Polynomials on a Field: Basics and Operations

Related lectures (32)

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Explores polynomial equations, their degree, solutions, and domain definition.

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

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Explores digital derivation, function evaluation, and polynomial approximations for accurate measurements and evaluations.

Explores the properties and applications of polynomials on a field, including formal derivation and uniqueness.

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

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

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

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

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