Chaos: A Mathematical Introduction (Australian Mathematical Society Lecture Series) [Paperback]

John Banks (Author), Valentina Dragan (Author), Arthur Jones (Author)

Book Description

Publication Date: June 3, 2003 | ISBN-10: 0521531047 | ISBN-13: 978-0521531047

This text presents concepts on chaos in discrete time dynamics that are accessible to anyone who has taken a first course in undergraduate calculus. Retaining its commitment to mathematical integrity, the book, originating in a popular one-semester middle level undergraduate course, constitutes the first elementary presentation of a traditionally advanced subject.

Editorial Reviews

Review

'The tone, pace and level of the book are nicely judged for middle level undergraduates studying mathematics. The authors' friendly style, and the fact that the material has been developed from taught courses make the book ideal for self-study, and as a prelude to reading extensive treatments of chaos theory.' The Mathematical Gazette

'... presented in such a form that it is accessible to anyone who has taken an undergraduate calculus course ... This textbook is highly recommended for a one semester undergraduate introduction to chaos theory.' Acta Sci. Math.

Book Description

Here is a textbook that presents ideas about chaos in discrete time dynamics in a form where they should be accessible to anyone who has taken a first course in undergraduate calculus. Remarkably, it manages to do so without discarding a commitment to mathematical substance and rigour. The book has evolved from a very popular one-semester middle level undergraduate course and has therefore been well class-tested. It includes a number of innovative features and is the first elementary presentation of what is traditionally an advanced subject.

Product Details

• Paperback: 306 pages
• Publisher: Cambridge University Press (June 3, 2003)
• Language: English
• ISBN-10: 0521531047
• ISBN-13: 978-0521531047
• Product Dimensions: 9 x 5.9 x 0.6 inches
• Shipping Weight: 1.1 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #2,381,744 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

4 of 4 people found the following review helpful:

4.0 out of 5 stars You Don't Need a Math Degree to Understand this, January 2, 2004

By 

W Boudville (Terra, Sol 3) - See all my reviews
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This review is from: Chaos: A Mathematical Introduction (Australian Mathematical Society Lecture Series) (Paperback)

Chaos is such a visually stunning field of study, since you invariably run into those computer generated figures of Julia sets or random fractal landscapes or cloud formations.

But can we get a rigorous, first principles explanation that is broadly accessible to undergraduates with good, but not advanced math preparation? Well, you might consider this recent book. The authors have gone to some length to explain events without appealing to more than simple calculus.

Nothing flashy. But you can obtain a good understanding of fractal dimensions, self iterating systems (like a Sierpinski gasket) and noise.

2 of 2 people found the following review helpful:

4.0 out of 5 stars An interesting approach, May 17, 2007

By 

J. MOLDOVAN - See all my reviews
(REAL NAME)   

This review is from: Chaos: A Mathematical Introduction (Australian Mathematical Society Lecture Series) (Paperback)

Firstly, this is one of those rare technical books which one can thoroughly enjoy. It can be read at a number of levels and rewards any effort put into understanding the concepts and the mathematics. One needs decent calculus, basic set theory and a bit of topology to wade through the maths. The text and diagrams are clear and unambiguous. The fonts and layout are well chosen for easy reading, always an important consideration for technical books. As this is a text book for a course in elementary chaos theory, the authors write out the proofs fully, in an almost bullet point fashion which makes it very easy to follow the argumentation. I like this style very much.

What I don't like is the lack of solutions (preferably worked solutions) to the excellent exercises at the end of each topic. This is one of my major bugbears about textbooks. Without worked solutions one simply cannot get the feedback required for a full understanding of the subject. Not everyone who buys the book will be attending classes and they will never know if they are on track or not. To make me even crankier, the authors will provide worked solutions to "bona fide" teachers who contact them. How about letting teachers, bona fide or otherwise, write their own exercises instead of taking the easy way out, and letting students learn using the well accepted techniques of feedback and reinforcement.

A star is lost! Hufff!