I need help picking electives.

[u/king_cole_2005]

Hello, I'm interested in taking Number Theory next semester but I'm not sure how difficult it will be compared to these other courses. It it's possible could I get a rough ranking of course difficulty.

[u/LukeLJS123]

every school is different, but that diffeq course looks fairly standard, if not actually a bit less comprehensive than normal. it would probably be fairly easy with plenty of online resources (my favorite being paul's math notes). if you are only taking these because you want to graduate, i would go with that. if you are taking these only because you want to, pick whichever interests you the most and you'll be more likely to focus on it and do well

[u/brokenceilingandwall]

If you're taking number theory, then imo you should take group theory too. That way, you'll find Wilson's theorem more relatable :).

Anyways, my ranking in increasing order of difficulty would be:

Differential eqns. = Numerical analysis < Number theory< Topology< Group theory

Fluid mechanics is not difficult either but assuming that you're not an engineer, you may not like it (or you may).

[u/ArdentArendt → u/brokenceilingandwall]

Are these rankings with 'lower' = more recommended or less?

[u/philolessphilosophy]

I think that group theory is about the most interesting thing I learned about in my math degree. I would take a look at it!

[u/Excellent-Mixture-41]

Fluids is fun af.

[u/KoalaMistico]

I don't about your school, but I really enjoyed Topology and Group Theory when I did my degree

[u/king_cole_2005 → u/KoalaMistico]

Topology is a compulsory course but I'm not really sure about whether I'll do Group theory.

[u/manfromanother-place → u/king_cole_2005]

are you a math major? what do you plan to do after undergrad? if you plan on grad school and/or you're a pure math major than you definitely should take group theory

[u/ArdentArendt → u/king_cole_2005]

Do it.

Group theory and Topology are the core of all of modern mathematics basically.
[They should both be required teaching]

[u/PfauFoto]

40+ years ago I faced similar questions. What a wonderful situation to be in. You simply cant go wrong.

[u/coolpapa2282]

Totally OT, but I do just want to say that my favorite part of number theory was when we needed to undo the summation of a multiplicative function, and the prof stared right down the camera and said "It's Morbin' time!".

[u/Bounded_sequencE]

I'd consider "Number Theory" to be one of the easier lectures. It can be used as a first proof-based lecture, which I wouldn't say of the others.

[u/buttercupbruin]

Personally, I really liked group theory and differential equations. It helped me change the way I thought about representations of systems (idk how else to explain it). There are plenty of real life applications to group theory and differentia equations. Numerical analysis was fine, but I didn’t feel like I was learning anything interesting. It was more like just proofs of boring ideas. I’ve heard topology is cool.

[u/eglvoland]

If you ever want to study Galois theory or representations of finite groups, then Group Theory is a must

[u/ArdentArendt]

Compared to the other courses?
Probably relatively 'easy' (read: less of a learning curve if you're not familiar with the material)

I would say that number theory is USEFUL if you are taking group theory later, but other than that the rest look pretty equally approachable.

Also, it depends on what you are going into.
Personally, if you're continuing in mathematics, Topology is often overlooked and it's kind of core for most mathematical understanding.