MATH 2240

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

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

Measure theory

  • 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
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