Foreword
by Jon Lee

This is an outgrowth of my involvement with the Wright-Connection program held at Wright-Patterson Air Force Base near Dayton, Ohio during 1995-1999. It was an 8-week summer program for the local middle/high school math and science teachers to participate in the real-world applications of math and science in Air Force research laboratory, so that they can infuse the excitement of math and science into their classroom teaching. As a mentor I had the privilege of hosting Garry Barhorst (1995), Dick Abbott (1996), David Carr (1997), John Carroll (1998), and Craig Robinson (1999), and thereby guiding them to prepare lesson plans in fractals and chaos for their classroom use.

The topics of this lesson book do not fall neatly in the traditional math topics, but they touch upon many areas, such as algebra, numbers, function, geometry, probability, etc. Besides, as an archetypical nonlinear model the population dynamics that we study here is a subject of life science. Perhaps, you may sample the scope of this lesson book by searching for the topics of fractals, complex patterns, and chaos from the website of Eisenhower National Clearinghouse. [http://enc.org] This will lead you to many sources of academic and practical interests. The distinguishing feature of this lesson book is learning by doing. To facilitate doing, we have therefore provided many programs that students can experiment and explore in a wide parameter range. In fact, some programs are integrated into the main lesson text, so that student participation is mandatory. That is, one cannot simply read through the lesson text without the knowledge of the outcome of accompanying programs. Besides, there are individual and classroom projects.

There are many books dealing with the lesson topics presented here. In fact, Reference [1] is intended for the high school classroom use. We cite here only a few of these in References [2] - [4] that are most relevant to the selection of our lesson topics. Clearly, it is not possible to tell everything about fractals and chaos in a small lesson book as this. Yet, our main goal is to explain the basic ideas underlying what is now known as nonlinear or chaos science in simple language, so that the students can build up a repertoire of terminologies as they study further in this subject area.

I wish to thank Mrs. Suzanne Alejandre for her kind invitation to place this lesson book on the Math Forum web site of Drexel University, Philadelphia, PA. As an honor student project, Lisa Brown did the hard work of configuring the Word lessons.doc into a web-based lessons.html. Since the programs are not accessible to the Apple Mac type of computers, Lisa has converted some of them to the flash format for the Mac users. Also, as a Wright Scholar research assistant in the summer of 2002, Bradford Loesch offered numerous suggestions for improvement. It would be amiss not to acknowledge the advice and moral support that I received from Dr. Carl Benner, a retired mathematics professor from Wright State University, who firmly believed this lesson book should be made available beyond the immediate locality of Dayton.

References

[1] Heinz-Otto Peitgen, Harmut Jurgens, and Dietmar Saupe, Fractals for the Classroom, Volume 1: Introduction to fractals and chaos, Springer-Verlag, NY, 1992.

[2] Manfred Schroeder, Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise, Freeman, NY, 1991.

[3] Hans Lauwerier, Fractals: Endlessly Repeated Geometrical Figures, Princeton University Press, Princeton, NJ, 1991.

[4] Deborah J. Bennett, Randomness, Harvard University Press, Cambridge, MA, 1998.