
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.)
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 selfsimilarity and fractal dimension.
Stewart, Ian. Does God Play Dice? The Mathematics of Chaos. Cambridge, MA: Blackwell Publishers,
1989.
This book is the perfect followup 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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