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Polytechnic School's Mathematical Modeling II with Calculus BC

Textbooks and Other Reading

Textbooks

Bedford, Crayton W. Introduction to Fractals and Chaos:Mathematics and Meaning. Andover, MA: Venture Publishing, 1998. (See the table of contents. Also, note that some of the exercises in this text require Richard Parris' free, but outstanding, Windows software called Winfeed. Download it from Parris' Peanut Software Homepage. Unfortunately, there is no Macintosh version, so if you only have a Mac at home, you will need to visit Poly's PC lab to do those exercises.)

Click the peanut to download the Winfeed software.

Peanut Software

 

Robinson, Steve. AP Calculus: The "C" Topics. Fullerton, CA: Gainsway Press, 2001. (See the table of contents.)

Other Reading

Crichton, Michael. Jurassic Park. New York: Ballantine Books, 1990.

Oh, sure, the dinosaurs get all the press, but Crichton's best seller also has a chaos theorist who correctly predicts most of the havoc brought about by human hubris and rampaging monsters. Instead of chapters, this book has "iterations", each of which is represented by an increasingly complex stage of a fractal curve.

Ellert, Glen. The Chaos Hypertextbook. http://www.hypertextbook.com/chaos/, 1999.

This is an online tutorial covering most of the key topics of chaos theory. Included is an extensive index of online resources dealing with chaos and fractals.

Gleick, James. Chaos:Making a New Science. New York: Viking Penguin Inc.,1987.

For a fascinating history of the people and events that shaped chaos theory and fractal geometry, it doesn't get any better than this. Atop the New York Times bestseller list for months when it first appeared in 1987, Gleick's book reads more like a novel than an expository account.

Kellert, Stephen H. In the Wake of Chaos. Chicago: University of Chicago Press, 1993.

Do not go here unless you have a decidedly philosophical turn of mind. Kellert is a philosopher of science who painstakingly analyzes chaos theory in an effort to determine how it arose, why there has been so much resistance to it among mainstream mathematicians, how is it effecting modern science, what are its implications for deterministic science and philosophy, and how, if at all, is the uncertainty implied by chaos theory connected to the uncertainty implied by quantum mechanics. You get the idea. This one does not read like a novel.

Mandelbrot, Benoit. The Fractal Geometry of Nature. New York: W. H. Freeman and Company,1983.

A twentieth century masterpiece, this "essay", as Mandelbrot calls it, launched the discipline of fractal geometry. Michael Barnsley has said, "Once you have studied fractal geometry, you will never again look at the world in the same way." Mandelbrot's book is the first person account of the world seen as no one else had ever seen it. It is nothing less than a revolutionary work of science and mathematics.

McGuire, Michael. An Eye for Fractals: A Graphic and Photographic Essay. Redwood City, CA: Addison Wesley Publishing Company, 1991.

Beautiful photographs of nature are interspersed with beautiful fractal graphics to visually illustrate the fractal geometry of nature. Also included are discussions of self-similarity and fractal dimension.

Stewart, Ian. Does God Play Dice? The Mathematics of Chaos. Cambridge, MA: Blackwell Publishers, 1989.

This book is the perfect follow-up to Gleick's. (See above.) It covers roughly the same ground, but in a slightly more mathematical and less personal way. This is to be expected since Stewart is a mathematician, whereas Gleick is not. The prose is less fluid than Gleick's, but the mathematical insights tend to be deeper.

Stoppard, Tom. Arcadia. London: Faber and Faber Limited, 1993.

Stoppard is at his brilliant best as he unfolds the story of a young female mathematics prodigy who discovers the ideas behind chaos theory and fractal geometry at the beginning of the 19th century. Her work is discovered by a 20th century descendant of her's who is also a mathematician. The playwright's usual cleverness and wit are sufficient to make this play a delight to someone who knows nothing about chaos or fractals. For someone who does, it is simply amazing.



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