MATH 2240 – Honors Linear Algebra/Calculus
I’ll talk about some ideas that relate to, but may go beyond the scope of the course.
Geometry of surfaces
- The first fundamental form – an important tool in study of surfaces in
- Gaussian curvature and the second fundamental form – we look at the differential of the Gauss map and use it to define all kinds of curvatures!
de Rham cohomology
- Differential forms on manifolds – we first need to generalise the notions introduced in Hubbard to manifolds, at the same time introducing better terminology
- de Rham cohomology – we use Stokes’ theorem to motivate the definition of de Rham cohomology and compute the simplest example
- Construction of a non-measurable set – we talked about this in class a while back, but perhaps hadn’t covered all the necessary background to fully appreciate it. In particular we have since discussed taking quotients by equivalence relations, and I briefly go over that here