- gille@ualberta.ca

**Areas**

Quadratic Forms & Chow Motifs

Rings, fields, polynomials, algebras. Homomorphisms, ideals, quotients. Ring extensions, field extensions, construction of finite fields. Integral domains: Euclidean, principal ideal, unique factorization. Chain conditions. Introduction to modules. Modules over a principal ideal domain, finitely generated abelian groups, matrix canonical forms. Prerequisite MATH 227, or both MATH 225 and 228.

Winter Term 2021Groups, subgroups, homomorphisms. Symmetry groups. Matrix groups. Permutations, symmetric group, Cayley's Theorem. Group actions. Cosets and Lagrange's Theorem. Normal subgroups, quotient groups, isomorphism theorems. Direct and semidirect products. Finite Abelian groups. Prerequisite: MATH 227 or 228. This course may not be taken for credit if credit has already been obtained in MATH 229.

Fall Term 2020Valuations and their extensions, ramifications; integral dependence, algebraic number fields, ideals and divisors, class number. Prerequisite: MATH 326 or equivalent.

Winter Term 2021Valuations and their extensions, ramifications; integral dependence, algebraic number fields, ideals and divisors, class number. Prerequisite: MATH 326 or equivalent.

Winter Term 2021