Lectures related to Generating set of a group

Matrix Operations: Linear Systems and Solutions

Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

Explores bases and vector subspaces in R³, discussing properties and examples of bases.

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

Covers rings, modules, exact sequences, and finitely generated modules in the context of Noetherian and Artinian properties.

Additivity of Dimension & Height

Explores the additivity of dimension and height in a finitely generated k-algebra domain, showcasing its applications and implications.

Synchronization Inference

Explores automatic synthesis of correct and efficient synchronization in programs, focusing on removing redundant atomicity and adding synchronization metadata.