Hitting Probabilities: Markov Chains

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Explores the chain rule for compositions of differential functions in higher dimensions, emphasizing gradients and directional changes.

Explains the proof of the ergodic theorem and the concept of positive-recurrence in Markov chains.

Explores the theory of optimal transport, focusing on Lipschitz functions and uniqueness of solutions.

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

Explores the theorems on maximum and minimum values of functions and their relation to continuity.

Covers the generalization of the TAF theorem, lateral derivatives, limits of derivatives, and indeterminacy.

Covers Markov chains decomposition, LLN proof, Inventory Model application, and average costs.

Covers the definition of the center of a function using finite differences and provides step-by-step proofs.

Introduces Coq, covering defining propositions, proving theorems, and using tactics.

Explores modular arithmetic, emphasizing inverses and equations in Z/mZ, with practical examples and exercises.