Math 331: Undergraduate Abstract Algebra I, Fall 2026
Professor: Darij Grinberg

Organization

Classes:
Mon, Wed 4:00 PM - 4:50 PM in One Drexel Plaza, GL 13; Fri 3:00 PM - 4:50 PM in One Drexel Plaza, GL 13.
Office hours:
Tue 12:00 noon - 2:00 PM in my office (Korman Center 263); Sunday 1:00 PM -- 2:00 PM (as well as by appointment) on https://drexel.zoom.us/j/2350700617.
Text:
See day-by-day lectures below.
Canvas:
https://drexel.instructure.com/courses/9597.
Instructor email:
darij.grinberg@drexel.edu

Course description

An introduction to groups and monoids, including homomorphism theorems, group actions, Sylow theorems and the Cauchy--Frobenius lemma. Some basic theory of rings and fields will also be featured if time allows.

Level: undergraduate.

Prerequisites: Math 220 (or CS 270) and Math 201 (with some alternatives; see TMS for details).

Course materials

Required:
  • There is no required text; everything I type in class will appear below on this page.
Other:

Course calendar

Week 0:
Week 1:
Week 2:
No Copyright:
The above lecture notes and assignments have been released under the CC0 license, i.e., are dedicated to the public domain. They can be copied, modified and distributed without permission. See the license for details.

Grading and policies

Grading matrix:
  • 40%: homework sets. (Your lowest homework score will be dropped.)
  • 20%: midterm 1.
  • 20%: midterm 2.
  • 20%: midterm 3.
Grade scale:
These numbers are tentative and subject to change:
  • A+, A, A-: (80%, 100%].
  • B+, B, B-: (60%, 80%].
  • C+, C, C-: (40%, 60%].
  • D+, D, D-: (20%, 40%].
Homework policy:
  • Collaboration and reading is allowed, but you have to write solutions in your own words and acknowledge all sources that you used.
  • Asking outsiders (anyone apart from Math 331 students and Drexel employees) for help with the problems is not allowed. (In particular, you cannot post homework as questions on forums before the due date!)
  • The use of generative AI (GPT, Claude, etc.) in solving problems or formulating the solutions is not allowed.
  • Late homework will not be accepted. (But keep in mind that the lowest homework score will be dropped.)
  • Solutions have to be submitted electronically via Canvas. Solutions must be typeset; handwriting will not be accepted! To typeset text with formulas, you can use any of LaTeX (a free online editor is Overleaf), Markdown (a free online editor is Stackedit), LibreOffice (which has a built-in equation editor), Google Docs (which, too, has an equation editor inside), or many other tools. You can use AI for typesetting as long as you don't let it change the wording, only the typesetting/formatting. If there are problems with submission, send your work to me by email for good measure.
Midterm policy:
  • Midterms will be written in-class on three Fridays (probably Oct 23, Nov 13 and Dec 4).
  • No collaboration or use of technology is allowed on midterms.
Expected outcomes:
The students should have an understanding of the basic multiplicative objects of abstract algebra: groups, monoids, group actions. This includes fundamental theorems like the isomorphism theorems, the Sylow theorems and the orbit-stabilizer formula, as well as features of permutations like signs and cycles.

Other resources

Homework help:
  • Math Resource Center; see schedule. Starts Sep 24.
Further resources:

Back to Darij Grinberg's teaching page.