Covers the Fourier transform on Schwartz space and its properties, including continuity and linearity, as well as the density of smooth compactly supported functions.
Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.
Covers the proof of the Green theorem, showing how the integral of a vector field along a domain's boundary equals the integral of the curve within the domain.