Lectures related to Polynomials, Division, and Ideals

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

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

Delves into using polynomials for combinatorial computations and explores operations and identities with binomial coefficients.

Explores ideals in K[X], including PGCD, uniqueness, coprimality, and theorems of Bézout and Gauss.

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

Covers important examples related to operations and multiplication in real vector spaces.

Covers irreducible polynomials, fundamental theorem of algebra, and factorization in complex and real polynomials.

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

Covers polynomials, their operations, division theorem, and provides illustrative examples.

Covers the concept of ideals in polynomial rings and their properties.

Explores the properties and applications of finite fields, including isomorphism and cyclic properties.

Explains the Euclidean algorithm for polynomials over a field K, illustrating its application with examples.

Explores examples and properties of continuous functions, including limits and continuity.

Explores Viète's formula for finding roots of degree two polynomials and their significance.

Explores polynomial operations, properties, and subspaces in vector spaces.

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

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

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

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Covers the operations in rings, ideals, classes, and quotient rings.