One of the most intricate and fascinating images in all of mathematics is the Mandelbrot set, discovered by Benoit Mandelbrot in 1980. Most people within the mathematics community and many people outside of the discipline have seen this image and have marveled at its geometric intricacy. Unfortunately, only a few of these people are acquainted with the equally beautiful mathematics lurking behind this image.
In this workshop, we look at some of the mathematics in an elementary setting and perform computer experiments to illustrate the ideas. All of these ideas have been presented to high school students in an effort to introduce them to the beauty and excitement of contemporary mathematics.
The lessons that follow are intended to be interactive. That means you should not go through them passively. Your active participation is essential. At several points along the way, you will encounter exercises marked by an army sergeant blowing his bugle. Here's an example:
Try it!
When you reach an exercise, be sure to do it! If you prefer, you may work in small groups. And, of course, if you experience any difficulty, just yell. But don't move on to new material until you can do an exercise.
OK. If you're ready, take a deep breath and let's begin the first lesson.
