Suppose I give you a set of elements and some operation, and I tell you six very basic facts about this set. Can you tell me what the set is? With a topic as well-studied and foundational as group theory, the simplest of facts can develop into some incredibly powerful results. Group theory is one of the most central studies in math; in fact, most everything you've dealt in with math belongs to a group. The integers form a group; so are the symmetries of a square. Because of its ubiquity, group theory both generalizes our already familiar knowledge and provides various tools to tackle problems in other areas of math, some of which we'll see near the end of the class. This class will hopefully make large parts of basic group theory much more accessible to facilitate future, more advanced studies!

How do you calculate pi? The boring way is to measure around a circle and divide by its diameter. But pi is everywhere, from river lengths to the ESP logo to random integers. We'll calculate pi in lots of different ways for class.

Alan Turing was a revolutionary thinker in the field of computer science. In this course, we explore the various ideas and projects that Turing was involved in throughout his life, including Turing Machines, the Enigma, and the Turing Test. Students will have the chance to design their own basic Turing Machines.