Mathematics 225 - Chaos and Fractals

The first half of the course will be devoted to the topic of chaos. This occurs when the long-term behavior of a system is unpredictable in predictable ways. The underlying mathematical construct is called a dynamical system, which can be discrete or continuous. We will study discrete dynamical systems in one and two dimensions and say a few words about the continuous case, which involves differential equations. The second half of the course will study fractals, which are wonderfully complicated mathematical objects that often have surprisingly simple descriptions. Some fractals will be encountered in the first half of the course, while others will be introduced in the second. A rich supply of fractals arises when dealing with complex numbers. This is where we will meet the famous Mandelbrot set.

Requesite: MATH 211 or consent of the instructor. Limited to 35 students. Fall semester.  Professor Cox.