Characterization of Tori and Diagonalizable Groups

Covers homomorphisms between affine varieties, birational maps, regular groups, and connectedness.

Explores the Mayer-Vietoris sequence, exact homomorphisms, embedded spheres, and path-connected spaces.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

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

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.