PMATH 465Smooth Manifolds
- Units
- 0.50
- Faculty
- Mathematics
- Subject
- Pure Mathematics
When it runs
- F24
- W25
- S25
- F25
- W26
- S26
- F26
- W27
- S27
Ran in 4 of the last 7 terms. Winter 2027: not on the schedule. Spring 2027: schedule not out yet.
Smooth manifolds, smooth maps, and tangent vectors; the tangent and cotangent bundles; vector fields, tensor fields, and differential forms; Stokes' theorem; integral curves, Lie derivatives, the Frobenius theorem; de Rham cohomology.
Prerequisites
Antirequisites
None listed.
Leads to
No course lists it as a requisite.
Fall 2026 sections
| Section | Class | Enrolled | Meets |
|---|---|---|---|
| LEC 001 | 6244 | 18 / 81 | MWF 13:30–14:20 |
Reviewed on UW Flow
100% liked it43% easy75% useful
From 8 ratings and 6 comments on UW Flow. The most helpful comments, quoted as written, without names. Read them all on UW Flow.
This is a very difficult class overall, regardless of who’s teaching. Being invested in learning about manifolds is crucial, otherwise it just feels like you’re at a hot dog eating contest struggling to get down your 10th glizzy
Dec 2022 · liked it · 2 found this helpfulOn UW FlowRemove this
grades take forever to come out
Jan 2026 · liked itOn UW FlowRemove this
Ruxandra is an amazing professor and person too. Her office hours were incredibly helpful and she’s very kind. I wish I did better on the final but I just got handed an unfortunately terrible final schedule.
Dec 2025 · liked itOn UW FlowRemove this
With Doug Park, who is a nice prof but maybe too easy. Geometry and manifolds are awesome and cool, love the topic. We followed Lee, Introduction to Smooth Manifolds nearly verbatim.
Dec 2024 · liked itOn UW FlowRemove this
Content is extremely interesting and useful for almost all advanced subjects in geometry. Seeking out motivation is super useful or else it just feels like a bunch of abstract nonsense.
Dec 2024 · liked itOn UW FlowRemove this
Discussed on r/uwaterloo
13 posts and comments in 13 threads mention PMATH 465, October 2011 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.
Spring 2023
Suggestions for PMath grad courses in 4th year 1 point, 2 comments
u/peevedoldfart: “… I have the prerequisite material (I did PMath 365 & 465 last year, will have the whole analysis sequence, and most of the other algebra courses), but am kind of wary about PMath 833. …”
Spring 2022
Any good PMATH course recs for physics? 6 points, 6 comments
“I'm a second-year Math-Phys student looking for some good PMATH courses that accommodate theoretical physics and its framework well (for a minor). …”
u/AirPodGoose: “PMATH 336/334/343/347/365/465 can be good courses, u don’t have a lot of options for pmath electives since you are in math phys (and assuming you take 5 courses per term) but a minor is doable with no problem.”
Fall 2021
Anyone here take PMATH 465 in Fall 2019? 3 points, 2 comments
u/FortyNotes: “If anyone here has Stephen New's notes for this class, please share them as I don't have mine anymore. I am going back to school this year and am reviewing some undergrad stuff (I know I could use a textbook but thought it was worth trying here first). Thanks.”
Winter 2021
What course teaches Gauge Theory? 1 point, 5 comments
u/Paul_A_M_Dirac1: “Are you interested in pmath gauge theory or physics? If its pmath then 965 teaches gauge theory”
u/yet_another_lemma: “… You need a lot of background to do the mathematician's take on gauge theory; PMATH 347/365/465 are absolutely necessary, but you'll also probably want a course on Lie groups (of which there is no regular one; it's offered sporadically as a PMATH 7xx course). …”
Fall 2020
Anyone has exprienced an undergraduate math research? 6 points, 8 comments
“Hello everyone, wish u all have gone through a wonderful weekend. I am a 3B math student and haven't declare the major yet. …”
[deleted]: “Find a prof you want to work with around 5-6 months before your term would start, come to an agreement with them, then apply for an NSERC USRA grant with the help of the faculty. …”
[deleted]: “… If you want to do work in gauge theory but haven't taken PMATH 365 and PMATH 465 yet, you might spend the whole term learning the background material instead of doing research (which is relatively common as an outcome to a USRA, but it doesn't have to be that way). …”
Fall 2019
I think I learn better when studying myself 32 points, 7 comments
u/cabbagemeister: “… I find lectures either too slow or not productive, except in some cases where the lecture is a good pace (such as pmath365/465 have been) Self study is totally realistic in classes where there assignments. The assignments keep you from falling behind as long as you do them. …”
Spring 2019
Can more new grads post their undergrad stats please? 26 points, 64 comments
“They're fun to read.”
