Lectures related to Isoperimetric Qualities: Inequalities & Proofs

Covers the Meyers-Serrin theorem in analysis, discussing the conditions for functions in different spaces.

Covers examples of direct and indirect proofs in mathematics.

Covers basic properties of conditional expectation and Jensen's inequality in probability theory.

Explores optimal transport in heat equations and metric spaces.

Explores tail bounds, information bounds, and maximal leakage in the context of generalization error.

Covers the Zig Zag Lemma and the long exact sequence of relative homology.

Covers induced homomorphisms on relative homology groups and their properties.

Introduces Coq, an interactive theorem assistant based on the Curry-Howard isomorphism.

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

Covers the concepts of contraposition and contradiction in proofs.