Customer Reviews

Fractal Geometry: Mathematical Foundations and Applications

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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".

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.

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.

The book opens the doors of mathematics: it isn't an easy door, but well worth the effort. It bridges the gap between beginner texts and advanced study and covers the basic material in a hard hitting manner. Those looking for "giltz" should look elsewhere. It is a book of great understanding and depth. Your unique Associates ID is: thefractaltransl.

I agree with all that was said by the other reviews here but add one important point. The physical layout, (typeface, drawings, whitespace etc.) of this book is brilliantly done. This is often overlooked by the producers of technical works who do it "on the cheap", but it is vital if one is to use the book day after day, as I have had to.

While the subject matter is not easy, this is an excellent book to motivate one to get stuck into the underlying mathematics. The reward is a little insight into the often beatiful theorems and practical results found in this stimulating field of study.

Fractal Geometry:Mathematical Foundations and Applications by Kenneth Falconer(second edition)is one of the most important mathematical books of this beginning of the 21-st century.It is a book of high mathematical level which can be very useful to non-mathematicians possessing a reasonable mathematical instruction and a logical mind.Mathematicians will find in this book deep and sophisticated notions and proofs and non-mathematicians will find all the concrete applications of the theory of fractals(see e.g.the new paragraph dedicated to fractals in finance). Prof.dr.Ion Chitescu
Faculty of Mathematics and Computer Science
University of Bucharest