Monodromy: Action and Classes

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

Covers the concept of outer measure and properties of measurable sets.

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

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

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Covers proof techniques including direct proof, contraposition, contradiction, cases, and counterexample.

Explores the proof of the Prime Number Theorem and its implications in number theory.

Covers the approximation of functions in Sobolev spaces using smooth functions.

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

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