Lectures related to Finite Differences: Definition and Proof

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

Explores sub/super harmonic functions and their applications in a theoretical context.

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

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

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Explains the definition and calculation of finite difference centers with proofs and examples.

Covers the joint equidistribution of CM points in algebraic structures and quadratic forms.

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

Covers the Theoreus Chain Role for Lipschitz functions and its practical applications.

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

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

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

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

Covers hitting probabilities in Markov chains with disjoint subsets, the function h(i), theorems, proofs, and expected time to hit calculations.

Covers the concept of differential operators and presents theorems and proofs related to scalar and vector fields.

Explores the lower bound on total variation distance in Markov chains and its implications on mixing time.

Covers advanced topics in numerical analysis, focusing on techniques for solving complex mathematical problems.

Covers the basic theory for continuous time Markov chains and discusses communication, hitting probabilities, recurrence, and transience.