Algebra 2: Rings and Modules - Math 2501, Fall 2019

Course Information

Meeting time:	Mondays, Wednesdays, and Fridays, 11:00AM-11:50AM (First meeting: August 26) Thackeray Hall, Room 525
Instructor:	Carl Wang-Erickson	Office: Thackeray 421
	carl.wang-erickson@pitt.edu	Office Hours: Monday 1:30pm-3:00pm and Wednesday 1:00pm-2:30pm, unless otherwise announced via email

Course Summary

This is an introductory graduate-level course in algebra, focusing on the theory of fields, rings, and modules. It is complementary to Algebra 1, but neither class is meant to be a pre-requesite for the other.

The first main example will be the one-variable polynomial ring over a field, along with its modules, relating this back to linear algebra. Further topics may include representations of finite groups and introductory commutative algebra.

These further topics, and the arc of the course overall, will be determined based on an survey of the students attending the first session of the course. If you are interested in the course and cannot attend the first session, please be in touch with me.

Syllabus

All of the course information will be available in the syllabus. It has now been updated after the initial survey of students.

Problem Sets

Problem set 1, due on September 6.
Problem set 2, due on September 13. Solutions, by Tyler Gaona.
Problem set 3, due on September 20.
Problem set 4, due on September 27.
Problem set 5, due on October 4.
Problem set 6, due on October 11. Solution to (2), by Tyler Gaona.
Problem set 7, due on October 18.
Problem set 8 (revised version), due on October 25.
Problem set 9, due on November 15.
Problem set 10, due on November 22.
Problem set 11, due on December 6.

Resources

Midterm reivew. The midterm will occur in class on Wednesday, October 30. Here is a review.

Reference books will be added here as the course progresses.

Abstract Algebra (3rd edition), by Dummit and Foote. It looks like this will be the only reference necessary for a while.
Algebra: Chapter 0, by Aluffi, is a nice complement to Dummit and Foote's book and treats everything we have discussed in the course.

Return to Carl's webpage.