  We introduce the exciting field of complex dynamics at an undergraduate level
while reviewing, reinforcing, and extending the ideas learned in an typical
first course on complex analysis. Julia sets and the famous Mandelbrot set will
be introduced and interesting properties of their boundaries will be described.
We will conclude with a discussion of problems at the boundary between complex
dynamics and other areas, including a nice application of the material we have
learned to a problem in astrophysics.
