Math 332: Undergraduate Abstract Algebra II, Winter 2023
Professor: Darij Grinberg

Organization

Classes:
Classes are over now.
Text:
An introduction to the algebra of rings and fields (work in progress). Source code. Also, see the notes below.
Blackboard:
https://learn.dcollege.net/ultra/courses/_331049_1/cl/outline.
Gradescope:
https://www.gradescope.com/courses/487831.
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:
  • 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

All weeks:
ZIP archive containing all the lecture notes and assignments listed below.
Week 0:
Week 1:
Week 2:
Week 3:
Week 4:
Week 5:
Week 6:
Week 7:
Week 8:
Week 9:
Week 10:
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 staff) for help with the problems is not allowed. (In particular, you cannot post homework as questions on math.stackexchange before the due date!)
  • 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. Make sure that what you submit is readable (e.g., your text is not cut off). 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

Homework help:
University policies:
Disability resources:

Back to Darij Grinberg's teaching page.