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PMATH 333Introduction to Real Analysis

Units
0.50
Faculty
Mathematics
Subject
Pure Mathematics

When it runs

  1. F24
  2. W25
  3. S25
  4. F25
  5. W26
  6. S26
  7. F26
  8. W27
  9. S27

Ran in 5 of the last 7 terms. Winter 2027: scheduled, 2 lecture sections. Spring 2027: schedule not out yet.

This course is designed to enable students who did not take the MATH 147/MATH 148/MATH 247 sequence of advanced calculus courses to fill in the missing gaps from analysis needed to prepare them for studying further topics in analysis in PMATH 351/PMATH 352. Topics discussed include: completeness of the real numbers, supremum and infimum, sequences and the Bolzano-Weierstrass theorem; the topology of Euclidean space: open, closed, connected, and compact sets, the intermediate value theorem, the Heine-Borel theorem, and the extreme value theorem; continuity and uniform continuity, sequences of functions and uniform convergence; the Riemann integral over rectangles and the integrability of continuous functions.

Prerequisites

  • Complete 1 of the following
    • Must have completed the following:
      • MATH148 - Calculus 2 (Advanced Level) (0.50)
    • Earned a minimum grade of 70% in each of the following:
      • MATH128 - Calculus 2 for the Sciences (0.50)
    • Earned a minimum grade of 60% in each of the following:
      • MATH138 - Calculus 2 for Honours Mathematics (0.50)

Corequisites

  • Complete all of the following
    • Completed or concurrently enrolled in:
      • MATH237 - Calculus 3 for Honours Mathematics (0.50)
    • Completed or concurrently enrolled in at least 1 of the following:
      • MATH235 - Linear Algebra 2 for Honours Mathematics (0.50)
      • MATH245 - Linear Algebra 2 (Advanced Level) (0.50)

Antirequisites

  • Not completed nor concurrently enrolled in any of the following:
    • MATH247 - Calculus 3 (Advanced Level) (0.50)
    • PMATH351 - Real Analysis (0.50)

Leads to

Fall 2026 sections

Enrolment from UW Open Data, which can trail Quest by up to two days. Instructors and rooms: Schedule of Classes.
SectionClassEnrolledMeets
LEC 001634476 / 96MWF 10:30–11:20

Winter 2027 sections

Enrolment from UW Open Data, which can trail Quest by up to two days. Instructors and rooms: Schedule of Classes.
SectionClassEnrolledMeets
LEC 00161120 / 75MW 13:00–14:20
LEC 701238245 / 9999Online or by arrangement

Resources

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Reviewed on UW Flow

75% liked it39% easy70% useful

From 59 ratings and 29 comments on UW Flow. The most helpful comments, quoted as written, without names. Read them all on UW Flow.

  • i tried so hard to convince myself i liked this class. it didnt work. at least it was easy with leigh foster

    Apr 2026 · didn’t like it · 2 found this helpfulOn UW FlowRemove this

  • Essentially covers what MATH 147,148,247 taught that was missed in the corresponding regular courses. This course is not so easy, and the professor really matter. I personally had an *extremely* frustrating time with the teaching team when I took the offering (Late Piazza posts, no typed course notes, extremely delayed solutions to assingments). We got our marks for A4 back a month after we submitted it and our marks for A5 & A6 on the night before the Final (!!). Just do a thorough background check of the Professor teaching the course before taking it.

    Nov 2022 · liked it · 2 found this helpfulOn UW FlowRemove this

  • This review is for people who took MATH 147 and MATH 148, and is also a review of the instructor Leigh Foster, because she doesn't show up as an option for professors in UW Flow. Tl;dr as the course description suggests, this course is not meant for people who took advanced calculus in first year and you are most likely better off in MATH 247. A lot of the topics that were covered in MATH 147 and MATH 148 are presented in this course for the first time for people who took MATH 137 and 138. For people who took advanced, a lot of the course will be stuff you've seen already. There are some new topics too, and under a normal offering there is likely a good number of new things to see in this…

    Apr 2026 · didn’t like it · 1 found this helpfulOn UW FlowRemove this

  • Highest grade in my university career. Didn't learn a thing. Incredible stuff.

