University of Alberta · Fall Term 2026

MATH 327: Algebra 1

Basic group theory: groups, subgroups, normal subgroups, homomorphisms, quotient groups, coset decomposition, example: permutation group and general linear group; basic (commutative) ring theory: rings, subrings, homomorphisms, ideals, quotient rings, modules over rings, submodules and quotient modules, fraction field; further group theory: groups operating on a set, Sylow theorems.

Instructor: Manish Patnaik
Email: patnaik@ualberta.ca
Office: UCOMM 5-254
Office hours: To be announced

Announcements

Class announcements

Tuesday, August 25, 2026

Welcome to MATH 327. Lecture notes will be posted here after each class, and problem sets appear under Problem sets as the term goes on. Note that they are not to be turned in. They are just for your practice.

Office hours will start on the second week of class.

The plan is to use this website for most things, but I will still use Canvas to send out emails to the entire class (as the website isn't synced to the class roster) and to upload your midterm/final grades.

Syllabus

Course information

Meets: MWF, 9:00 – 9:50 AM
Location: CAB 281

Algebra 1 syllabus PDF · not yet posted Download →

Grading

Component	Weight
Midterm 1	25%
Midterm 2	25%
Final exam	50%

Schedule & Notes

Lecture schedule

Lecture	Date	Topic	Notes
1	Wed, Sep 2	Groups, examples 2.1, 2.2	PDF
2	Fri, Sep 4	More examples, 2.1-2.2	—
3	Wed, Sep 9	Subgroups, cyclic groups 2.3, 2.4	—
4	Fri, Sep 11	—	—
5	Mon, Sep 14	—	—
6	Wed, Sep 16	—	—
7	Fri, Sep 18	—	—
8	Mon, Sep 21	—	—
9	Wed, Sep 23	—	—
10	Fri, Sep 25	—	—
11	Mon, Sep 28	—	—
12	Fri, Oct 2	—	—
13	Mon, Oct 5	—	—
14	Wed, Oct 7	—	—
15	Fri, Oct 9	Midterm 1	Details →
16	Wed, Oct 14	—	—
17	Fri, Oct 16	—	—
18	Mon, Oct 19	—	—
19	Wed, Oct 21	—	—
20	Fri, Oct 23	—	—
21	Mon, Oct 26	—	—
22	Wed, Oct 28	—	—
23	Fri, Oct 30	—	—
24	Mon, Nov 2	—	—
25	Wed, Nov 4	—	—
26	Fri, Nov 6	Midterm 2	Details →
27	Mon, Nov 16	—	—
28	Wed, Nov 18	—	—
29	Fri, Nov 20	—	—
30	Mon, Nov 23	—	—
31	Wed, Nov 25	—	—
32	Fri, Nov 27	—	—
33	Mon, Nov 30	—	—
34	Wed, Dec 2	—	—
35	Fri, Dec 4	—	—
36	Mon, Dec 7	—	—

Homework

Problem sets

Practice problems to test your understanding. These are not to be turned in. Please attempt as many as you can!

Set	Covers	PDF	Solutions
HW 1	Def of group, examples (2.1-2.3)	Not yet posted	Not yet posted

Assessment

Midterm 1

Held at lecture 15.

Date & time: Friday, October 9, 2026 · In class
Format: In-class, closed book
Coverage: Lectures 1–14
Review materials: Posted closer to the exam

Assessment

Midterm 2

Held at lecture 26.

Date & time: Friday, November 6, 2026 · In class
Format: In-class, closed book
Coverage: Lectures 16–25
Review materials: Posted closer to the exam

Assessment

Final exam

Cumulative — comprehensive coverage of the full term, weighted most heavily in the final grade.

Date & time: Set by the registrar — TBA
Format: Closed book, comprehensive
Coverage: All course material
Review materials: Posted in the last week of term