This class will focus on some neat, and non-trivial, properties of what could be considered the most amazing geometric object in history: the circle. Specifically, we will explore some fascinating pictures that arise through looking at limit sets of circle inversions. This talk will touch on Kleinian groups, Apollonian gaskets, limit sets and, because I love it so much, complex dynamics. Come for the pictures, stay for the knowledge. This class will touch on some deep mathematical concepts, but no specific knowledge is required.

What does it mean for a mathematical function to behave chaotically? What exactly is the Mandelbrot set and what is the big deal? We will explore the field of Complex Dynamics, where math, art and chaos. You will need an inquisitive mind and basic algebra to understand this talk.

25 years ago the Transformers came to the US. Not the giant robots, but their toy counterparts. Today, the Transformers label is seeing a huge increase in popularity with the live-action movies and the Transformers: Animated television series. However, between the original Transformers cartoon, which left the air in 1987, and the arrival of the TF live-action film in 2008 the Transformers line was far from dormant. In this class we will discuss the various time-lines and continuities existing in the TF universe (this will include watching clips from the various US and Japanese series and checking out the comics). We will discuss the Transformers as an epic story, including an analysis of the characters' "Jungian Archetypes". We will also, of course, get to play with toys. I will be bringing select toys from each of the various Transformers lines along with some rare figures.

This course is designed for students that already know what the Mandelbrot set is and wish to learn more about Complex Dynamics. In this course we will discuss the dynamics of complex rational maps. While many results regarding the Mandelbrot set still hold, the dynamics of a rational map often has features not found in the complex quadratic case. We will look at the notion of a connectedness locus, examining the connectedness loci for various rational maps (the most popular connectedness locus is the Mandelbrot set itself, the connectedness locus for $$f(z)=z^2+c$$ with $$c\in \mathbb{C}$$). Strikingly, the Mandelbrot set seems to permeate the connectedness loci of many rational maps. We will see that this is not as strange as it seems and can be easily understood using the notion of polynomial-like mappings. Examples of polynomial-like mappings will be discussed and we will investigate a few different parameterized complex functions.