# Math 742 - Spring 2019

# Nigel Boston

## Contact Information

303 Van Vleck Hall
Telephone: 263-4753.

E-mail: *boston@math.wisc.edu*

Homepage

Course Syllabus

Office Hours: W 11-12, Th 1:30-2:30, or by appointment (303 Van Vleck).

## Sections

- Lecture: MWF 9:55-10:45, B235 Van Vleck.

## Text

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.
## Course Description

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.
## Homeworks

HW1, due Feb 8
HW2, due Feb 22
HW3, due Mar 8
HW4, due Apr 5
HW5, due Apr 19
## Grading

The midterms will be worth 40% each and the homeworks worth 20%.
## Exams

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.