Math 512 syllabus
A graduate level introduction to ring theory and fields. Topics include ring homomorphism, quotient rings, ideals, rings of fractions, Euclidean domains, principal ideal domains, unique factorization domains, modules, finite fields, and field extensions. This course is taught in the traditional lecture format. 3 Credits.
Prerequisites: C or better in MA 511.
Suggested Text: Algebra, Second Edition, by Michael Artin.
Coverage: Chapters 11 and 12 as well as selected topics from chapters 13 through 16.
Students are expected to gain a deep understanding of the fundamental algebraic concepts of rings and fields, their properties and applications.
Students are expected to be able to state definitions precisely, to construct proofs of mathematical statements, to read and understand proofs of mathematical theorems, and to apply these theorems and learned techniques to new situations.
Last updated: October 16, 2014.