An excellent book., 17 Jun 2004
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.

It is all there--whole and parts!!, 10 Feb 2003
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.

An excellent book., 17 Jun 2004
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.

It is all there--whole and parts!!, 10 Feb 2003
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.

Calculus made difficult, 01 Dec 2004
If you can start at the beginning of this book and work through to the end, you don't need it. If you want to learn calculus by yourself, or refresh forgotten knowledge, go elsewhere.
This book seems to have been designed to make the subject as difficult as possible. Apart from the turgid and theory-laden text, the so-called 'you try it' exercises are next to useless. Not only are they of a magnitude more complex than the preceding examples, you have no idea if you have achieved the correct result. There aren't any answers! Let alone an explanation of how to get there.
Even though I am not entirely ignorant of the subject, I found this book confusing and unnecessarily difficult. An example -
"Let a < c < b... etc." Why? What's wrong with a < b < c ?
Then you don't have to perform mental gymnastics when trying to understand what follows.
Written by an academic, for academics. Unfortunately the star ratings don't allow a negative value which is what I wanted to apply. One star is the lowest I'm allowed.
I loathe this book. It could put someone off maths for life.

An excellent book., 17 Jun 2004
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.

It is all there--whole and parts!!, 10 Feb 2003
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.

Calculus made difficult, 01 Dec 2004
If you can start at the beginning of this book and work through to the end, you don't need it. If you want to learn calculus by yourself, or refresh forgotten knowledge, go elsewhere.
This book seems to have been designed to make the subject as difficult as possible. Apart from the turgid and theory-laden text, the so-called 'you try it' exercises are next to useless. Not only are they of a magnitude more complex than the preceding examples, you have no idea if you have achieved the correct result. There aren't any answers! Let alone an explanation of how to get there.
Even though I am not entirely ignorant of the subject, I found this book confusing and unnecessarily difficult. An example -
"Let a < c < b... etc." Why? What's wrong with a < b < c ?
Then you don't have to perform mental gymnastics when trying to understand what follows.
Written by an academic, for academics. Unfortunately the star ratings don't allow a negative value which is what I wanted to apply. One star is the lowest I'm allowed.
I loathe this book. It could put someone off maths for life.

Good introduction, 13 Oct 2001
Extremely good introduction to all areas of topology, starts off so elementary that most GCSE kids could understand it, and has carefully explained, rigorous proofs for all its assertions. It also has excercises which are useful for checking that you haveunderstood the text.