Lectures related to Proofs: Direct and Indirect Methods

Covers the basics of analysis, including real numbers, proofs, sets, and operations.

Explores prime numbers and Euclid's Theorem through a proof by contradiction.

Covers the Fourier inversion formula, exploring its mathematical concepts and applications, emphasizing the importance of understanding the sign.

Explores optimal transport in heat equations and metric spaces.

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Explores convergence in law for random variables, including Kolmogorov's theorem and proofs based on probability lemmas.

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

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