different constructions of cohomology allow us to measure different properties of manifolds. to construct either the singular cohomology or the de rham cohomology groups, the representatives of each are distinct things: cochains and closed differential forms. yet the de rham theorem states there is a correspondence between them. and we can see this directly via examples displaying how integration on a manifold is greatly influenced by the manifold’s topology. in this talk, i will cover highlights of the proof of the de rham theorem and show how stokes’ theorem lends itself to defining an explicit homomorphism between the two cohomology groups: de rham and singular. i will also discuss a further direction that this correspondence allows which leads us into hodge theory.