Lectures related to Introduction to Finite Fields

Covers the concept of orthogonal complement in Rn and related propositions and theorems.

Covers advanced topics in linear algebra, including finite fields, invertible matrices, and vector spaces.

Covers kernels and images of linear transformations between vector spaces, illustrating properties and providing proofs.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Covers the definitions and properties of vector spaces, including axioms and examples.

Explores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.

Explores weak derivatives in Sobolev spaces, discussing their properties and uniqueness.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.