Introduction to Chaos and Fractals

This course presents an elementary introduction to chaos and fractals. The main focus will be on using discrete dynamical systems to illustrate many of the key phenomena of chaotic dynamics: stable and unstable fixed and periodic points, deterministic chaos, bifurcations, and universality. A central result of this study will be the realization that very simple non-linear equations can exhibit extremely complex behavior. In particular, a simple deterministic system (i.e., physical system governed by simple, exact mathematical rules) can behave in a way that is unpredictable and random, (i.e., chaotic). This result suggests that there are potentially far-reaching limits on the ability of science to predict certain phenomena. Students in this class will also learn about fractals—self-similar geometric objects—including the Mandelbrot set and Julia sets. We will also read about and discuss the development of the field of chaos. In so doing, we will examine the nature of scientific communities, with a particular eye toward how changes in scientific outlooks occur. Throughout the course, students will be encouraged to explore the relations between chaos, fractals, and other areas of study such as literature, art, and cultural studies. Students who successfully complete this class should gain a quantitative and qualitative understanding of the basic ideas of chaos and fractals, a greater understanding of the cultural practice of science, and improved mathematical skills. Evaluation will be based on class and lab participation, weekly problem sets several short writing assignments and a final project.

Always visit the Registrar's Office for the official course catalog and schedules.