Lectures related to Proof Techniques: Examples

Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Introduces logic, proofs, sets, functions, and algorithms in mathematics and computer science.

Explores Bourgain's theorem on sparsest cut in graphs, emphasizing semimetrics and cut optimization.

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

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Explores Newtonian potential in bounded domains, discussing its conditions and properties.