Covers the Meyers-Serrin theorem in analysis, discussing the conditions for functions in different spaces.
Covers hitting probabilities in Markov chains with disjoint subsets, the function h(i), theorems, proofs, and expected time to hit calculations.
Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
Covers continuous differentiability, the Bernoulli-l'Hôpital rule, and finding extrema using derivatives.
Introduces Coq, covering defining propositions, proving theorems, and using tactics.
Covers the basic theory for continuous time Markov chains and discusses communication, hitting probabilities, recurrence, and transience.
Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.
Introduces informal proofs and their practical applications in computer science and mathematics, emphasizing the importance of proving theorems through direct and indirect methods.
