Grad student Adam Martens has kindly allowed us to post a breakdown of math courses for the upcoming winter term. You can also read the original Reddit post and the ensuing discussion!
These are the remarks of one person and do not represent the opinions of the entire UMS!
Here is a somewhat quick breakdown of most of the math courses that are offered in WT1 2020. I made a similar post last year but I figured I would make a new one that may be more relevant. A few things to keep in mind:
as of today, no one knows who is going to be teaching which courses. Having a particularly good/bad prof will drastically change your experience of the course. When we do know who is teaching what, make sure you use RMP for a general idea but remember that site is very unreliable.
everyone will have different experiences with the same course. I personally struggled through Group Theory (322) and studying algebra still gives me PTSD. At the same time, I have friends that thought that 322 was a breeze.
100/102/104: All three of these courses cover basically the same material just with slightly different applications. Some people claim that 104 is the easiest but imo, they're all about the same. Ultimately, the trick with Calc 1 is to just practice. The math department has TONS of old final exams from these posted online and you can find many of the solutions on various websites. Start practicing early and practice often. An A+ is readily available but you'll have to work for it. Despite being basically the same material, these courses are MUCH harder than HS calculus. Just cause you were a hot shot in your high school calculus class, doesn't mean that you'll breeze through Calc 1 at UBC.
110: I really don't understand how anyone can manage to drag out the topics of Calc 1 over 2 semesters but here we are. Is this course easier than 100? Yes but only because you have more time. Keep on top of the weekly work. If you don't you can still easily fall behind.
120: This course is HARD but extremely fun. It remains one of my favorite courses to this day. It is full right now, but some people will definitely drop as the class gets started. I would only recommend this class if you were one of the top math students in your HS and you really want a challenge, or if you intend to pursue math related topics. Some advantages to this class is that the grades for honours courses are usually significantly higher (avg around 75 compared to ~67 for 100) and that it is usually taught by some of the best profs that our department has to offer. If anyone is reading this from when I was your TA for this course, shoot me a message. I'd love to know what you're up to now.
200: This course is typically pretty heavy but not a heck of a lot harder than first year calc. Again, the trick is to just put the time and effort in. There are tons of practice problems and practice exams to be found online. This course isn't inherently challenging, but it can be very easy to fall behind. Stay on top of the weekly work/exercises. If there is WebWork, NEVER just plug the problems into Wolfram Alpha. Instead, take the time to struggle with the problems and work it out for yourself. The webwork is never worth very much of your grade so it doesn't really matter if you don't finish them. Don't lull yourself into a false sense of security by using technology.
215: Turns out that this is an incredibly important subject (too bad no one really tells you that in second year). It is quite easy to get an A in this class if you just pay attention and do the HW. When I took it, the class was less than 1/2 full and the instruction was pretty slow. I ended up just playing on my phone most of the class so I don't really remember much of it unfortunately. You should find this class easier than 200.
220: If you're at all familiar with proofs, this class is going to be quite easy for you. If you've never done any proofs, you may end up struggling a lot here. You can expect weekly homeworks, either 1 or 2 midterms and a final. The final is usually worth 60%+ of your grade but that may be different this year with things online. If you're wondering how difficult you'll find this, I recommend looking at HW 1 from a previous offering. If you can complete it all without too much difficulty, then you'll be find in this course.
221: I wish someone would have told me that I would use Linear algebra literally every single day in my (young) math career and that it is probably the most important stream of math (maybe more important than calculus). There is a reason why this class is required for so many different majors. That being said, you may not see the applications until a few years after you take this class. I encourage you to pay very close attention if you're taking this because I guarantee that you'll be using it later. It is very hard for me to speak to the difficulty of this class as it can vary so much from person to person. You can very easily succeed if you stay on top of the concepts.
223: If you took 120/121, you should find this course to be about the same difficulty. If you haven't taken any other honors courses and you want to try one, this is probably the one to try first. It will be quite challenging, but very rewarding.
226: This one can drastically vary depending on the prof. Again, if you did well in 120/121, then you'll do fine here. Personally, this course was one of the easiest honors classes that I've taken, but I think that is because of the prof. I later was a TA for this course with a different prof and it was substantially more difficult.
253/254/255/256/257/258/264: I've literally no idea why any of these courses exists... they're just cross listed with other math courses and are reserved mostly for engineers. oh well...
300: complex analysis remains one of my favorite field of math to this day. Everything just works out and fits together so nicely (when compared to regular calculus which is so messy). I highly recommend taking at least this class... you should also consider taking 301 or 440 if you feel comfortable. As far as difficulty, it should be about the same as 200.
302/307/316/340/341: I group these together as I think they're about the same difficulty level. If you're a math major or just like math, these courses shouldn't be a big issue for you. You can expect weekly assesments (either HW or quizzes) and a final exam with a high weight. I personally recommend 302 over any of the others. I think it is the most useful. 340 is really applied which doesn't really interest me (I don't find it very exhilarating solving a bunch of linear systems over and over). I've never actually taken 307 or 316 but I hear that they are pretty simple. 341 was very straight-forward when I took it but I think that was the first year it was offered so it may have gotten harder.
312: number theory can be super cool but can also be quite hard. I don't know how this course relates in difficulty to the other 3xx major courses as I took 437 instead but I hear that it is probably slightly harder. This is definitely a must-take if you're a math major. If you are confident, jump right into 437 instead. That was a fun ride.
320: This course is often quoted as being one of the hardest undergrad classes at UBC. I would say that it is very hard for most students. There are a handful of students who have been familiarizing themselves with this material for a while and find the course to be a breeze, but these students are few and far between. Personally, I took 120,121,226,227 and did quite well in all of them; but when I got to 320, I felt somewhat out of my depth. I actually failed a couple homeworks (which was not like me at all). With a lot of hard work and perseverance, I ended up doing OK. The point is, this course lives up to its reputation as being super challenging. There have been several posts giving tips in how to succeed in this class, so I recommend looking there. The one tip I have is to do ALL the Rudin problems before the tests. Often they are copied word-for-word on the exams.
322: This course can differ a lot depending on the prof teaching it. It can range from being as challenging as 320 to being much much easier. When I took it, I was also taking several other hard classes and fell behind and I found it hard to keep up with the material. This class is really the first time that you will encounter purely algebraic math which can be fairly jolting for some people. I highly recommend doing pre-lecture and post-lecture readings for each class. This will help ingrain the material in your head.
The other 3xx classes are either second term classes or are cross listed with classes already listed here. I won't comment on any 4xx classes as if you're taking one of those, you surely already know what you're getting yourself into. If anyone has anything to add, or disagrees with any of my comments, I'd love to hear it. Good luck in your math courses this term everyone!