Lectures related to Complex Roots and Polynomials

Complex Polynomials and Factorization

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

Complex Roots: Conjugate Pairs and Quadratic Equations

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

Factorisation: Polynomials and Theorem

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

Complex Numbers: Roots and Polynomials

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

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.

Complex Numbers: Operations and Applications

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

Polynomials with Real Coefficients

Explores polynomials with real coefficients, complex roots, and sequences' 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.

Complex Factorization Examples

Explores complex polynomial factorization examples, demonstrating the process and implications of complex roots in real polynomials.

Polynomials, Division, and Ideals

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

Finite Fields: Properties and Applications

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

Reed Solomon Codes: Basics and Applications

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

Stein Algorithm: Polynomial Identity Testing

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

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.

Polynomial Identity Testing

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

Analyse 2: Division euclidienne

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

Complex Plane and Polynomials

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

Division Euclidienne: Exemples

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

Factorisation: The Fundamental Theorem of Algebra

Covers the Fundamental Theorem of Algebra, polynomial division, and complete factorization of complex polynomials.

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.