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

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.