120 credits including 90 credits in mathematics or 60 credits in mathematics and 60 credits in physics. Participation in Algebraic Structures or Mathematical Methods of Physics II. Participation in Linear Algebra III or Quantum Physics. Proficiency in English equivalent to the Swedish upper secondary course English 6.
Free groups and algebras. Generators and relations. Modules. Noether's isomorphism theorems. The structure of finitely generated modules over principal ideal rings. Categories and functors. Equivalence for categories. Adjoint functors. The hom and tensor functors. Projective, injective, simple and indecomposable modules. Quiver algebras and their modules. Complexes. Homology. Exact sequences. Diagram chase.
