Lectures related to Azuma's Inequality: Martingale and Bounded Differences

Covers the long exact sequence of relative homology groups and chain complexes.

Covers examples of direct and indirect proofs in mathematics.

Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.

Covers the proof of the theorem of implicit functions and the concept of class C functions.

Explores Newtonian potential in bounded domains, discussing its conditions and properties.

Covers the properties of harmonic functions and the concept of mollification.

Covers Coppersmith's method for attacking RSA encryption by efficiently finding small roots of polynomials modulo N.

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

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.