Courses

Non-credit Abroad Experience.

Students study advanced topics from group theory and ring theory. Other topics extensions, and an introduction to Galois theory.

Algebraic structure is emphasized in this course, which includes a study of groups, cryptography.

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.

Theory of groups, including cyclic and permutation groups, homomorphisms, normal subgroups and quotient groups. Theory of rings, including integral domains and polynomial rings. Additional topics may be discussed. Not open to students who are taking or who have received credit for MATH 333, 601 or 702.

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.