PMATH 464Introduction to Algebraic Geometry
- Units
- 0.50
- Faculty
- Mathematics
- Subject
- Pure Mathematics
When it runs
- F24
- W25
- S25
- F25
- W26
- S26
- F26
- W27
- S27
Ran in 2 of the last 7 terms. Winter 2027: not on the schedule. Spring 2027: schedule not out yet.
An introduction to algebraic geometry through the theory of algebraic curves. General algebraic geometry: affine and projective algebraic sets, Hilbert's Nullstellensatz, co-ordinate rings, polynomial maps, rational functions and local rings. Algebraic curves: affine and projective plane curves, tangency and multiplicity, intersection numbers, Bezout's theorem and divisor class groups.
Prerequisites
- Must have completed the following:
- PMATH348 - Fields and Galois Theory (0.50)
Antirequisites
None listed.
Leads to
No course lists it as a requisite.
Resources
Around the web
Found by uwloo’s link finder, which checks that each page names PMATH 464.
- notes.html Course notes · math.uwaterloo.ca · from Stephen New’s site Remove
Reviewed on UW Flow
83% liked it25% easy85% useful
From 6 ratings and 4 comments on UW Flow. The most helpful comments, quoted as written, without names. Read them all on UW Flow.
Took with Xuemiao Chen. This course pushed me to my limits but it was very rewarding to make it through. We covered a lot of topics in this course, and Xuemiao expected us to focus on developing an intuitive understanding of the material by working through examples and problems. The background expected for this class was pretty high, should be comfortable in Galois theory and some commutative algebra, and quite strong in complex analysis. Some basic category theory might be helpful in very specific situations, but was not strictly necessary. Weekly assignments took me about 10-15 hours, some a good bit more, but I spent almost all my waking hours thinking about this class even when not…
Jul 2025 · liked itOn UW FlowRemove this
With Xuemiao Chen it was extremely difficult and time consuming (20+ hours a week on the weekly assignment), and covered a very disparate and confusing set of topics that didn't feel like they had anything binding them together.
Jul 2025 · didn’t like itOn UW FlowRemove this
Took it with Prof.Xuemiao Chen. This was really a course on complex analytic geometry, following something along the lines of "Principles of Algebraic geometry" by Griffiths and Harris. Was extremely challenging, but rewarding. Algebraic geometry is a synthesis of many neighbouring topics like : Riemann surfaces, complex analysis, algebra and differential geometry.
Jul 2025 · liked itOn UW FlowRemove this
Hard.
May 2024 · liked itOn UW FlowRemove this
Discussed on r/uwaterloo
15 posts and comments in 15 threads mention PMATH 464, October 2017 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 2023
About cryptography co-ops! 2 points, 2 comments
u/Aggravating_Dingo_74: “… Also, I would like to know how to prepare for a research term in cryptography, I have taken PMATH 347 (groups and rings) and next term, I plan to take PMATH 464 (algebraic geometry) and PMATH 441 (algebraic number theory) the term following that. …”
Spring 2023
What's like a relatively lightweight elective that doesn't have anything due until the end of May 0 points, 2 comments
“So I'm thinking about adding another elective to make it 6 cuz the 6th course is free, but Im gonna need some time to catch up with the courseload. Any ideas folks?”
u/Flirtacious_cutiepoo: “pmath 464. first assignment is due on the 23rd, it's super fun!!!”
BIRD COURSES !!! 18 points, 26 comments
“No surprise, Spring 2023 courses suck. Please drop below chill courses that are offered this term (can be random, trying to find a final elective).”
u/Sufficient-Cry-1255: “pmath351”
u/LostPizza3290: “pmath 464 is easier”
Winter 2023
Math courses without a midterm 0 points, 3 comments
u/LostPizza3290: “CO 342 had 2 in person quizzes in F22, no idea about the other 3, but CO 446 and PMATH 464 are probably 2 of the hardest undergrad courses offered at uwaterloo, so I don't think it's a good idea to take them without going to lectures.”
What elective(s) are you taking next semester? 6 points, 7 comments
u/LostPizza3290: “pmath 464”
Winter 2022
Most liked and least liked courses in Winter 2022? 6 points, 7 comments
“So exams are almost over, and it's reflection time. Did you take any courses that you especially liked or disliked? Why?”
u/BlazingMuddy-6305: “… PMATH 464: Taking this simply I learn more algebra from more perspective. On the other hand, I think this is the hardest algebra course I take during my whole undergraduate degree. Aside, I get out feeling slightly more algebraically mature. …”
Winter 2021
Easy bird courses 9 points, 23 comments
“Pls recommend me easy bird courses for spring 2021”
u/blank_anonymous: “PMath 464 of course. Algebraic geometry is known as the easiest undergraduate subject”
Fall 2019
What courses are you taking next term? 7 points, 40 comments
u/Spencer_Wilson: “CO 487, CS 240, ENGL 306A, PMATH 348, PMATH 446, PMATH 464, and STAT 241. Keeping a very close eye on the drop deadline.”
PMATH 334 + 336 vs 345 + 346 vs 347 4 points, 9 comments
“I have a really big love for cryptography and want to take CO 485 at some point. While looking at the prereqs, I noticed any of the above 5 courses will do. …”
u/1926toInfinity: “Don’t take it if you are not good at proofs because it’s the most proof intensive kind of course. Even the counting problems require justifications, which are basically proofs. …”
u/1926toInfinity: “If you are really into 485 and cryptography in general, take PMath 464 as well. The last 1/3 of co 485 is all about elliptic curves, which I had extreme difficulty with. I imagine that it would be painful for you not to understand 1/3 of the course.”
Spring 2019
Easy bird courses to take 6 points, 13 comments
u/Nyxeal: “PMATH464”
Winter 2019
Which is harder: Pmath 351 with Marcoux or 464 with New? 6 points, 4 comments
“Gotta pick one.”
u/PMATHbreaker: “Is it New teaching pmath 464 in this fall term? That's cool!”
Fall 2018
Math Courses 11 points, 11 comments
“What were some of your favourite math (ACTSC, AMATH, CO, PMATH, STAT, etc) courses? &x200B; Just realizing that there really aren't that many required for my degree, so it'll be up to me to figure …”
u/G_Wen: “Best Course: Stat 946 Deep Learning. Not for the memes but for structure of the class. Paper presentations + class wide kaggle competition + research paper. Great courses: Stat 444 Function Estimation PMath 464 Algebraic Geometry PMath 351 Real Analysis”
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