PMATH 453Functional Analysis
- 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: not on the schedule. Spring 2027: schedule not out yet.
Banach and Hilbert spaces, bounded linear maps, Hahn-Banach theorem, open mapping theorem, closed graph theorem, topologies, nets, Hausdorff spaces, dual spaces, weak topologies, Tychonoff's theorem, Banach-Alaoglu theorem, reflexive spaces.
Prerequisites
- Must have completed the following:
- PMATH450 - Measure Theory (0.50)
Antirequisites
None listed.
Leads to
No course lists it as a requisite.
Fall 2026 sections
| Section | Class | Enrolled | Meets |
|---|---|---|---|
| LEC 001 | 6276 | 16 / 81 | TTh 10:00–11:20 |
Resources
Around the web
Found by uwloo’s link finder, which checks that each page names PMATH 453.
- Course notes for PMath 453/753, An introduction to Functional Analysis. Course notes · math.uwaterloo.ca · from Laurent Marcoux’s site Remove
- notes.html Course notes · math.uwaterloo.ca · from Stephen New’s site Remove
Reviewed on UW Flow
86% liked it0% easy83% useful
From 14 ratings and 10 comments on UW Flow. The most helpful comments, quoted as written, without names. Read them all on UW Flow.
Insanely difficult course, especially with the Camila Sehnem/Erik Seguin double threat. Assignments were long, technical and challenging and the midterm was way too long. However, this course is possibly the most interesting and fulfilling one I have taken at University. The results are deep and powerful, and the topics interlace very nicely.
Dec 2024 · liked it · 1 found this helpfulOn UW FlowRemove this
Welcome to the final showdown in the analysis sequence! (as Prof. Brannan described it.) The reviews below are no joke, this really is a hard course that guzzles time and energy. In addition to working through the tedious assignments, I was forced to read through a monumental amount of material across various topics, at breakneck speeds, in order to keep up with the specific examples and arguments from class which often drew from the measure theory + Fourier analysis landscape. I am not alone. Several of us took an old version of PMATH450 which did not cover these topics deeply; it was a substantial amount of extra work to bridge the gap. That said, this has been an overwhelmingly rewarding…
Dec 2025 · liked itOn UW FlowRemove this
Hardest class I’ve taken at UW by far. Brannan was okay at teaching it, but I’d recommend a different prof if you can wait. This course felt like taking 3 courses, so beware.
Dec 2025 · liked itOn UW FlowRemove this
Very interesting but hard course, assignments were super long and some needed measure theory (which was not covered pmath 450). You will become a better mathematician at the end.
Brannan was an amazing prof and an incredible person!Dec 2025 · liked itOn UW FlowRemove this
Difficult but interesting. Lots of cool theorems
Dec 2025 · liked itOn UW FlowRemove this
Discussed on r/uwaterloo
76 posts and comments in 65 threads mention PMATH 453, December 2015 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/MeowntainDuwu: “What major? I can only answer for PMATH. Beyond the required courses: PMATH 453, PMATH 467, PMATH 446, PMATH 441”
Most academically difficult term so far? 25 points, 39 comments
“Wondering which year/term was the most challenging for you? Preferably students in engineering or more specifically mech eng.”
u/Unique-Doughnut9096: “3A (math) was the hardest for me. Pmath 451, Pmath 453, Pmath 940, Stat 433, Math 249, Actsci 372. Shit was not fun on top of coop search.”
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: “… PMATH Analysis route: PMATH 450, 451, 453 which are pretty popular. Some topics covered are pretty cool like Measure theory covered in more rigorous version. It's also applicable in lots topic like probability theory, analytics NT, operator theory, optimization, etc. …”
Spring 2023
Easy 300-400 math electives 1 point, 8 comments
“i’ve already taken stat 332,337, Cs 330,338 and Pmath 330. what else is there? heard pmath 340 was not bad on reddit but uw flow says not to take as a bird course. thoughts?”
u/XxSniipr0XDuoxX: “Pmath453”
Easiest 300/400 level Math Courses 1 point, 4 comments
“Hi, I need to take 300/400 level math courses for my degree and was wondering what the easiest courses are. Please let me know! Thanks!”
u/Fatdayuu: “Marcoux’s Pmath453 for sure”
Suggestions for PMath grad courses in 4th year 1 point, 2 comments
u/peevedoldfart: “… This fall, I will be taking PMath 453 (functional analysis) with Blake Madill (I've heard that he's a decent enough prof, if a large assignment load. …”
What are your core courses? 8 points, 11 comments
“Basically title - What are several courses that you think really define your program? Any thoughts on them, and how they went? Looking forward to the discussion (ﾉ◕ヮ◕)ﾉ\:･ﾟ✧”
u/kermit_9_11: “… If you really wanted things that define the program the required courses do a great job (with the addition of pmath 453 functional analysis!) That being said, pmath 347 is usually the first pmath course people take. …”
Winter 2023
Should I go to Waterloo?? 7 points, 35 comments
“Basically what the title says pls help im so confused. &x200B; I'm in hs right now and I can't really decide which uni I want to go to (for STEM things). …”
u/Acrobatic_Guidance14: “If you plan to do your masters don't come to Waterloo. Go to a 2nd tier uni like York or some noname Canadian university where you'll be in the top 5% of your class and get a 90% average. …”
u/blank_anonymous: “… If you compare what pmath 453 with Laurent Marcoux covers to any functional analysis course anywhere else (other than UofT/UBC/maybe McGill), the difference will be enormous. …”
Need some insight on the easiest bird courses 1 point, 5 comments
u/jadedwolf12: “PMATH 453”
Fall 2022
Bird Math courses 0 points, 6 comments
“Hey I need one Math bird course to graduate. I have already taken Math 135, 136, 137, 138, STAT 230. I am stuck between CO 227 or Math 207. Any suggestions?”
u/Burgundy_Blue: “Pmath 453”
Pmath 453 Classmates 1 point, 0 comments
u/Happythoughtspepesad: “Is anyone taking pmath 453 this fall, and wants to form a group to discuss assignments?”
Spring 2022
Which course has the hottest boys 57 points, 107 comments
“for context, im a girl in cs. i am sick of guys in my program. like i mean it. \+ i really would prefer if its a bird course <3”
u/Stranger_Natural: “pmath 453”
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
- Quest Class SearchWhere you enrol
- Course outlinesSyllabi from past terms (UW login)
- UW FlowStudent ratings and reviews
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