Lectures related to Laplace Equation: Decomposition and Solutions

Introduces Cartesian product and induction for proofs using integers and sets.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Explores the properties of invertible matrices, including unique solutions and linear independence.

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

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

Explores multicorrelation sequences, primes, and their intricate connections in number theory and ergodic theory.

Covers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

Explores Fourier series coefficients, periodicity, and series relations.