PMATH 348Fields and Galois Theory
- 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: scheduled, 2 lecture sections. Spring 2027: schedule not out yet.
Unique factorization domains, Gauss's lemma, and Eisenstein's criterion. Fields, algebraic and transcendental extensions, minimal polynomials, splitting fields, and the structure of finite fields. Galois theory. Solvable groups and the insolvability of the quintic.
Prerequisites
- Must have completed the following:
- PMATH347 - Groups and Rings (0.50)
Antirequisites
None listed.
Leads to
Winter 2027 sections
| Section | Class | Enrolled | Meets |
|---|---|---|---|
| LEC 001 | 5852 | 0 / 96 | MW 08:30–09:50 |
| LEC 701 | 2302 | 57 / 9999 | Online or by arrangement |
Resources
Around the web
Found by uwloo’s link finder, which checks that each page names PMATH 348.
- notes.html Course notes · math.uwaterloo.ca · from Stephen New’s site Remove
- pmath348-lecture-notes: Lecture notes from the winter 2024 offering of Fields and Galois Theory (PMATH348)… Course notes · Winter 2024 · github.com · by DanielJHorton on GitHub Remove
Reviewed on UW Flow
96% liked it52% easy79% useful
From 49 ratings and 18 comments on UW Flow. The most helpful comments, quoted as written, without names. Read them all on UW Flow.
Good course. Despite the name "Galois Theory" it's mostly build up to it with endless work on field extensions, but algebra is nifty and it's worth looking at. Proving irreducibility kind of sucks but most of the course is interesting.
Mar 2014 · liked it · 2 found this helpfulOn UW FlowRemove this
Galois theory was so great. Field theory was a bit less interesting but necessary for handling the Galois portion of the course.
Apr 2017 · liked it · 1 found this helpfulOn UW FlowRemove this
I did not internalize the concepts from 347 at all, but 348 made everything fall in place and provided good motivation and context. Entire course builds up to Galois correspondence and is super satisfying!! Started the course thinking I'm not an algebra person, came out of the course wanting more algebra. Love it, highly recommend, makes the pain of 347 worth it!!
May 2026 · liked itOn UW FlowRemove this
Great (and fairly easy) course with Yu-Ru. Galois theory is super cool, and at least for me I found the machinery that we developed to get to Galois theory was interesting in its own right.
Apr 2026 · liked itOn UW FlowRemove this
Galois Theory is nice, but it feels like you have to jump through a ton of hoops to get to the actually interesting content. Get ready to learn 11 different adjectives to describe field extensions
Apr 2026 · liked itOn UW FlowRemove this
Discussed on r/uwaterloo
76 posts and comments in 66 threads mention PMATH 348, April 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
CO331 vs. AMath 250 for Co-op Term? 9 points, 6 comments
“Hi, I need to take an online course during my co-op term and can’t decide between CO331 (Coding Theory) and AMath 250 (Intro to Differential Equations). …”
u/amsyed10385: “… The course itself is straightforward if you already learned abstract algebra (any of PMATH 347/348/MATH 145). …”
Spring 2024
Lin alg heavy courses 13 points, 10 comments
“I love math235 and I'm sad that there's no Lin Alg 3. What are some courses that use a lot of Lin alg? Would CS484 or CS480 fit this? CS475 isn't available next term, and I've already taken CS370”
u/Osteospermum: “… PMATH 347 and 348 cover abstract algebra if you liked the theorems and vector spaces. …”
PMATH 347 After MATH 235 7 points, 4 comments
“I’m interested in taking this course after having taken Math 235. Yu-ru is teaching it this Fall which I’ve heard is an easier offering than usual. …”
u/AirPodGoose: “I took pmath 348 with yuru without taking any advanced courses, i got 98 with not that much effort. Easy assignments, and she tell you whats coming on the 2 term tests, including the theorems you should memorize”
Fall 2023
Advice for CS major who doesn’t like CS? 30 points, 7 comments
“I’m a 4A CS major who will graduate in 2025 on my current plan, but I haven’t found a job the past two years and throughout this degree I found I don’t even like CS that much. …”
u/Ok_Meeting_2592: “… \- pmath 352: Also offered in the spring and winter \- pmath 347: Offered Spring and Fall \- pmath 348: Offered Fall and Winter \- pmath 365: Offered Winter (take it next term!) \- pmath 450: Offered Winter \- 3 more 4xx pmath courses, depending on your interests. …”
Taking 2 courses at the same time 11 points, 9 comments
u/Worgen660: “Next term I want to take PMath348 and Math249, which are both at the same time MWF 8:30 - 9:20. However, I would have to override into Math249. Who do I contact to make this possible? Thank you.”
Spring 2023
Polynomial-related math courses 1 point, 5 comments
“What are some math courses that focus on theory about real polynomials?”
u/LostPizza3290: “Maybe PMATH 348(Galois theory)”
u/XxSniipr0XDuoxX: “Pmath348 (Galois Theory) , loved this course!”
Should I consider additional MATH/CO/etc courses for CS? 7 points, 4 comments
“Is CO 250, or any other non-compulsory second year and up math dept. courses, useful or practical enough that should be taken for the CS field (broad ik, unsure what area to focus on in the future)? …”
u/chonglibloodsport: “If you're interested in programming language theory, functional programming, and type theory then an abstract algebra course can be useful. PMATH 334, 336, 347, 348 are all fine choices.”
Winter 2023
Is taking math courses worth it for cs major? 8 points, 12 comments
“1B cs student here. Would you recommend taking more math courses beyond the compulsory ones? I've heard some ppl say that having a more in depth understanding of linear algebra helps with computer …”
u/dexdex21: “Yes, basic software development has little to do with that, but I still recommend taking some additional math courses. If you want to go into deeper fields in CS, it can be useful. …”
u/dexdex21: “… I'd say the course progressions in these areas are roughly (only up to 3rd year because I'm not familiar with 4th year courses) Algebra: math136->math235->pmath347->pmath348. …”
How to pick a math major when I don’t know what to do in the future 0 points, 1 comment
“Entering my 2b next term and am still in undeclared math, with no idea what I want to do in the future. …”
u/pinkbestcolour: “… You will also need to take some upper year algebra courses (pmath 347, 348 at the bare minimum) if you want to go into grad school for pure math. …”
Fall 2022
how to balance a heavy pmath load. 13 points, 8 comments
u/Offset_Diagram: “Hi there. Next term I have pmath351 , 352, 365 and 348. I know it sounds like hell and probably will be but I am wondering what your advice is for people who did a huge load like this? Is it possible? Is there ways to make it easier? etc....”
Fall 2021
CO course recommendations 2 points, 3 comments
u/jadedwolf12: “… I already took PMATH 347/348 before taking it, but it's assumed that you don't know it. …”
What was your favourite course in math faculty? 10 points, 10 comments
“and why?”
u/Paul_A_M_Dirac1: “Pmath348 because of prof. Yu”
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