Math 4163 Course Outline

Week 1: Binary operations, groups, examples, functions/injectivity/surjectivity
Week 2: Simple theorems, subgroups, cyclic groups.
Week 3: Fundamental theorem of cyclic groups, permutation groups
Week 4: Isomorphism, cosets, Lagrange’s theorem
Week 5: Direct products, normality
Week 6: First test, more on normality, factor groups, homomorphisms
Week 7: Internal direct products (and, for 5163, semidirect products), Fundamental theorem
of finite abelian groups
Week 8: Equivalence relations, conjugacy, class equation, Sylow theorems
Week 9: More on Sylow theorems, rings (definition, examples, elementary theorems)
Week 10: Integral domains, ideals, maximal ideals, fields, factor rings
Week 11: Ring homomorphisms, second test
Week 12: Polynomial rings, principal ideal domains
Week 13: More on principal domains, unique factorization domains
Week 14: Field extensions, roots of polynomials
Week 15: Construction of fields.