Come ask all the math questions you've been dying to have answered to a panel of MIT math majors! We'll answer anything from conceptual questions (what are Lagrange multipliers?) to computational questions (how do I compute this integral?) to philosophical questions (what is math?)! We'll have teachers studying all areas of math, so hopefully we can answer any (reasonable) questions you throw at us.

We will try to present some main ideas in linear algebra that hopefully aren't emphasized in a typical first course. We will start with an introduction to matrices and their relation to linear maps. Then, we will talk about determinants, and how we can deduce the standard identities from the basic property of being multilinear and alternating. After that, the rest of the course will depend on the audience, but possible topics are the Cauchy Binet formula, matrix tree theorem, diagonalization, applications to linear recurrances and markov chains. Possible more advanced topics include deducing existance of the jordan canonical form from the rational canonical form, and the point of view of the exterior algebra. Since the goal is the make things understandable, we will only be doing a small subset of these topics.

We will introduce group theory from the very beginning and build up enough tools to prove Burnside's Lemma, which is a useful tool in counting things up to rotational symmetry. At the end, we will apply Burnside's Lemma to one or two problems.