Complex Numbers: Operations and Properties

Covers the construction and properties of complex numbers, introducing the new constant 'i'.

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

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.

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