I'm a bachelor math student...

I'm a bachelor math student, I already finished my classes and now I'm (trying) to write my thesis on quiver representations and co-representations. I studied mathematics for the last 7 years and learned a bunch of stuff buy still feel really stupid.

Ask me anything about maths, or quivers or whatever you want .

Pic related, is the stuff Im studying right now. Is not that hard.

bump just in case anyone cares

bemp

as an undergraduate math student can you do anything novel in your thesis yet?

Some students do, other dont. Usually is not important stuff, just minor details in a higly specialized area of maths. Usually what you can do is give your own lengthy exposition of the topic you studied. Give an exposition of the theory in your words/proofs and maybe work out some examples? That's pretty standard. Doing something novel in maths is really hard, and most students work out very particular examples.

does it really just take a bunch of practice to pass a math degree, or do you really have to "get it" to thrive?

Well, if you are taking a calculus class and you reach to the end of the quarter and didn't understand that some sets are neither open nor closed, then maybe pure maths is not for you. I think it just takes practice and a basic interest and ability on math. You don't have to be a genius or anything. Hell, even *I* am about to get my degree!

reason I'm asking is because I want to get into computability research (if possible, if not possible I want to work in some military job), I have a strong CS/infosec background, just need to train my maths. I can do problems, and I can apply math to other areas, like economic problems, and optimisation problems in CS, but I still feel like a brainlet sometimes because I don't "get" the theory behind math

ah, yeah I've been seeing sets pop up more and more out of the blue when I'm working on seemingly unrelated problems, I have much love and respect for pure analysts, and really enjoy reading a distilled version of what they have found out, but I don't think I'd ever be able to run with the big dogs in that respect

>he's an academic

kek

Sets are one of the most natural objects of all mathematics, and there is not much magic to them. Mathematics is founded on sets, basically everything is a set, so you need to be able to manipulate them pretty intuitively. I think the big difference is that we don't tend to see shapes in the plane as "sets", they are just geometric forms. A circle, a ball, a square, whatever. Maybe when you think of a set you think of {1,2,3}. Discrete, finite sets. But shapes and geometric forms are also sets, hell even functions are sets!

you don't have to though. If you want to study computers you don't really need a lot of pure maths, specially pure analysis. Algebra and combinatorics serve you better.

I think I get that, like even a square is just a set of points on the 2d plane, that is continuous between the discrete boundary points

Functions are contiunous, not sets. Also, what you mean by "the discrete boundary points"? The boundary is not discrete, if that's what you mean. A set is discret if you can isolate every element. That is, for each p in A there is an open ball in A that contains only p.

But does the set of all things contain itself?

the "set of all things" is not a set

is there any interesting notion of "higher" quivers, where instead of just vertices and edges, you also have faces, similar to CW complexes?

also how are quiver representations any different from diagrams in the category of R-modules?

The key to succeeding in mathematics professionally is to understand the prerequisite material as second nature. Otherwise, you'll end up reinventing the wheel, which is not what you want for novelty, but is perfectly fine as a hobby. Other than that, it's really a matter of how much time you put into it. Oftentimes, seeing a solution is much easier than getting to it. On the way you there you might find out it's not what you were looking for. At this point, how much of this difference in speed in ruling out or confirming solutions can be attributed to intelligence vs random chance is unclear. Is a more intelligent person faster, better at picking good routes, better able to construct a larger picture, less distracted, more novel, had better instruction, etc.? Without dedication to the field, intelligence really doesn't matter. I hope this offers some clarity in the manner.
Also, don't focus on your colleagues' progress. Some people are great at learning, but that often doesn't translate into being a good researcher. Many a "star" has ended up being useless deadwood without a pipeline. If you do become a star, don't let your advisors coddle you. Helping your colleagues is a great way to test your understanding of the material and is very important as a researcher as your job is to not only discover novel mathematics, but to convince others in your field that you have done so.
>I don't "get" the theory behind math
If you don't understand something, you certainly won't understand that something if you don't try to understand that something. It may be daunting, but you have to start somewhere to get somewhere else.

I don't know of any, sorry, but it seems interesting. I think it might be in line with 2-categories and so on. In fact you can see categories as a kind of quiver, so I guess 2-categories are the thing you describe.

Well in a quiver representation at each vertex you have a vector space, and the whole thing, including it arrows, is a module over the path algebra. I think in a diagram each point is an R-module instead of a vector space.

How/why have you been doing an undergraduate for 7 years?

I had to retake a lot of classes that I failed on my first try and also had to work inbetween.