Abstract Algebra
What are all finite simple abelian groups? What rings allow long division or computing greatest common divisors? What do straightedge and compass constructions have to do with fields, and why was Apollo mad at Athenians? Why is $ax^2+bx+c$ solvable using radicals but $x^5-x-1$ isn’t? This course is an introduction to groups, rings, and fields, with an emphasis on examples such as these.
- Instructor:
Mahrud Sayrafi<mahrud at ...> - TA:
Kieran Bhaskara<kieran.bhaskara at ...> - Textbook:
Abstract Algebra: Theory and Applications
Available for free download in English and Spanish. - Supplementary (bedtime) reading:
- “Groups and Symmetry” by M. Armstrong.
- “A Book of Abstract Algebra” by C. Pinter.
- “History of Abstract Algebra” by J. Gray.
- Prerequisites:
Mathematical Reasoning (MATH 1C03), and
Linear Algebra (MATH 2R03 or a grade of at least B in MATH 2LA3) - SimpleSyllabus: official course outline.
- Avenue to Learn: announcements and grades.
- 👉 How to get an A in this class! 👈
| Class | Title | Schedule |
|---|---|---|
| MATH 3GR3 (#1808) |
Abstract Algebra (Lecture) |
MoWe 11:30 - 12:20 Fr 13:30 - 14:20 |
| (#1809) | (Tutorial) | We 13:30 - 14:20 |
Fall 2025 Office Hours:
- Instructor: (all in HH 414)
- Monday 1:30-2:00
- Friday 1:00-1:30 (before lecture)
- And by appointment.
- TA:
- Wednesday 1:00-1:30 and 2:30-3:00 (before/after tutorial), Math Cafe
- Thursday 2:30-3:30, HH 410
Schedule
The topics are tentative and may be adjusted. The section numbers refer to sections in the textbook.
| Date | Topic | Notes |
|---|---|---|
| September 3 | Introduction | Proof Writing Diagnostic Quiz |
| September 5 | §1.2 | |
| September 8 | §1.2, §3.1 | Bonus points for Sonobe platonic solid |
| September 10 | §3,1, §3.2 | Last day to add/drop |
| September 12 | §3.2 | |
| September 15 | §3.3 | |
| September 17 | §4.1 | |
| September 19 | §4.2 | |
| September 22 | §5.1 | |
| September 24 | §5.1 | |
| September 26 | §5.2 | |
| September 29 | §6.1 | |
| October 1 | §6.2 | Test #1 on groups, during tutorial |
| October 3 | §6.3 | |
| October 6 | §9.1 | |
| October 8 | §9.1, §9.2 | |
| October 10 | §9.2 | |
| October 13 | No class | Mid-term recess |
| October 15 | No class | Mid-term recess |
| October 17 | No class | Mid-term recess |
| October 20 | §10.1 | |
| October 22 | §10.1 | |
| October 24 | N/A | Midterm Exam |
| October 27 | §10.2 | |
| October 29 | §11.1 | |
| October 31 | §11.2 | |
| November 3 | §11.2 | |
| November 5 | §16.1, §16.2 | |
| November 7 | §16.2, §16.3 | |
| November 10 | §16.3, §16.4 | |
| November 12 | §16.4, §17.1 | |
| November 14 | §17.2 | |
| November 17 | §17.3 | |
| November 19 | §18.1 | Test #2 (tentatively), during tutorial |
| November 21 | §18.2 | Last day to withdraw |
| November 24 | §21.1 | |
| November 26 | §21.2 | |
| November 28 | §21.3 | |
| December 1 | §22.1 | |
| December 3 | §23.2 (not on final) | Last day of class |
| December 9 | Final Exam | Time: 9am-11:30am, Location: TBA |