RING AND FIELD THEORY

Graduate

This course covers advanced algebraic structures. Topics including: polynomial rings, matrix rings, ideals and homomorphisms, quotient rings, Euclidean domains, principal ideal domains, unique factorization domains, introduction to module theory, basic theory of field extensions, splitting fields and algebraic closures, finite fields, introduction to Galois theory. Graduate students will have more challenging assessments than undergraduates to reflect the higher level of mastery of the material that they are expected to achieve. This course is cross-level listed with MATH 4620. Credit cannot be received for both MCS 8620 and MATH 4620. PREREQUISITE: Admission to a graduate program in Science HOURS OF CREDIT: 3