Lectures related to Algebra over a field

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Covers the density theorem in representation theory, focusing on endomorphisms of simple finite-dimensional modules.

Covers the precise description of the relative positioning of objects in space.

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

Explains the independence of events and sets in an algebraic context.

Explores random variables, sigma algebras, independence, and shift-invariant measures, emphasizing cylinder sets and algebras.

Covers simple modules, endomorphisms, and Schur's lemma in module theory.

Covers antiderivatives, fundamental theorems, integration techniques, and rational functions.

Covers rings and modules, emphasizing color codes and homological algebra concepts.

Introduces algebras over a field, k-linear endomorphisms, and commutative algebras.

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.

Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.

Introduces analytic manifolds, Berkovich spaces, and multiplicative semi-norms in K-algebras.

Covers the course evaluation results and an algebraic explanation of employment rate growth.

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

Covers the basics of probability theory, including probability spaces and random variables.