In addition to the above, we will cover all the necessary intermediate algrebra, including groups, fields, vector spaces, topological vector spaces,modules, and rings and modules. We will also cover a few applications ofalgebra. In particular, we will cover the solutions to some classificationproblems which start in Chapter 2 of the book.
The course will be made up of two different parts. In the first part, wewill cover aspects of the theory of rings and modules, and algebraic results,which do not necessarily involve a computation. The goal is simply tosee the shape of the theory, understand the approaches, and obtain sometools to do algebra. We will also cover group theory, and the structuretheory of finitely generated modules over a PID (where we will skip the proofsin Chapter 5). This will serve as preparation for the next part.
Examination Policy: I do not expect this course to be exciting, inspiring but alsochallenging. It should be just algebra and a bit of a background in algebra,and the desire to understand what is going on.
A few course notes will be given in class, followed by a reading assignment.I will assign a reading material; it should be done in the first class meeting. I havedelivered some homework, but I am not sure I will continue to do so. Youmay work on your homework, or at least read it, in the first class meeting. Ifyou are working on your assignment, you may share the work with each other,but each must submit his or her own solutions.
The second part of the course will be more algebraic. The aim here isto cover the theory of modules, and its applications to the theory of rings,and some basic results about finitely generated modules over a PID. Theaim is to see the shape of this theory, and get some tools for computation.
I will cover the theory of modules over a PID to establish a treatmentof the module theory of a field; this is done in Dummit and Foote,Section 13.1 and 13.6. The module theory of an integral domain is done inDummit and Foote, Section 11.2. 827ec27edc