Basic ring theory: rings and fields, the integers modulo n, polynomial rings, polynomials over the integers and rationals, homomorphisms, ideals and quotients, principal ideal domains, adjoining the root of an irreducible polynomial; basic group theory: groups, examples including cyclic, symmetric, alternating and dihedral groups, subgroups, cosets and Lagrange's theorem, normal subgroups and quotients, group homomorphisms, the isomorphism theorems, further topics as time permits, e.g., group actions, Cayley's theorem.
This course may not be repeated for credit.Syllabus

Sections