Advanced Topics in Mathematics: Complex Numbers, Groups, and Fractals

Course Description:

This course will take a deeper dive into fascinating concepts of mathematics: compelx numbers, groups, and fractals. Students will learn why the term “imaginary” number couldn’t be further from the truth and use complex numbers to introduce groups and famous examples of fractals. We will focus on building the student’s geometric intuition for what these objects are and hypothesize how they should interact with each other. We will then investigate and test these hypotheses! We finish the course with a visualization project in which students choose a specific fractal (such as Mandelbrot Set or Koch’s Snowflake), analyze its many properties, and create a basic computer model of it.

The skills and insights developed from this class will help students learn to think critically like real mathematicians, instead of merely emphasizing the application of algorithms. This course is a great starting pont for any student who is considering pursuing pure math or applied math at some point in their academic career.