Lectures related to Chain Rules: Higher Dimensional Versions

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

Explores optimal transport analysis and proofs, emphasizing weak convergence and compactness.

Covers the Triangle Inequality Theorem in triangles, showing side length relationships.

Explores recurrence, transience, and invariant distributions in Markov chains with proofs and examples.

Delves into the concept of proof in mathematics, emphasizing the importance of evidence and logical reasoning.

Explores differentiability in two variables and the chain rule for compositions.

Explores the extension of the chain rule to higher dimensions and compositions of functions.

Introduces informal proofs, explores practical applications, and explains theorem proofs using direct and indirect methods.

Covers the mathematical development of canonical correlation analysis, including population and sample CCA.