of the technical issues involved in the theory. I think it will be valuable as a textbook for undergraduate students in mathematics, and also for researchers wanting to learn fractal geometry from scratch. The material is well-organized and the proofs are clear; the abundance of examples is an asset for a book on measure theory and topology." (Fabio Mainardi, MathDL, February, 2008)

"This is the second edition of a well-known textbook in the field ... . The book may serve as a textbook for a one-semester (advanced) undergraduate course in mathematics. ... the book is also suitable for readers interested in theoretical fractal geometry coming from other disciplines (e.g. physics, computer sciences) with a basic knowledge of mathematics. The presentation of the material is appealing ... and the style is clear and motivating. ... the book will remain as a standard reference in the field." (José-Manuel Rey, Zentralblatt MATH, Vol. 1152, 2009)

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Gerald A. Edgar
Editore: Springer-Verlag New York Inc., United States (2007)
ISBN 10: 0387747486 ISBN 13: 9780387747484
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Descrizione libro Springer-Verlag New York Inc., United States, 2007. Hardback. Condizione libro: New. 2nd ed. 2008. Language: English . Brand New Book. 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. Codice libro della libreria AAU9780387747484

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Edgar, Gerald A.
Editore: Springer-Verlag New York Inc. (2007)
ISBN 10: 0387747486 ISBN 13: 9780387747484
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Descrizione libro Springer-Verlag New York Inc., 2007. Condizione libro: New. 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. Series: Undergraduate Texts in Mathematics. Num Pages: 288 pages, 149 black & white illustrations, 20 colour illustrations, biography. BIC Classification: PBMX; PBP. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 242 x 159 x 27. Weight in Grams: 586. . 2007. 2nd. Hardcover. . . . . . Codice libro della libreria V9780387747484

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Descrizione libro Springer New York 2007-11-26, New York, 2007. hardback. Condizione libro: New. Codice libro della libreria 9780387747484

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Descrizione libro Springer. Hardcover. Condizione libro: New. New copy - Usually dispatched within 2 working days. Codice libro della libreria B9780387747484

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Gerald A. Edgar
Editore: Springer-Verlag New York Inc., United States (2007)
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Descrizione libro Springer-Verlag New York Inc., United States, 2007. Hardback. Condizione libro: New. 2nd ed. 2008. Language: English . Brand New Book. 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. Codice libro della libreria AAU9780387747484

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Descrizione libro Springer-Verlag New York Inc. Condizione libro: New. 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. Series: Undergraduate Texts in Mathematics. Num Pages: 288 pages, 149 black & white illustrations, 20 colour illustrations, biography. BIC Classification: PBMX; PBP. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 242 x 159 x 27. Weight in Grams: 586. . 2007. 2nd. Hardcover. . . . . Books ship from the US and Ireland. Codice libro della libreria V9780387747484

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Descrizione libro Springer-Verlag New York Inc., 2007. HRD. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria BB-9780387747484

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