PMATH 467Algebraic Topology
- Units
- 0.50
- Faculty
- Mathematics
- Subject
- Pure Mathematics
When it runs
- F24
- W25
- S25
- F25
- W26
- S26
- F26
- W27
- S27
Ran in 3 of the last 7 terms. Winter 2027: scheduled, 2 lecture sections. Spring 2027: schedule not out yet.
We study algebraic structures which can be associated to topological spaces, and which are invariant under homotopy equivalence. Such topological invariants include homotopy groups, homology groups, and cohomology groups or rings. Possible applications include the classification of Platonic solids, the Brouwer and Lefschetz fixed-point theorems, the hairy ball theorem, the Borsuk-Ulam theorem, and the ham sandwich theorem.
Prerequisites
- Must have completed the following:
- PMATH367 - Topology (0.50)
Antirequisites
None listed.
Leads to
No course lists it as a requisite.
Winter 2027 sections
| Section | Class | Enrolled | Meets |
|---|---|---|---|
| LEC 001 | 6005 | 0 / 25 | MWF 11:30–12:20 |
| LEC 701 | 2354 | 23 / 9999 | Online or by arrangement |
Reviewed on UW Flow
67% liked it35% easy90% useful
From 6 ratings and 4 comments on UW Flow. The most helpful comments, quoted as written, without names. Read them all on UW Flow.
Content is extremely interesting. Probably the most fun I have had at UW. However, it is the most difficult course I have ever taken. Try to make this the last PMATH course you take. Fluency with point set topology and more advanced group theory is extremely helpful.
Mar 2023 · liked it · 1 found this helpfulOn UW FlowRemove this
Difficult course which requires some maturity with algebra. The main theorems proved in the course are beautiful and quite slick with the machinery built up.
May 2022 · liked it · 1 found this helpfulOn UW FlowRemove this
Difficult subject, the definitions go many layers deep and the theorems are hard to remember.
Apr 2017 · didn’t like it · 1 found this helpfulOn UW FlowRemove this
We covered simplicial homology from Munkres' book on algebraic topology (up to Mayer-Vietoris), which is neat and useful, though it felt like we could have gone (much) faster.
Apr 2026 · liked itOn UW FlowRemove this
Discussed on r/uwaterloo
14 posts and comments in 13 threads mention PMATH 467, April 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
UW Math "Must-Take" Upper Year Math Courses 16 points, 10 comments
“What would you say is a useful upper year math course that everybody should take, regardless of their specialization?”
u/Txwelatse: “PMATH 467”
u/MeowntainDuwu: “What major? I can only answer for PMATH. Beyond the required courses: PMATH 453, PMATH 467, PMATH 446, PMATH 441”
Winter 2024
Interesting pmath/co courses? 3 points, 2 comments
“What are some particularly interesting pmath/co courses? I don’t have space to take many of them, but wish to maximize my utility. One course I know I want to take is pmath 351. Any other suggestions?”
u/Alone_Letterhead2671: “There're two routes you can take with 351 in hand: 1. PMATH Analysis route: PMATH 450, 451, 453 which are pretty popular. …”
u/Stranger_Natural: “… Also, 351 offerings typically teach some level of topology, and if you take pmath 347, you can take algebraic topology (pmath 467). The new topology course (pmath 367, I think it’s being offered starting next fall or something?) might also be interesting to you. …”
Fall 2023
How do I move on from her? 1 point, 17 comments
u/Away_Recording1162: “Take PMATH467.”
Winter 2023
Nearest parking to ML. 1 point, 3 comments
u/azuwaterloo: “I'm going to have PMATH 467 next term and it's (for reasons I'll never know) in ML (Modern Languages). What's the nearest parking spot to the building?”
Spring 2022
Easiest course offered by UW? 13 points, 20 comments
u/PD_enjoyer: “Pmath 467 you just play around with playdough all day”
Spring 2021
PMATH 467 Course Notes 4 points, 1 comment
Spring 2020
Fuck this bird course bullshit: what is the theoretical hardest term you could do? 49 points, 27 comments
“You're limited to a maximum of 5 classes, you're only allowed to do courses that would be allowed for the program/major you pick. …”
u/cabbagemeister: “… PHYS444 (Intro Particle Physics) PHYS476 (General Relativity) AMATH474 (Quantum Theory 3) PMATH467 (Algebraic Topology) PMATH965 (Symplectic Geometry) The winter will definitely be harder, and I think constitutes one of the hardest terms a math phys major can do. …”
Fall 2018
Manageable course load 2 points, 6 comments
u/PrinzChiyo: “So I have pmath467 cs467 cs480 cs462 co487 co444 Is co487 bird enough to let me survive the term?”
Winter 2018
what are the easiest and hardest 400s PMATH courses? 6 points, 5 comments
“I want to challenge myself with a hard course, and after that reward myself with an easy course.”
u/OC_Poon: “PMATH 467, most trivial course offered at UW.”
Fall 2017
CS vs C&O for research/academia 6 points, 10 comments
“In your opinion, which is more important for machine learning/deep learning research? I'll probably combine one of them as a minor with Stats and Pmath, I'm leaning more towards C&O because I feel …”
u/GenesisTK: “Atm, neither really, both are strong fields but deep learning is essentially non-convex opt, so unless you figure out a way to find the global minima of non-convex functions using C&O, I'm not sure …”
u/GenesisTK: “… PMATH 351, PMATH 451 (if you can override 450, which a lot of people do) and PMATH 453, PMATH 467, for a major, you're going to need a lot more courses like Complex Analysis, Galois, and a few others. …”
PSA: Course selection has started 47 points, 45 comments
“Course selection is open from now until next Tuesday. For first years: this is NOT first come first serve. Take the time to look through and consider what you want to take. …”
u/waste420: “Anyone know what happened with some of the pmath courses listed on the adm courses site? They listed PMATH441 and 467 for next term, but the courses are not showing up in Quest's course selection.”
Spring 2017
What to read before taking PMATH 467 (Algebraic Topology) 4 points, 3 comments
u/osw_datboi: “The only pmath courses I have taken are the prerequisites (347 & 351). The old course outline suggest reading Munkres' point-set topology, but maybe there are more stuff the prof assumed. How does 467 compare with other 4th year pmath courses? Would taking 348 and 365 help?”
Check it elsewhere for Fall 2026
- Undergraduate Calendar, 2026–27The official entry
- Requirements for Fall 2026Waterloo’s requisite checker
- Schedule of Classes, Fall 2026Instructors, rooms, live seats
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