Math 742 - Spring 2019
303 Van Vleck Hall
Office Hours: W 11-12, Th 1:30-2:30, or by appointment (303 Van Vleck).
- Lecture: MWF 9:55-10:45, B235 Van Vleck.
For the first half of the course we will follow Atiyah-MacDonald "Introduction to Commutative Algebra", particularly Chapters 1-3 and 6-7. For the second half of the course we
will follow Milne's online notes Fields and Galois Theory.
Continuation of MATH 741. Usually the study of commutative rings and fields. Ring theoretic topics may include: modules over PIDs, Noetherian rings and the Hilbert basis theorem, the Lasker-Noether theorem, the Krull intersection theorem, integrality and the Hilbert Nullstellensatz. Field theoretic topics may include: algebraic extensions, Galois theory, solvability of polynomials and classical constructability problems.
HW1, due Feb 8
HW2, due Feb 22
HW3, due Mar 8
HW4, due Apr 5
HW5, due Apr 19
The midterms will be worth 40% each and the homeworks worth 20%.
There will be two midterms, one covering Commutative Algebra (on Fri, March 15, in class) and the other covering Fields and Galois Theory. There will be no final.