Modern Algebra

MATH 6303-01 (12708), TuTh 2:30-4:00,  F162

Text: Thomas W. Hungerford, Algebra, Springer Verlag (required).  But I will teach the course from my own  classroom notes:
Modern Algebra

Additional Reading: Finitely generated torsion-free modules are free. If you drop finitely generated then this is no longer  true. The additive group of rational numbers (Q,+) is a nice example of a torsion free group which is not free. Another example is provided by the  product of countably many copies of the additive group (Z,+) of integers. The  article Baer's result: The infinite product of the integers has no basis by Stefan Schroer, University of Düsseldorf,  explains this exceptionally well.
You also might profit from my notes on Advanced Linear Algebra. These notes are based on the classic linear algebra text by K. Hoffman and R. Kunze. I had prepared these notes about twenty years ago with a by now defunct word processor. Typesetting is not very good, compared to LaTeX. For doing the problems you need the Hoffman-Kunze book. which I highly recommend. 

Prerequisites: Graduate Standing

Course Description:

The second semester of Modern Algebra will be mainly on modules over principal ideal domains, Sylow theory, free algebras and sums, ultraproducts.

You will receive weekly homework assignments and there will be a midterm and final. Grading: HW 20%, Midterm 30%, Final 50%

HW1 TeX        HW1 PDF

HW2 TeX        HW2 PDF

HW3 TeX        HW3 PDF

HW4 TeX        HW4 PDF

HW5 TeX        HW5 PDF

HW 4 and HW are part of the final which has been scheduled for May 12, 2-5 pm. The first hour is a 90 minute test and then you present your solutions on the blackboard. Every student t has to present at least one problem.