Lectures related to Error Analysis for Galerkin Scheme

Explores orthogonal and orthonormal bases, Gram-Schmidt process, and orthogonal polynomials in physics.

Explores the process of division euclidienne in polynomials, emphasizing the importance of polynomial degrees during operations.

Explores polynomials, their operations, and the concept of ideals in polynomial rings.

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

Explores parameter estimation of SDEs using Linear Response Theory and covers challenges, examples, algorithms, and convergence.

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

Explores correlations of the Liouville function along deterministic and independent sequences, covering key concepts and theorems.

Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.

Covers Reed-Solomon codes for error handling in communication and practical applications in 2D barcodes.

Covers important orthogonal polynomials in physics used to represent angular and radial dependencies in fields and quantum systems.

Introduces Reed Solomon Codes, their applications, polynomial definitions, interpolation, roots, and the Fundamental Theorem of Algebra.

Explores complex roots, conjugate pairs, and quadratic equations solving strategies.

Explains how to find particular solutions for first-order differential equations using different types of functions.

Covers the least squares method for approximating data and handling errors.

Explores algebraic functions, limits, and behavior as x approaches infinity.

Explores Gauss-Legendre quadrature formulas using Legendre polynomials for accurate function approximation.

Explores Legendre polynomials and their role in numerical integration techniques.

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.