Week 1: Definition of rings, examples, polynomial rings, homomorphisms.
Week 2: Ideals, prime and maximal ideals, quotient rings.
Week 3: Noetherian rings, Hilbert basis theorem.
Week 4: Integral domains, quotient fields.
Week 5: Unique factorization domains, principal ideal domains.
Week 6: Definition of fields, examples, degree of field extensions.
Week 7: Adjoining roots, primitive element theorem.