MW 9:45 a.m. - 11:00 a.m. in Vincent Hall 207
Math 8202
Christine Berkesch Zamaere
Office: Vincent Hall 254
Email: cberkesc -at- math.umn.edu (For faster response time, please include "Math8211" in the subject line.)
Office hours:
Monday 11:00 a.m. - 12:15 p.m.,
or by appointment (in Vincent Hall 254).
Commutative Algebra with a View Toward Algebraic Geometry by David Eisenbud, 1995. There is a copy on reserve in the Mathematics library in Vincent Hall.
This is an introductory course in commutative and homological algebra. We will dicuss topics including localization of rings, primary decomposition, completions, and dimension theory.

The course grade will be based on the homework and a paper.
All homework must be typed using LaTex. I am willing to provide a template to get you started.

I encourage collaboration on the homework, as long as each person understands the solutions, writes them up in their own words, and indicates on the homework problem or whole assignment with whom they have collaborated. The assigned problems are available here.
The paper will be 3-5 pages typed in 12pt font. Details can be found here.
Students with disabilities, who will be taking this course and may need disability-related accommodations, are encouraged to make an appointment with me as soon as possible. Also, please contact U of M's Disability Services to register for support.

September 6   First Math 8211 meeting
September 18   Project topic choice due
October 7   Project outline due
October 23   Project progress report due
November 13   Project paper rough draft due
November 20   Project paper peer review due
December 6   Final 8211 meeting: homework and paper final draft due

Below is a list of topics and corresponding reading for the semester. No topic next to a date means that we will continue with the previous topic. Note that lectures more than a week in advance are subject to change.

Date      Topic   Textbook references
09-06   Introduction and connections, Modules   1.1, 1.2, 1.3, 1.6, 0.3
09-11   Fractions   2.1
09-13   Noetherian and Artinian rings   2.4
09-18   Hilbert's basis theorem   1.4
09-20   Hom and Tensor   2.2
09-25   Associated primes, Prime avoidance   3.1, 3.2
09-27   Primary Decomposition   3.3
10-02   More primary decomposition   3.6, 3.8
10-04   Nakayama's Lemma and the Cayley--Hamilton Theorem, Normalization   4.1, 4.2
10-09   Primes in an integral extension   4.4
10-11   The Nullstellensatz   4.5
10-16   Graded rings, Hilbert functions   1.5, 1.9
10-18   Associated graded rings   5.1
10-23   The blowup algebra, The Krull Intersection Theorem, Free resolutions   5.2, 5.3, 1.10
10-25   Macaulay2, Flat families   demo.m2, 6.1
10-30   Tor, Flatness   6.2, 6.3
11-01   Direct and inverse limits   A6
11-13   Completions, Cohen Structure Theorem   7.1, 7.2, 7.4
11-15   Maps from power series rings   7.6
11-20   Resolutions   A3.2, A3.3, A3.4
11-22   Homotopies and long exact sequences   A3.5, A3.6, A3.7, A3.8
11-29   Derived functors   A3.9, A3.10, A3.11
12-04   Dimension theory   8.1, 9.0
12-06   Dimension zero   9.1


Christine Berkesch Zamaere  ***  School of Mathematics  ***  University of Minnesota