Finite Fields: Properties and Applications

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Related lectures (28)

Page 2 of 3

Linear Combinations and Vector Spaces

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

Polynomials: Definitions and Operations

Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.

Polynomials: Roots and Factorization

Explores polynomial roots, factorization, and the Euclidean algorithm in depth.

Complex Numbers: Roots and Polynomials

Covers the properties of complex numbers, including finding roots and factorizing polynomials.

Polynomials: Operations and Properties

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

Polynomials: Rings and Operations

Covers the basics of polynomials, focusing on rings, operations, and properties.

Factorisation: Real Coefficients Examples

Covers the factorization of polynomials with real coefficients in the complex domain, demonstrating how to find complex roots and obtain irreducible factors.

Irreducibility Criteria in Rings

Explores irreducibility criteria in rings, emphasizing linear and reducible polynomials.

Integration on H_pxH and Arithmetic

Explores integration on H_pxH and arithmetic properties, including norms, structures, and polynomial factorization.

Polynomials: Theory and Operations

Covers the theory and operations related to polynomials, including ideals, minimal polynomials, irreducibility, and factorization.