Here's a problem: Say you have 3 colors of paint and you want to color the sides of a triangle. Two colorings are considered the same if you can rotate or reflect one of the triangles to get the other one. How many different colorings are there? Here's another problem: Say you have 3 colors of paint and want to color the faces of a cube. Two colorings are considered the same if you can rotate one of the cubes to get the other one. How many different colorings are there? Here's a third problem: Say you have 1000 colors of paint. How many different colorings of the faces of a cube are there? In this class we will explore a theorem known as Burnside's Lemma which will help us to solve these types of problems. Along the way, we will develop some of the framework of group theory, a topic typically not taught until late in college, if ever. This class is going to be a very fast-paced introduction to these new areas of mathematics. Be prepared! (By the way, the answers were 10, 57, and 41,666,792,167,000,000.)

This class will be a fast-paced, hardcore introduction to group theory. We will start off looking at group actions and their applications in combinatorics and then move to developing a theory of groups and techniques to help classify finite groups. Topics covered may include normal subgroups, quotient groups, cosets and Lagrange's Theorem, direct and semidirect products, cyclic groups, the Chinese Remainder Theorem, the orbit-stabilizer theorem, Burnside's Lemma, and the Sylow theorems.

What does visualizing lines in 4D space, ridiculously hard counting problems, and making people think you have ESP have in common? They all have to do with the game SET! SET is an awesome card game of visual perception and pattern matching with even more awesome math behind it! Come to this class prepared to have fun playing SET and to work with others to figure out some of the awesome combinatorics and geometry involved in the game.

Did you know that math is really really awesome? Come to this class to hear about the coolest and most ridiculous facts in mathematics, from fairies and multiplying bunnies to dragons that eat ridiculously strange infinite series!

You heard tales of a far off land occupied by dragons that would challenge their victim to a game for their life. It was a game of skill and intellect involving taking coins from various piles of loot. If you won, you got to keep the treasure, but if you lost, the dragon would eat you. You traveled to this far off land in search off treasure, but found that the tales lied. Instead of this mythical game, they made you do something completely different. Involving queens or sheep or something? What strangeness is this? Come to this class to learn how to beat dragons at every game they could possibly think of so they don't eat you!

Say you really want to beat dragons at games and take all their loot. Unfortunately, when you come upon the specific variety of game playing dragons that will give away their loot when they lose instead of just eating you, you find out that while these dragons will play nice when they lose, they only play unfair games, stacking the odds in their favor. Come to this class to learn how to beat dragons at their own games, even when they have completely unfair rules!

Come play the awesomest game in existence! SET is a game of visual perception and pattern matching. Come to learn how to play and challenge yourself against others!