Content: Revision of groups/rings/fields/modules. Basics of category theory, free groups, group presentations, tensor products, multilinear and homological algebra. Brief introduction to representation theory and Galois theory.

Aims: The main aim is to give an overview of various topics in advanced algebra to prepare PhD students for research in all fields.

Objectives: By the end of the module the student should have a more solid and sophisticated understanding of material covered in the undergraduate curriculum, and also familiarity with topics that are not normally part of the undergraduate curriculum, but are assumed by research seminar speakers, such as the basics of category theory and homological algebra.

Books: Sample reference texts:

1. Dummit and Foote "Abstract Algebra"

2. Hungerford "Algebra"

3. Lang "Algebra"