    Apr 2026 · didn’t like it · 1 found this helpfulOn UW FlowRemove this

  • Cool course if you like proofs for theorems in Math 137 / 138

    Apr 2023 · liked it · 1 found this helpfulOn UW FlowRemove this

Discussed on r/uwaterloo

323 posts and comments in 204 threads mention PMATH 333, November 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

Mathematical Finance 7 points, 5 comments

“I’m a 2B student in Math/FARM, but the courses in Mathematical Finance look way more interesting to me. I know Mathematical Finance is hard, and I don’t have the best grades. …”

u/Outside_Buddy6449: “Did you take the advanced math courses in first/second-year? Those might be the best indicators to your success in math finance. …”

u/Outside_Buddy6449: “… I would suggest trying some of the harder math finance courses to see if those types of courses are for you (STAT 333 and PMATH 333/351 for example), since they are very different from first/second year math courses. …”

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PMATH 333 HELP!!!!!!! 4 points, 3 comments

u/rhinooman: “ok so i feel sick to my stomach knowing that my pmath 333 final is in about two weeks and i still don’t know how to study for this fucking course. …”

u/djao: “PMATH 333 is a gateway to "advanced" math courses like PMATH 351 -- the only other pathway to satisfying the PMATH 351 prerequisites is to take MATH 247, which is an advanced class. As such, it's not just a run of the mill math course. …”

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how hard is pmath333? 6 points, 6 comments

u/Maximum_Boot_2314: “is it comparable to an advanced course in terms of difficulty?”

u/Regular_Maybe5937: “Not sure if anyone can tell you exactly since pmath333 is mutually exclusive with advanced calc 1-3. But the course intends to cover everything from math 147, 148, 247 excluding those already covered in 137, 138, 237. …”

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For those in mathfin 6 points, 5 comments

“I know this is a hard major but what courses do you think are a good indicator of whether or not you’re fit to pursue it? …”

u/rsdyu777: “Iirc theres a lot of analysis in that major, try pmath 333 and see how it is”

u/mreifslp: “Second this, take PMATH 333 as soon as you can.”

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Spring 2024

Computer Science vs Comp engineering which is the harder major at waterloo 1 point, 21 comments

u/Adventurous_Bee_2799: “CE probably harder generally but I think if u take all advanced courses in first and 2nd year in cs + maybe including co255, it becomes much much harder than CE.”

u/Adventurous_Bee_2799: “Why not I suppose? You learn a lot more and get to be surrounded by probably more talented and motivated peers. You also get to skip a couple classes like pmath333 if you are doing a pmath or co double major.”

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Waterloo Exchange Application 8 points, 1 comment

“I am a 2A math student from the University of Waterloo, and I would like to go to Korea/Hong Kong for an exchange program in 3A or 3B. Are there any fellow math students who want to go together? …”

u/PrinceAdebayo: “… PMATH 333) if the course content is similar enough to a UW course, or a generic transfer credit (e.g. PMATH 3XX) if there is no UW equivalent. If you get a direct transfer credit, you can't take the UW equivalent of that course after you return to UW. …”

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Math 147 2 points, 3 comments

“Heyyy I’m an incoming math student this fall. I’ve been scared out of taking 135 but really like the mathfin major which recommends taking math 147 during my first year. …”

u/Osteospermum: “… (If you take 247 you also don’t need to take PMATH 333, and save yourself a course.) At least try it out, you can drop from 14x to 13x any time before the WD deadline (1 month before the end of the term) so there’s no penalty to taking it.”

u/Worgen660: “… Now, to do PMATH351, you can either take MATH247 (Calc 3 Advanced), or you can take MATH 237 (Calc 3) and PMATH333 (Introduction to Real Analysis). …”

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Check it elsewhere for Fall 2026

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