Lectures related to Kernel (algebra)

Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.

Groups: Definitions, Properties, and Homomorphisms

Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.

Variety Defined as the Closure of VCA

Explores the concept of variety defined as the closure of VCA and its applications in algebraic geometry.

First Isomorphism Theorem

Covers the first isomorphism theorem in group theory and its applications.

Groups and Homomorphisms

Covers Euler's totient function, group theory, homomorphisms, and group isomorphisms.

Applications of Lagrange's Theorem

Explores the applications of Lagrange's theorem in algebra, covering corollaries, cyclic groups, and quotient groups.

Kernel Regression: Basics and Applications

Explores kernel regression, the curse of dimensionality, and random features in neural networks.

Principal Ideal Domains: Structure and Homomorphisms

Covers the concepts of ideals, principal ideal domains, and ring homomorphisms.

Group Homomorphisms

Explores group homomorphisms, isomorphisms, and generators in abstract algebra.

Normal Subgroups and Quotients

Introduces normal subgroups, group quotients, and their applications in group theory.

Algebra of Matrices: Properties and Fields

Covers the properties of the algebra of matrices and related concepts.

Chinese Remainder Theorem: Rings and Fields

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

Automorphism Groups: Trees and Graphs III

Explores automorphism groups of trees and graphs, including actions on trees and group homomorphisms.

Ring Homomorphisms and Ideals

Explores ring homomorphisms, bilateral ideals, ring features, and ideal operations.

Groups & Rings: Morphisms, Kernels, and Injectivity

Explores group morphisms, kernels, and injectivity in group theory.

Kernel Ridge Regression: Equivalent Formulations and Representer Theorem

Explores Kernel Ridge Regression, equivalent formulations, Representer Theorem, Kernel trick, and predicting with kernels.

Linear Applications: Kernel

Introduces the kernel of a linear application and its properties.

Quotients de groupe: Un cas particulier

Explores a categorical perspective on group quotients, focusing on a specific case.

Group Homomorphisms: Kernels, Images, and Normal Subgroups

Explores group homomorphisms, kernels, images, and normal subgroups, using the dihedral group D_n as an example.

Group Actions on Sets

Explores group actions on sets through homomorphisms and Cartesian products, illustrating their properties and equivalent definitions.