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Explores the proof of Weyl's theorem, focusing on discrete spectrum, ground states, and potential energy continuity.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Covers the proof of the Jordan Curve Theorem and the properties of embedded spheres.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.