Time and Place:
- Groups, the factor group and the homomorphism theorems, Sylow’s theorems and permutation actions of groups.
- Rings, Integral Domains and Fields. Ideals: maximal and prime. Unique Factorization Domains, Principle Ideal Domains, Euclidean Domains.
- Modules, structure theorems for finitely generated modules over a PID, application to finitely generated abelian groups and to the Jordan Canonical Form.