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MATH 247Calculus 3 (Advanced Level)

Units
0.50
Faculty
Mathematics
Subject
Mathematics

When it runs

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

Ran in 6 of the last 7 terms. Winter 2027: not on the schedule. Spring 2027: schedule not out yet.

Topology of real n-dimensional space: completeness, closed and open sets, connectivity, compact sets, continuity, uniform continuity. Differential calculus on multivariable functions: partial differentiability, differentiability, chain rule, Taylor polynomials, extreme value problems. Riemann integration: Jordan content, integrability criteria, Fubini's theorem, change of variables. Local properties of continuously differentiable functions: open mapping theorem, inverse function theorem, implicit function theorem.

Prerequisites

  • Complete all of the following
    • Must have completed the following:
      • MATH146 - Linear Algebra 1 (Advanced Level) (0.50)
      • MATH148 - Calculus 2 (Advanced Level) (0.50)
    • Enrolled in Honours Mathematics

Antirequisites

  • Not completed nor concurrently enrolled in any of the following:
    • MATH237 - Calculus 3 for Honours Mathematics (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 001601131 / 50MWF 15:30–16:20
TST 101649031 / 50Oct 22 19:00–20:50

Resources

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Reviewed on UW Flow

95% liked it41% easy94% useful

From 92 ratings and 30 comments on UW Flow. The most helpful comments, quoted as written, without names. Read them all on UW Flow.

  • Started off with some topology then went through all the standard results from 147/148 in multiple dimensions. There were some new results as well, like the inverse function theorem, implicit function theorem, and Lagrange multipliers. All theorems were proved rigorously (except the change of variables one) and sometimes it was difficult to keep up with the proofs. The assignments were difficult but doable, and the exams were also similar. Overall, a satisfying course. I felt like I learned a lot.

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

  • This is not an easy course, even for an advanced course. Professor Al-Faisal described it as 16 weeks of material stuffed into 12. There was a lot to study for the midterm/final, and the assignments were on average 1.5 times as long as Faisal's 148 assignments.
    That being said, it was the best course I've taken at Waterloo.
    Like a matrix with all positive eigenvalues, this course is definitely positive.

    Dec 2025 · liked it · 1 found this helpfulOn UW FlowRemove this

  • This course is amazing, really prepares you for analysis courses in the future. Faisal has clear and excellent teaching skill, with the only complaint being he kept going overtime. Couldn't ask for more really.

    Aug 2025 · liked it · 1 found this helpfulOn UW FlowRemove this

  • This course will make you much better at analysis. Prof. Nica is very humorous, attentive to detail, and rigorous in his proofs. Overall, very informative course and doesn't require an insane amount of effort.

    Aug 2026 · liked itOn UW FlowRemove this

  • Best course I've taken this semester. 100% worth taking, you really expand your brain a lot. Faisal called it "three courses shoved in one". This made me love analysis in the same way Jerry145 made me love number theory

    Dec 2025 · liked itOn UW FlowRemove this

Discussed on r/uwaterloo

331 posts and comments in 256 threads mention MATH 247, June 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.

Fall 2024

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

“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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any 2nd year cs courses that you can take with cs 116? 5 points, 6 comments

“Is there any 200 CS courses that are direct successors of 116? or do I need to take 136 no matter what?”

u/fisherfam: “There are no CS major courses (CS 24X) that are direct successors of CS 116. There are however the non-CS major courses (CS 23X) that have only 116 as a requirement.”

u/CSplays: “This needs math 235/245 and math 237/247, so you wouldn't be able to take it until after 2A anyway.”

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how hard is pmath333? 6 points, 6 comments

“is it comparable to an advanced course in terms of difficulty?”

u/Regular_Maybe5937: “… But the course intends to cover everything from math 147, 148, 247 excluding those already covered in 137, 138, 237. …”

u/rsdyu777: “It's definitely easier than math 247 + it's probably more interesting cuz you don't have to do computational stuff like derivatives/integrals It's basically the epsilon delta part of math 137 on crack”

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Spring 2024

please don’t come here if your plan is to transfer in to a program you didn’t get into 290 points, 43 comments

“lot of posts this week about getting rejected from program x but got deferred/got a different offer from y and wondering if you can transfer to x transfers are exceedingly rare and no matter what you …”

u/djao: “CS is actually overrated. I'm the academic advisor for a non-CS math department, so call me biased or whatever, but really. CS is overrated. I went to MIT, where every major is open to every student. …”

u/notoh: “I definitely see that philosophy shining through (I sat in on your 145 in 2021). It ended being Math 247 that made the same transition happen for me (even up to the specialization, differential geometry).”

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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/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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Winter 2024

Question on double counting 4 points, 5 comments

“Hi guys! I am a math student who's currently considering doing a double major and a cs minor. Since all plans under the math faculty require courses from table 2, would courses from table 2 (e.g. …”

u/Worgen660: “This is an explanation I got from David Jao about triple counting with having to triple count Math247 for PMath, Mathfin, and CO major: &x200B; The rule is: if a class C belongs to an equivalence class of courses which is mandatory for plan X, and is an element of the set of …”

u/Valuable-Brick-6081: “So in this case MATH247 is considered counted once since it's not a usage for either pure math or math fin? What does "The triple counting rule permits up to two usages" mean tho loll?”

u/Worgen660: “Basically Math247 is required for mathfin and puremath, but its an optional requirement for CO. Thus, one usage of Math247 is used for CO since its not a mandatory requirement. …”

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2a course selection 1 point, 3 comments

“is math235 237 stat230 amath250 afm101 and mthel131 doable? I know these courses r not hard courses but there’re 4 maths. Wanna take mthel131 since im not sure if I’ll do actsci or mathfin rn”

u/Stranger_Natural: “looks doable. 333 might be a bit too abstract for 2A, but if you feel confident in your math abilities then go for it.”

u/Minute-Wolverine417: “… just have one more question, I took math147&148 during first year, but since math247 requires both146&148 so I don't think I could take it. …”

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Check it elsewhere for Fall 2026

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