Forbidden Maths - Differential Forms & de Rham Cohomology

In the 5th lecture of Forbidden Maths we are talking about differential forms and (most of) what we can do with them: wedge product, exterior differential, Hodge star, and integration over (smooth) chains. Using these tools (esp. exterior differential and integration) we then construct a cohomology theory (de Rham cohomology) that can be used to describe the topology of manifolds. In particular it turns out that integration on chains is a bilinear map that defines a dual pairing between de Rham cohomology and singular homology.