differential topology.

these notes are a work in progress.

This course has a bit of a scattered collection of topics, but is ultimately aimed towards the construction of abstract manifolds and the proof of Stokes' theorem. We cover submanifolds of euclidean space, abstract manifolds, tangent and cotangent spaces, partitions of unity, vector fields, differential forms, exterior differentiation, integration of forms, Stokes' theorem, deRham cohomology, and Riemannian metrics.