Lectures related to Algebraic Geometry

Explores vector spaces, focusing on properties, examples, and subspaces within a practical exercise on polynomials.

Complex Roots: Conjugate Pairs and Quadratic Equations

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

Covers the integration of rational functions, focusing on decomposing functions into simpler elements.

Algebraic Functions: Two Gendarmes MOOC: Analysis I MOOC: Analysis I (part 4) : Limit of a function, continuous functions

Explores algebraic functions, limits, and behavior as x approaches infinity.

Orthogonal/Orthonormal Bases and Polynomials

Explores orthogonal and orthonormal bases, Gram-Schmidt process, and orthogonal polynomials in physics.

Integration: Rational Functions

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

Polynomials: Roots and Factorization

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

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.

Algebraic Identities and Trigonometry

Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

Polynomials, Division, and Ideals

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

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

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.

Algebraic Expressions

Covers algebraic expressions, operations, factorization, and equation solving.

Polynomials and Endomorphisms

Covers the fundamentals of polynomials, endomorphisms, division, roots, matrices, and algebraic homomorphisms.

Polynomials: Definition and Operations

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

Intersection Numbers: Algebraic Counting Solutions Log in to Mediaspace to watch this video

Explores intersection numbers for counting solutions to polynomial equations algebraically and their geometric significance in intersection theory and enumerative geometry.

Integration on H_pxH and Arithmetic Log in to Mediaspace to watch this video

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

Polynomials: Definitions and Operations Log in to Mediaspace to watch this video

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

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.

Weil Conjectures: Rationality and Function Equation Log in to Mediaspace to watch this video

Covers the Weil conjectures on rationality, functional equation, and the Riemann hypothesis, exploring properties of varieties in algebraic geometry.