Customer Reviews

Encounters with Chaos

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Denny Gulick opens here a direct access to the mathematical technics for understanding chaotic phenomena. Any undergraduate with some pre or calculus knowledge, little algebra and very few differential equations (rich introductions to these topics are included in every chapter)can access the basics of this growing "Chaos Theory", that is beeing applied to dynamics in all fields. Professor Gulick makes an outstanding aproach with this book. He makes accesible this field to beginners, self-students or newcomers to mathematics, covering so a huge gap in the literature. It is full of examples, detailed exercises and explained in a very comprehensible and student-friendly way, without losing rigour and technic. It has a companion booklet to order separately that includes "all the solutions to the exercises, done step by step and a true Basic software for Pcs or Macs.

In the field of chaotic dynamics, does there exist _the_ standard textbook for undergrads? I think not. Still, in most colleges, _chaos_ is a subtopic you briefly go through (most of the time just `skipped' through) while studying differential equations, mathematical physics or classical physics. To be competely honest, my impression is that those ``subtopics'' usually don't make a good intro to chaotic dynamics, either. I have read some textbooks targeted at undergraduates and Gulick's was not too bad to skim through what we have in chaotic dynamics. However, Gulick pays too much attention on the basics (analysis and differential equations) and this may seem such a waste of space given the limited number of pages (some two hundreds). Naturally, his explanations are not detailed and gives the impression that things are done rather hastily. But, I must say, this book is superier to some other books that spends time neither on the basics nor the analytic aspects of chaotic dynamics.

In short, everything that a textbook should be. Granted, I had a very good professor who explained the concepts well, but it follows that he would choose a good textbook. Takes a pure mathematics approach with a strong emphasis on proofs and iterated function maps, rather than applications and differential equations. Nonetheless, the text is extremely accessible and should be understandable to most people with only a minimum (first year) of university-level mathematics, or even to a determined highschool graduate.

I had to use this book for a class I took at Bryn Mawr college called "Chaotic Dynamical Systems". There are some mistakes in the book, although I don't remember specifically what they were, and my instructor had to point some of them out. The book, to my knowledge, only covers discrete dynamical systems, and contrary to what the above reviewer says, there is some real analysis involved: i.e. some proofs and definitions involving epsilon and delta. That's about all I can say because I don't remember the book very well, and we only got through about half of it. I recall that most people in my class didn't like the book very much either.