on 28 October 2005
This book is not for the faint hearted but if you like mathematics at high level (i.e. degree level and beyond) then you may well appreciate this book. If you enjoyed dynamical systems theory, control systems theory and/or manifold theory at university, or at least thought you did (or thought you should have done), then this book may give you the insights that the drier, purely mathematical (text book) approaches failed to do. If you are a professor of mathematics, you might hate the book on the grounds that the mainly non-mathematical treatment lacks rigour. But, hey, it's a popular science book!
Amazingly, Casti covers five fascinating theories with only the barest minimum of absolutely essential but non-trivial(!) mathematics. The cleverness of this book, for me at least, is that it provides deep insights to sometimes highly abstract mathematical notions and connects one to the usual mathematical equations for each area without the need for preliminary mathematics (but this requires the reader to be comfortable with diving in at the deep end). Casti's powers of explanation using plain English replace the need for much of the mathematics that one typically finds in books about these five theorems. But it's not easy going. It's a book that demands your undivided attention and concentration. A good time to read it would be on a long aeroplane journey.
In summary, most people, in fairness, won't be equipped to read this book and therefore won't like it (one star). If the title piques your interest and you're not in the first category, you might really like it, as I did, hence 4 stars. Maths purists might be cooler about it: maybe 2 - 3 stars.