PMATH 331Applied Real Analysis
- Units
- 0.50
- Faculty
- Mathematics
- Subject
- Pure Mathematics
- Cross-listed
- AMATH 331
When it runs
- F24
- W25
- S25
- F25
- W26
- S26
- F26
- W27
- S27
Ran in 5 of the last 7 terms. Winter 2027: scheduled, 2 lecture sections. Spring 2027: schedule not out yet.
Topology of Euclidean spaces, continuity, norms, completeness. Contraction mapping principle. Fourier series. Various applications, for example, to ordinary differential equations, optimization and numerical approximation.
Prerequisites
Antirequisites
Leads to
Fall 2026 sections
| Section | Class | Enrolled | Meets |
|---|---|---|---|
| LEC 001 | 5995 | 13 / 96 | MWF 08:30–09:20 |
Winter 2027 sections
| Section | Class | Enrolled | Meets |
|---|---|---|---|
| LEC 001 | 5969 | 0 / 35 | MW 10:00–11:20 |
| LEC 701 | 2353 | 12 / 9999 | Online or by arrangement |
Resources
Around the web
Found by uwloo’s link finder, which checks that each page names PMATH 331.
- notes.html Course notes · math.uwaterloo.ca · from Stephen New’s site Remove
Reviewed on UW Flow
80% liked it28% easy53% useful
From 10 ratings and 5 comments on UW Flow. The most helpful comments, quoted as written, without names. Read them all on UW Flow.
I liked this course a lot more than I thought I would. A very reasonable amount of content is covered and covers every topic that you would want in an intro analysis course. Definitely leans heavy on the proofs as opposed to calculations, but some applications are presented near the end. There is a lot of content by the end of the course, so it can be hard to keep it all straight. Assignments, midterm, and final were all reasonable. Workload is reasonable to light for a third year PMATH course.
Dec 2024 · liked itOn UW FlowRemove this
Enjoyable class. Typically the class is supposed to be boring, but with this prof it was awesome.
Mar 2023 · liked itOn UW FlowRemove this
Took PMATH 331 with Stephen New in Fall 2020. Pretty difficult, but interesting course. There weren't any lectures, but the notes he posted were decent enough for learning the content.
May 2021 · liked itOn UW FlowRemove this
Good class, but be warned: You can no longer override into 351 having only taken this as a prerequisite.
Dec 2018 · liked itOn UW FlowRemove this
A really interesting, awe-inspiring course. I realized I actually liked real analysis after I took this course. It develops many very useful skills for applied mathematicians.
May 2017 · liked itOn UW FlowRemove this
Discussed on r/uwaterloo
96 posts and comments in 80 threads mention PMATH 331, March 2012 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
pmath 331 final 3 points, 0 comments
u/farmnotpharm: “how was it”
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/AirPodGoose: “AMATH 351/353, PMATH 347, PMATH 331/333/351, PMATH 332/352, AMATH 342, CO 250”
PMATH 331 or PMATH 333 which is easier for FAMR student? 2 points, 2 comments
u/FewEntertainment1066: “I am a FARM student and have stat minor. I wonder which one could be easier if i only want to get a high mark? THANKS!”
Fall 2023
PMATH331 / 332 / 334 1 point, 1 comment
u/whoTouchMySpaghetti: “Anyone have an idea of the difficulty level of these courses and how they compare to one another?”
Easiest 300-400 Math Course? 1 point, 4 comments
“Better if I can take it online. Math course includes ACTSC, AMATH, CO, CS, MATBUS, MATH, PMATH, and STAT.”
u/Kassaking777: “… CO487 if you have time reading the course note (no need to know how to prove and how to compute for final except for some easy techs) PMATH331/AMATH331 should be easy if you did MATH247 before()”
Spring 2023
PMATH 331 or 333 4 points, 13 comments
u/alysha_xx: “While doing course selection, I'm caught between PMATH 333 or PMATH 331 to fulfill one of my degree requirements. I would really appreciate advice on which of the two might be considered easier!”
u/jadedwolf12: “I took neither of them, but as far as I know, 331 is the non-specialist version, so it should be easier. 333 will cover topics with much more rigour.”
u/thehedgepart2: “It was almost entirely (90%+) proof-based and felt extremely dense for a introductory PMATH course. The following are the notes from Stephen New's offering: https://www.math.uwaterloo.ca/\snew/pmath331-2020-F/LectureNotes/ Obviously he could be an exceptionally "pure" professor.”
2B course selection thoughts? 3 points, 6 comments
“2B BMATH CS (Want to do a math minor, prolly stats) Which option would you guys recommend for manageable workload but to also take upper year AI courses sooner? …”
u/KrispyPopcorn: “If you want to get your grades up then why slot in so many tough courses together? Add some birds and moderate courses instead?”
u/ReportSensitive6087: “That’s a good point. I wanted to take all the CS courses + MATH239 so I can take CS341/350 In 3A and either STAT231 so I could take CS486 in 3B or MATH237 so I could take PMATH331/332 in 3A/B.”
Winter 2023
What courses are good for grad school in AI/ML? 2 points, 3 comments
“I’m currently in 2A CS and planning out my courses in the future. I’ve been told recently that if I want to pursue graduate school, I should begin thinking about it now. …”
u/reinforceMe: “Currently also trying to pursue an ml masters. From what I’ve gathered, you wanna take up to CO 463 (the pre reqs are useful for ML too, but take pmath 331 not 351) Then take enough stats for the 4th year ml courses, but take stat 333 too.”
u/meateaterranean: “Why pmath 331 instead of 351?”
Fall 2022
PMATH331 1 point, 0 comments
u/luizloo: “Did Andrew give us a huge curve？Anyone's mark much higher than expected? Otherwise I think I got a 95 on the final which is kinda impossible.”
UW Math Major Declaration 4 points, 8 comments
u/No_Inspector_8321: “… &x200B; Table 1 + the following CS 371 Math 237 Math 239 CO 250 CO 342 CO 351 CO367 CO456 PMATH 336 PMATH331 PMATH332 STAT330 STAT331 STAT332 STAT333 STAT440 STAT437 STAT340 STAT442 AMATH250 MTHEL 300 CS371 CS230 CS234 AMATH250 ECON 212”
Fall 2021
What are your favourite classes at UW 56 points, 87 comments
u/angerygoosepopo: “STAT 333, STAT 240, STAT 441, PMATH 331”
What‘s the difference between PMATH 333 and PMATH 331? 1 point, 11 comments
u/sixrunnerupjames: “The course descriptions are similar. Which course should I take if I wanna learn some basic real analysis? I am a STAT student who is going to apply to grad school (STAT major). I am about to graduate, so I won‘t consider taking PMATH 351 in future terms.”
u/heartuary: “PMATH 351 is real real analysis; continuation of MATH 247. PMATH 333 is materials of MATH 247 for those who took 237 which helps to bridge the knowledge needed to take PMATH 351. PMATH 331 is not really real analysis. Much easier version for non specialists.”
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
- WClassesPast sections back to 2004, and who taught them