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Title: Fractal Geometry : Mathematical Foundations and Applications by Kenneth Falconer ISBN: 0-470-84862-6 Publisher: Halsted Press Pub. Date: 31 October, 2003 Format: Paperback Volumes: 1 List Price(USD): $49.95 |
Average Customer Rating: 5 (4 reviews)
Rating: 5
Summary: What every student should know about fractals.
Comment: 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.
Rating: 5
Summary: Theoretical as well as practical insight
Comment: 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.
Rating: 5
Summary: Exposes fractal geometry as a real mathematical discipline.
Comment: 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".
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Title: The Geometry of Fractal Sets by K. J. Falconer ISBN: 0521337054 Publisher: Cambridge University Press Pub. Date: 24 July, 1986 List Price(USD): $32.00 |
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Title: Fractals Everywhere by Michael Barnsley, Michael F. Barnsley ISBN: 0120790696 Publisher: Morgan Kaufmann Pub. Date: April, 2000 List Price(USD): $60.95 |
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Title: The Fractal Geometry of Nature by Benoit B. Mandelbrot ISBN: 0716711869 Publisher: W H Freeman & Co. Pub. Date: 15 August, 1982 List Price(USD): $42.50 |
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Title: Chaos and Fractals: New Frontiers of Science by Heinz-Otto Peitgen, Hartmut Jurgens, Dietmar Saupe ISBN: 0387979034 Publisher: Springer Verlag Pub. Date: May, 1997 List Price(USD): $69.95 |
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Title: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering by Steven H. Strogatz ISBN: 0738204536 Publisher: Perseus Book Group Pub. Date: 15 January, 2001 List Price(USD): $49.00 |
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