Courses

Propositional and predicate logic; set, relations, and functions; the induction principle; Groups, in particular symmetry groups, permutations groups, and cyclic groups; cosets and quotient groups; group homomorphisms; rings, integral domains, and fields; ideals and rings homomorphisms; factorization; polynomial rings.

Groups, subgroups, factor groups, homomorphism theorems, rings, ideals, factorization theory, fields, modules and vector spaces.

This course is a study of algebra as it relates to elementary number theory (such as factorization, primes, and common factors), groups, rings (such as, division rings), integral domains, and elementary field theory and the relationship between structures of number systems and symbolic calculations, modeling those relationships and operations.

Introduction to abstract algebra, groups, rings, and fields. Topics include binary operations, groups, subgroups, cyclic groups, groups of permutations, cosets, finitely generated groups, homeomorphisms, isomorphisms, factor groups, rings, fields, and integral domains. Additional topics may include fields of quotients, rings of polynomials, factor rings, ideals, unique factorization domains, and the Sylow Theorems.

Sets, relations, and functions; properties of integers and induction; permutations; groups, group homomorphisms, and quotient groups; Cartesian and direct products.

Properties of the integers, modular arithmetic. Elementary theory of groups, finite groups, subgroups, cyclic groups, permutation groups. Group isomorphisms and homomorphisms.

A study of properties of the integers, modular arithmetic. Elementary theory of groups, finite groups, subgroups, cyclic groups, permutation groups. Group isomorphisms and homomorphisms. This course contains additional graduate-level content equivalent to a one-hour recitation with the instructor which will further investigate the theoretical aspects of or applications of the topics discussed in the permission of the instructor.

General group theory including cyclic groups and permutation groups, homomorphism and isomorphism theorems.

A continuation of MTH 301. Rings, ring homomorphisms, ideals, quotient rings; integral domains; fields and polynomial extensions of fields.

Elementary theory of rings, polynomial rings, divisibility, unique factorization domains. Integral domains, ideals, factor rings, divisibility in integral domains. Elementary theory of fields. Extension fields.