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Instructor: Dave Feldman
Ilva Letoja, a first year student from Pittsburgh, Pennsylvania says that she is "not really an algebra person." She was looking for a math course that would meet COA's quantitative reasoning requirement and settled on Dave Feldman's Introduction to Chaos and Fractals, an introductory algebra-based math and physics class, despite her trepidation. To her surprise, not only did the course enhance her mastery of mathematics, it also enriched her understanding of linguistics and philosophy, as she was able to apply concepts and theories from the field of chaos in the two other courses she took during the spring 2006 term: Genealogies of Contemporary Continental Philosophy and The Danger of Words-Wittgenstein and Derrida. Says fellow first year student Michael Griffith of Florence, Alabama, who took the same three courses, "you encounter the same concepts and terminology in these different fields, but they are applied very differently."
The course is designed with students like Ilva in mind. According to Dave, almost all the students entering his course are certain that it will be their last math class, but he says "it is possible to teach the central ideas and insights of chaos in a rigorous and genuine way to students with relatively little math background." Some of these students have surprised themselves by choosing to enroll in more advanced math courses such as Calculus.
Introduction to Chaos and Fractals is one of only a handful of introductory courses on chaos offered in the United States. The lecture format and computational exercises that one would expect to find in a traditional math class are balanced with group activities and class discussions. Dave received a grant from the Maine Space Grant Consortium to develop a lab component for the course. In lab experiments like the "Chaotic Double Pendulum," which illustrates the so-called "butterfly effect," students actually observe chaos.
Because no introductory algebra-based chaos and fractals textbook exists, Dave is currently writing a text whose first iteration was used by students in the spring 2006 term. Students also read the popular science book Chaos by James Gleick, as well as literary works such as "Corson's Inlet" by A.R. Ammons and the short story "The Library of Babel" by Jorge Luis Borges, which describes a fractal library universe, "a sphere whose exact center is any one of its hexagons and whose circumference is inaccessible."
The class culminates in the presentation of student research papers or projects dealing with applications of chaos to a variety of fields including economics, game theory, African architecture and anthropology. Projects have included an illustrated children's book on the butterfly effect, an experimental documentary video on fractals, an exploration of software that creates "fractal forgery" landscapes, an original song about fractal patters in a pond, a sixth grade lesson plan on fractals, and a pair of earrings based on the Sierpinski triangle.
- Chaos: Making a New Science, James Gleick
- Introduction to Chaos and Fractals, Dave Feldman
- Selected short papers, stories and poetry
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