Basic group theory: Groups, subgroups, normal subgroups, homomorphisms, quotient groups, coset decomposition, Example: Permutation group and general linear group; basic (commutative) ring theory: Rings, subrings, homomorphisms, ideals, quotient rings, modules over rings, submodules and quotient modules, fraction field; further group theory: Groups operating on a set, Sylow theorems. Prerequisite : One of MATH 226 or MATH 227. Note: Credit can be obtained in at most one of MATH 326 and MATH 327.
Basic group theory: Groups, subgroups, normal subgroups, homomorphisms, quotient groups, coset decomposition, Example: Permutation group and general linear group; basic (commutative) ring theory: Rings, subrings, homomorphisms, ideals, quotient rings, modules over rings, submodules and quotient modules, fraction field; further group theory: Groups operating on a set, Sylow theorems. Prerequisite : One of MATH 226 or MATH 227. Note: Credit can be obtained in at most one of MATH 326 and MATH 327.
