PMATH 445Representations of Finite Groups
- Units
- 0.50
- Faculty
- Mathematics
- Subject
- Pure Mathematics
When it runs
- F24
- W25
- S25
- F25
- W26
- S26
- F26
- W27
- S27
Ran in 2 of the last 7 terms. Winter 2027: scheduled, 2 lecture sections. Spring 2027: schedule not out yet.
Basic definitions and examples: subrepresentations and irreducible representations, tensor products of representations. Character theory. Representations as modules over the group ring, Artin-Wedderburn structure theorem for semisimple rings. Induced representations, Frobenius reciprocity, Mackey's irreducibility criterion.
Prerequisites
- Must have completed the following:
- PMATH347 - Groups and Rings (0.50)
Antirequisites
None listed.
Leads to
No course lists it as a requisite.
Winter 2027 sections
| Section | Class | Enrolled | Meets |
|---|---|---|---|
| LEC 001 | 6228 | 0 / 40 | MW 13:00–14:20 |
| LEC 701 | 2392 | 32 / 9999 | Online or by arrangement |
Resources
Around the web
Found by uwloo’s link finder, which checks that each page names PMATH 445.
- PMATH 445/745: Representations of Finite Groups Course notes · math.uwaterloo.ca · from Faisal Al-Faisal’s site Remove
Reviewed on UW Flow
100% liked it30% easy85% useful
From 8 ratings and 3 comments on UW Flow. The most helpful comments, quoted as written, without names. Read them all on UW Flow.
Absolutely amazing course.
Nov 2025 · liked itOn UW FlowRemove this
This course was definitely interesting, was a combination of group theory and linear algebra. The first half is representation theory of groups and character theory and then it moves to modules/algebras which relies on a lot on rings and fields. As someone with limited other PMATH courses other than the pre-reqs I found it challenging at times, it was hard to visualize some of the concepts and it required lots of use of facts from the 347 that I had forgotten. Overall, I definitely didn't understand all the content, but with a lot of work but in managed to do well. The assignments were time consuming, lots of time in office hours, but helped reinforce the concepts. The tests were fair.…
Apr 2025 · liked itOn UW FlowRemove this
My first 4xx pmath course but there's no way it gets better than this. Everything is well motivated and it's just a beautiful mix of linear algebra, group theory, ring theory and some black magic that lets you prove some truly wild things.
Apr 2025 · liked itOn UW FlowRemove this
Discussed on r/uwaterloo
18 posts and comments in 18 threads mention PMATH 445, September 2016 to December 2024. Quoted word for word, newest first; each reply sits under the post and the comment that started its branch. Search r/uwaterloo for newer posts.
Fall 2024
Any must-have profs in Math/CS/Stat that one should take a class with, regardless of major? 22 points, 28 comments
u/threethousandstars: “Faisal al-Faisal. Idk if he teaches classes above 2nd year but had him for math 237 and he was the GOAT for learning purposes Also Joe West. Juggling tricks in class!”
u/amsyed10385: “Yes he does, Faisal is teaching PMATH 445 next semester”
Spring 2024
Lin alg heavy courses 13 points, 10 comments
“I love math235 and I'm sad that there's no Lin Alg 3. What are some courses that use a lot of Lin alg? Would CS484 or CS480 fit this? CS475 isn't available next term, and I've already taken CS370”
u/Far_Bookkeeper6488: “quick someone get faisal to make lin alg 3”
u/Burgundy_Blue: “pmath 445 is representation theory”
Winter 2024
Pmath445 1 point, 0 comments
u/Traditional_Beach461: “Anybody here take it before? I have it this term coming up for my final semester and was wondering what people thought about the course in terms of content and / or difficulty, or basically what you thought in general about it. It’s being taught by Ben Webster this term.”
Winter 2022
Does anyone actually enjoy their courses? 114 points, 45 comments
“Honestly for as long as I remember, when I think of taking courses, listening to lectures, completing projects, and doing assignments/assessments, I only feel dread. …”
u/blank_anonymous: “… I'm so excited about class and learning I find that the courses I've enjoyed most have been 400-level (PMath 445 and PMath 453 with Bell and Marcoux respectively were two of my favourite courses), and I've also found that I enjoy courses in PMath substantially more than most …”
Spring 2021
Easiest PMATH 400 level courses? 2 points, 8 comments
u/BabuWithNoName: “pls help ive already killed my gpa enough i just wanna graduate My choices are between PMATH 440, 445, and 451.”
Officially Awarded Degree by UWaterloo! AMA for my university experience 4 points, 27 comments
“Background information for question drafting: \- CS, PMath, co-op (used to consider Math Finance) \- Almost non-existence programming experience prior to entering Waterloo \- International \- Joined …”
u/iKDX: “Really interested in your PMath component coming from a CS major. Which classes did you take? Was it double major or PMath minor? Was it easy? Was it useful? Did employers care you did PMath? …”
u/new_jan_2018: “The 6 required PMATH courses, and also PMATH 440, 445, 433. Double major. No :) For me it's manageable, but that's because I am strong in writing proofs and enjoy it a lot! …”
Fall 2020
PMATH 445 vs. 446 vs. 464 6 points, 4 comments
u/BlazingMuddy-6305: “Hi, I just opened my course plan, and I realized that I'm kinda strapped for availability slots. For the PMATH 400s requirement, I plan to have PMATH 440 and 441, but for the last slot I'm still indecisive between those in the title. …”
Spring 2020
BIRD COURSES FALL 2020 HELP???!!! 0 points, 13 comments
“I just need to take one course to fill in my course load and i need a birdie!!! Since all classes were online this term, what are some of the easiest courses online?? …”
u/QwerbyKing: “PMATH 445”
Alumni of UW, looking back— what was your favourite classes/memories from your uni life? Do you miss any of it? 45 points, 19 comments
u/mrbanana4: “Favourite classes: MATH147, PMATH446, and PMATH445 Favourite memories: Living with all my friends in first and second year”
Spring 2019
[Advice needed] What course should I take? 3 points, 13 comments
u/Hyacinth_s: “… Switch 231 to PMATH 445 (I meet the prerequisite but haven't take Galois' theory yet, and I suppose it will be helpful) and wait for STAT 241 this coming winter. 2. Alternatively, I'm also thinking about switch 231 to AMATH 231 (and wait for STAT 241). …”
Can more new grads post their undergrad stats please? 26 points, 64 comments
“They're fun to read.”
u/snewdity: “… course: PMATH 347 (90) Favorite PMATH course: PMATH 433 (97) Least favorite PMATH course: PMATH 445 (99) Favorite elective: RUSS 101 (93) Least favorite elective: ECON 101 (94) Number of all nighters: 0 Honourable mention: stayed up to 6:30am once on a CS 136 assignment Number …”
Spring 2018
Stat 333 override 1 point, 12 comments
“I am in 2B and this term I would like to override stat 333.which advisor should I ask to have a higher chance? I heard some advisors are reluctant to do this. …”
u/carey11: “Just curiosity, why would you want to override a course? Is it because you already covered the material somewhere else before?”
u/ZYXBob: “I guess the best answer is I want to learn more, I feel there is no huge difference for me to learn it in 3A or 2B in terms of math maturity. If I don’t take 333 I will take pmath 445, but I learned too much algebra this term so I want to switch my mind.”
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