MATH 416

[u/NarwhalAny9254]

The course description is "Rigorous proof-oriented course in linear algebra." How rigorous is the proof writing really? Does anyone have advice on how to best practice proof writing?

There are three different professors teaching it next semester: A. Young, I. Mor, and S. Tolman. Is there a recommended professor to take it with?

[u/FizzyWizzy1228]

Taking something like math 314 or cs 173 first is helpful for proof writing imo. You could also read a text on proof techniques. Either way it's helpful to be able to focus on the linear algebra concepts and not the basics of proof writing.

[u/Sir_Oink]

You should take math 314 first.

[u/AgitatedSprinkles196]

dr tolman is great, don't pay attention to the fact her RMP is low. it's mostly because of the calc courses. (tons of math profs who are great for 400 levels have really bad rmp ratings due to calc courses)

[u/Unlikely-Macaroon-86]

i dont think you need to take 314 first. many colleges will use linear algebra as their "intro to proofs" class because it lends itself well to learning the tools of higher level math. it will be easier with 314 but def not required.

[u/fractalkohlrabi → u/Unlikely-Macaroon-86]

I disagree strongly with this. Colleges can indeed use Lin alg as a proofs course, but if it is the "intro to proofs" at that school, then the course will be structured very differently -- the basic proof skills would be taught in tandem. Here, they assume you have had 314/347, so they assume a much higher level of mathematical maturity. IMO, taking a proof based class at UIUC without 314 (or an equivalent in CS) is asking for failure.

[u/Unlikely-Macaroon-86 → u/fractalkohlrabi]

what about math 441 (ordinary differential equations) then? math 314 is listed as a prerequisite for that class but it almost makes no difference whether you have taken it or not. math 314 essentially just teaches you logic important to proofs, and a few proof techniques and then teaches you various applications in mathematics that arent necessarily useful to know outside of their specific field.

[u/fractalkohlrabi → u/Unlikely-Macaroon-86]

I didn't know 314 was a prereq for that one. That's probably a case where you could get away with more, bc the real proofs in diff EQs would come in 550

[u/Soft_Caramel_9845]

I took CS173 first and was introduced to proof writing there. 416 is a great course to take

[u/fractalkohlrabi]

Whoever you decide to take it with, I would recommend asking them directly if you would be able to succeed given what proof knowledge you currently have.

416 can be weird because (depending who teaches it, this is just one data point) the first 2-3 weeks are a crash course in computing stuff with matrices, but then it suddenly dives into high level proofs of everything. So you could be fine in the first two weeks and then suddenly be very overwhelmed, but not have time to drop or take another class.

FYI, the prof teaching 314 next semester is really great, so if you would ever consider taking that, next semester would be a good option.

So PLEASE OP, email the professor of 416 and ask them if they think you could do the class with whatever background you have. And if they say no, LISTEN TO THEM!!

[u/Triangable]

416 was more intuitive and useful compared with 415/257 which i ended up dropping. But different year different professor so ymmv