Finite Fields: Properties and Applications

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Related lectures (31)

Reed Solomon Codes: Basics and Applications

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

Complex Polynomials and Factorization

Explores complex polynomials, factorization, roots of equations, equilateral triangles, and infinite sums in sequences.

Stein Algorithm: Polynomial Identity Testing

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

Polynomials, Division, and Ideals

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

Factorisation: Polynomials and Theorem

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

Analyse 2: Division euclidienne

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

Polynomial Identity Testing

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

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.

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.

Complex Numbers: Operations and Applications

Explores complex number properties, roots, and polynomial equations in the complex plane.

Division Euclidienne: Exemples

Explains the Euclidean division of polynomials and demonstrates its application through examples and root-based divisibility.

The Fundamental Theorem of Algebra MOOC: Analysis I MOOC: Analysis I (part 2) : Introduction to complex numbers

Covers the fundamental theorem of algebra, explaining how every polynomial has complex roots.

Integration: Simple Elements MOOC: Analysis I MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)

Covers the integration of simple elements using various techniques to solve integration problems.

Complex Plane and Polynomials

Covers the complex plane, operations, transformations, and complex polynomials.

Integration: Rational Functions

Covers integration techniques for rational functions, including decomposition and factorization.

Complex Roots and Polynomials Log in to Mediaspace to watch this video

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

Polynomials on a Field: Basics and Operations Log in to Mediaspace to watch this video

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

Linear Algebra: Abstract Concepts Log in to Mediaspace to watch this video

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

Linear Combinations and Vector Spaces Log in to Mediaspace to watch this video

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

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