In light of the current pandemic, this course will be offered virtually and using a "flipped classroom" model. Before each class, students are expected to read assigned sections of the lecture notes and to attempt the corresponding recommended exercises. (See the syllabus.) Course meetings will take place on Zoom, where students will have the opportunity to ask questions about the course material and the exercises.
This is a first course in ring and module theory. In this course, we study the general definition of a ring and the types of maps that we allow between them, before turning our attention to the important example of polynomial rings. We then discuss classes of rings that have some additional nice properties (e.g. euclidean domains, principal ideal domains and unique factorization domains). We then discuss modules, which are generalizations of vector spaces, where we allow scalars to lie in a ring.
Official course description
Rings and ideals, homomorphisms and isomorphism theorems, principal ideal domains and factorial rings, polynomial rings and the construction of finite fields. Modules, direct sums and annihilators of modules, free modules, classification of modules over a principal ideal domain.
MAT 2141 and MAT 2143.
Click the above header to download lecture notes for the course. They are a single file that may be updated as the course progresses. Students will be expected to read assigned sections of these notes before class. (See the syllabus.)
There are two main locations for information regarding the course: