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Review
“The new edition describes recent developments, bearing in mind the rapid spread of the subject, in particular multifractal theory.” (Mathematika, No.50, 2005)
Review
“The new edition describes recent developments, bearing in mind the rapid spread of the subject, in particular multifractal theory.” (Mathematika, No.50, 2005)
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This chapter reviews some of the basic mathematical ideas and notation that will be used throughout the book. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index
This chapter reviews some of the basic mathematical ideas and notation that will be used throughout the book. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index
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Most Helpful Customer Reviews
15 of 15 people found the following review helpful
Format:Hardcover
Fractals make headlines from time to time[--are they everywhere?], and and they make lovely color pictures; but they are also part of a substantial mathematical theory, one with an
exciting mathematical history. This very important book presents
the subject in a way that it can be taught to students, and it starts with the basics, systematically, step by step, building up the material. Or it can be used for selfstudy! It has great exercises too! In view of the many applications to geometric analysis, to PDE, and to statistics, it is likely that fractal geometry will soon be a standard math course taught in many (more) math departments. By now it is widely recognized that the selfsimilarity aspects of the wavelet algorithms are key to their sucess. The book came out in 1990, and the author has an equally attractive book on the subject from 1985[The geometry of fractal sets] with a slightly more potential theoretic bent.
exciting mathematical history. This very important book presents
the subject in a way that it can be taught to students, and it starts with the basics, systematically, step by step, building up the material. Or it can be used for selfstudy! It has great exercises too! In view of the many applications to geometric analysis, to PDE, and to statistics, it is likely that fractal geometry will soon be a standard math course taught in many (more) math departments. By now it is widely recognized that the selfsimilarity aspects of the wavelet algorithms are key to their sucess. The book came out in 1990, and the author has an equally attractive book on the subject from 1985[The geometry of fractal sets] with a slightly more potential theoretic bent.
13 of 13 people found the following review helpful
Format:Paperback
This book is a superset of the content of the Advanced Fractal Geometry undergraduate course at Prof. Falconer's university, St Andrews. Those parts of the book relevant to the course - most of Part One, as well as the chapters on self-similar sets, Julia/Mandelbrot sets and multifractals - explain and illustrate the concepts as clearly as is possible, so that even highly complex concepts (such as the relationship between Legendre transformation and dimensional spectra) are easily understood - well, with a little bit of effort...!
As someone who has done that course, I can say that this book is a perfect reference for it and for any other courses that cover similar material.
Well worthy of my five, good sir.
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com:
6 reviews
22 of 22 people found the following review helpful
Exposes fractal geometry as a real mathematical discipline.
13 April 2000
Format:Hardcover
I appreciate Falconer's books on fractal geometry because they show the topic as it really is: a whole mathematical discipline on its own right and not just a nice temporary fashion.
It begins introducing basic topological concepts and then proceeds to develop the theory for several possible definitions of fractal dimension, showing the relations between them. Then it explores deeply the local geometry of different kinds of fractal objects, and studies some other geometrical situations, like the pojection of fractals (ever thought of a DIGITAL sundial? Here it is described!).
The book also includes a lot of applications to other areas of mathematics and physics, a great amount of graphics, and much more.
The text is suitable from third year undergraduate school and on. It is a larger but lighter version of "The Geometry of Fractal Sets".
17 of 18 people found the following review helpful
What every student should know about fractals.
10 Feb 2003
Format:Hardcover|Amazon Verified Purchase
Fractals make headlines from time to time[--are they everywhere?], and and they make lovely color pictures; but they are also part of a substantial mathematical theory, one with an
exciting mathematical history. This very important book presents
the subject in a way that it can be taught to students, and it starts with the basics, systematically, step by step, building up the material. Or it can be used for selfstudy! It has great exercises too! In view of the many applications to geometric analysis, to PDE, and to statistics, it is likely that fractal geometry will soon be a standard math course taught in many (more) math departments. By now it is widely recognized that the selfsimilarity aspects of the wavelet algorithms are key to their sucess. The book came out in 1990, and the author has an equally attractive book on the subject from 1985[The geometry of fractal sets] with a slightly more potential theoretic bent.
exciting mathematical history. This very important book presents
the subject in a way that it can be taught to students, and it starts with the basics, systematically, step by step, building up the material. Or it can be used for selfstudy! It has great exercises too! In view of the many applications to geometric analysis, to PDE, and to statistics, it is likely that fractal geometry will soon be a standard math course taught in many (more) math departments. By now it is widely recognized that the selfsimilarity aspects of the wavelet algorithms are key to their sucess. The book came out in 1990, and the author has an equally attractive book on the subject from 1985[The geometry of fractal sets] with a slightly more potential theoretic bent.
15 of 16 people found the following review helpful
Theoretical as well as practical insight
13 Aug 2001
Format:Paperback
The first part of the book is essentially of a theoretical nature, with a thorough treatment of fractal geometry at a mathematical point of view. The second part on the other hand provides a flavour of the problems of fractal geometry in practice...so mathematicians as well as people interested in applications only should both find this book interesting. The maths are not easy but quite "understandable" for science undergrads...some notions of calculus or topology would help... but the introduction is excellent and allows anyone to follow the course of the book (but for understanding the proofs a good math background is required).
Excellent for understanding the geometrical properties of fractals.
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