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.