Math 332: Undergraduate Abstract Algebra II, Winter 2025
Professor: Darij Grinberg

Organization

Classes:
Classes are over now!
Office hours:
Also by appointment on https://drexel.zoom.us/j/2350700617.
Text:
An introduction to the algebra of rings and fields (work in progress). Source code. Also, see the class notes from Winter 2023.
Blackboard:
https://learn.dcollege.net/ultra/courses/_380313_1/cl/outline.
Gradescope:
https://www.gradescope.com/courses/930606.
Piazza:
https://piazza.com/drexel/winter2025/math332.
Instructor email:
darij.grinberg@drexel.edu

Course description

An introduction to rings and modules, including the structure of finite fields and field extensions and some number-theoretical applications. Polynomial rings and Gröbner bases will also be discussed, as will multilinear algebra and Galois theory if time allows.

Level: undergraduate.

Prerequisites: Math 331 (Undergraduate Abstract Algebra I).

Course materials

Required:
Recommended:
  • The Winter 2023 iteration of this course, also available as a ZIP archive for downloading. We will likely reuse most of the homework exercises.
  • David S. Dummit, Richard M. Foote, Abstract algebra, 3rd edition, Wiley 2004: Long and comprehensive text containing almost all the abstract algebra that anyone could teach in an undergraduate sequence and then some. Available at the usual places in various formats (e.g., PDF). Mind the errata. We will use Chapters 7-14.
Other:
The following list gravitates towards freely available and new sources. See here or here or here or here for more standard references.

Course calendar

Diary:
  • Diary. Note: These are unedited and unpolished archives of blackboard writings; they are not a replacement for the lecture notes.
Week 0:
Week 1:
Week 2:
Week 3:
Week 4:
Week 5:
Week 6:
Week 7:
Week 8:
Week 9:
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. (Homework set #0 is worth 20 points; each remaining homework set is worth 50 points, no matter what gradescope says. Your lowest homework score, not counting homework set #0, will be dropped.)
  • 20%: midterm 1.
  • 20%: midterm 2.
  • 20%: midterm 3 (due on finals week).
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 332 students and Drexel employees) for help with the problems is not allowed. (In particular, you cannot post homework as questions on math.stackexchange before the due date!)
  • The use of generative AI (ChatGPT, Bard, etc.) in solving problems or formulating the solutions is not allowed. However, it is permitted to consult AI for typesetting and formatting questions.
  • 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 Gradescope. 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 even type in a text editor if you use standard conventions to write your formulas in ASCII. In either case, convert to PDF (e.g., by printing to PDF) and submit to Gradescope. If there are problems with submission, send your work to me by email for good measure.
Midterm policy:
  • Late midterms will not be accepted unless agreed in advance and with serious justification.
  • Collaboration is not allowed on midterms.
  • Everything else is the same as for homework (yes, midterms are take-home).
Expected outcomes:
The students should have an understanding of the basic objects of abstract algebra including rings and modules. They should also gain an understanding of homomorphisms, direct sums and products. They should have a knowledge of the basic theorems in this area including isomorphism theorems and universal properties. They should be familiar with the elementary properties of Gröbner bases, finite fields and field extensions.

Other resources

University policies:
Disability resources:

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