This course, now in its second offering, is not for the weak. My goal is to make your brain dazzled at how cool mathematics is, but also familiar with things you may see in the future. You should come to this class ready to "learn," or rather be inundated with, years of college-level mathematics-- condensed into 2 hours. I will touch upon topics in linear algebra (vector spaces and their algebraic operations), real and complex analysis (analytic functions, functional analysis, some classical results,...), algebra (groups, rings, algebras, etc.), algebraic and differential topology/geometry (Riemannian manifolds, co/homology, Lie groups,...). Applications to other fields like physics or finance can be discussed depending on demand. You won't understand most of what I say. You may get intimidated. But I promise you'll also be inspired. Are you up to the challenge?

Ever wondered why classical systems (like a mass hanging on a spring) "like" to minimize energy? Or how macroscopic properties like energy or pressure come from just a bunch of atoms? What you need is a bit of stat-mech Kool-Aid. In this class, we'll cover some interesting areas of the modern field known as statistical mechanics, going over enough material to understand statistical ensembles. See http://en.wikipedia.org/wiki/Statistical_mechanics. But you also want to learn about some current research topics, you say? After we talk about stat mech, we will talk about applications of modern physics in biology. Time permitting, topics in computer science, finance, astrophysics, and other fields will also be introduced.

My goal is to make your brain hurt but dazzled at how awesome mathematics is. You should come to this class ready to learn years of higher-level mathematics-- condensed into 2 hours. You will leave the lecture hall feeling more mathy and intelligent. For the record, I will cover topics in linear algebra (vector spaces and their algebraic operations), group theory (group structure and operations), real analysis (analytic functions, Hilbert spaces,...), probability theory (distributions, expectations, martingales), complex analysis (holomorphic functions, contour integration...), algebraic and differential topology (fundamental group, manifolds, differential forms, cohomology...), and differential geometry (vector bundles, Lie groups,...). If I can cram everything in as fast as I think I can, we will also explore applications to physics, chemistry, biology, biochemistry.... You won't understand most of what I say. You will be intimidated. But I promise you'll also be inspired-- very inspired. Are you up to the challenge?