Modern Algebra

MATH 6303-01 (13710), TuTh 11:30AM-1:00PM, PGH 348

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 .

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(pdf)            HW1(LaTeX)

HW2(pdf)            HW2(LaTeX)

HW3(pdf)            HW3(LaTeX)

Midterm: Tuesday, March 20

HW4(pdf)            HW4(LaTeX)

HW5(pdf)            HW5(LaTeX)

Final: Tuesday, May 8, 11am-2pm