Lectures related to Theorems in Analysis

Covers the properties and operations of convex functions.

Explores the Cauchy-Schwarz inequality in integrals and functions, offering a comprehensive understanding of its applications.

Covers the extension and periodicity of Fourier series and the interpretation of coefficients.

Explores injective functions in linear algebra, demonstrating how to prove injectivity step by step.

Covers optimization algorithms, stable matching, and Big-O notation for algorithm efficiency.

Covers topics in probability theory, focusing on uniform integrability and convergence theorems.

Covers the concepts of sequences, convergence, and boundedness in mathematics.

Covers independence between random variables and product measures in probability theory.

Covers the duality principle in linear algebra and its implications in mathematics.