u/snewdity: “Since you asked so nicely, here you go: Program: PMATH Highest grade: 9-way Tie: MATH 147, PHYS 121, MATH 146, STAT 230, PMATH 351, PMATH 352, PMATH 465, PMATH 950, SCI 238 (100) Lowest grade: ENGL 109 (78) Lowest PMATH course: PMATH 347 (90) Favorite PMATH course: PMATH 433 …”
Spring 2018
PMATH 365 and 465 2 points, 3 comments
u/datphysboi: “I will be taking these courses in the future and was wondering if anyone know what the required textbook is or if anyone has any resources that can help me prepare beforehand thanks!”
Fall 2017
Any way to disable UWCourseLinker from posting? 16 points, 26 comments
“posting a reply to my comment I find the bot annoying.”
u/Jackhofmann: “PSYCH 483 PSYCH 484 PSYCH 485 PSYCH 486 PSYCH 490R PSYCH 499A PSYCH 499B PSYCH 499C PSYCH 621 PSYCH 630 PSYCH 677A PSYCH 704A PSYCH 704B PSYCH 707 PSYCH 710 PSYCH 714 PSYCH 717 PSYCH 720A PSYCH 721A …”
u/Jackhofmann: “… PMATH 331 PMATH 336 PMATH 340 PMATH 347 PMATH 351 PMATH 440 PMATH 445 PMATH 451 PMATH 453 PMATH 465 PMATH 499 PMATH 651 PMATH 665 PMATH 740 PMATH 745 PMATH 753 PMATH 930 PMATH 940 PMATH 950 PMATH 990 PORT 101 PS 611 PS 614 PS 621 PS 624 PS 625 PSCI 100 PSCI 231 PSCI 252 PSCI 255 …”
Winter 2017
How is Waterloo Physics? 4 points, 19 comments
“Hey so I got in for Physics and Astronomy at Waterloo back in like December, before I did really shitty in grade 12 physics. Is it still possibke to survive waterlo physics? …”
u/FlagCapper: “I'm currently completing a minor in Physics and I've taken most of the 1st and 2nd year courses, the 1st and 2nd year labs, and lots of higher level 3rd and 4th year courses (Quantum Mechanics 2, 3, …”
u/FlagCapper: “PMATH 465. Eduardo is very generous with his marking, office hours, extra lectures, etc., so you're right that people are doing well, but I don't think it's because it has been easy necessarily. I mean, the final is an open book exam with 150 points marked out of 100. …”
Fall 2014
Why isn't PMATH 365 being offered this winter? 1 point, 4 comments
“Are there any math folks out there who know why PMATH 365 isn't being offered this coming Winter term? …”
u/jasonl5: “… It will instead be offered in Fall 2014 as PMATH 465. Since PMATH 365 is a required course for the Pure Mathematics major, students taking PMATH 465 in Fall 2014 will have it count as PMATH 365 towards the Pure Mathematics major. …”
Spring 2013
What would an ideal course planner be like? 7 points, 17 comments
“My friend and I are building a course indexer that may also have some course planning features in the future. …”
u/Chris24: “There are so many things to consider when planning out courses for future terms -- it's pretty insane. I had also considered writing a course planner web app, but then I looked at the undergrad calendar and realized how confusing degree requirements can be (or at least, …”
Check it elsewhere for Fall 2026
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