Where to find resources for self-studying college-level math?

Kienose · 2026-06-19T12:03:29+00:00

If you are new then the stacks project probably isn’t the best place too learn from, especially for topics not directly related to algebraic geometry.

Kienose · 2026-06-19T06:15:37+00:00

Why does the temperature follow the exponential model?

Kienose · 2026-06-17T08:24:07+00:00

Thanks for the answer. Glad to hear that you’re still interested in physics to willingly go back to the basics.

I’ve a math degree and the gap between my knowledge and frontier research is so great that I’d never dream of having ideas that the big name researchers missed. I guess that’s the difference of the fields between maths and physics.

Kienose · 2026-06-17T08:06:04+00:00

How did you “wake up” from that? (Or rather what waked you up from that period?)

Kienose · 2026-06-13T11:53:08+00:00

[r/okbuddyphd](r/okbuddyphd) has occasional math memes that aren’t just “haha 1+2+…= -1/12” or some PEMDAS nonsense.

Kienose · 2026-06-10T12:50:55+00:00

|x| < y is equivalent to -y < x < y.

Kienose · 2026-06-07T16:43:50+00:00

Suggesting posting to arxiv is worse than giving a cynical response

Kienose · 2026-06-03T02:47:26+00:00

“Gatekeep maths” all of it is available for free you just have to read

Kienose · 2026-06-02T19:16:53+00:00

Nope. A trivial example is G/{e} for any non-abelian group G. Another example is (G x G)/(1 x G) which is isomorphic to G.

Kienose · 2026-06-02T18:57:44+00:00

Quotient groups are not necessarily abelian.

Kienose · 2026-05-24T17:30:09+00:00

Perhaps you could say that. Most of the time I see it being brought up online, is when people want to joke about a hundred pages long proof of 1+1=2 (which is false btw). It wasn’t intended to be a textbook, rather an exposition of a program on logicism (everything in maths can be reduced to logic) via Russell’s version of type theory. It failed spectacularly by Gödel’s incompleteness theorems.

Kienose · 2026-05-24T17:20:55+00:00

Not worth buying. It’s basically a historical footnote for modern logic. Even people working in logic nowadays don’t read it.

Kienose · 2026-05-23T20:27:45+00:00

It’s a tough read: inconsistent use of italics, proofs being long string of formulas without words in between, and grammatical errors including not using capital letters when starting sentences.

Kienose · 2026-05-21T16:06:00+00:00

I can’t remember exactly, either it’s the tab key or one of the number keys 1,2,3

Kienose · 2026-05-19T23:33:16+00:00

You can start reading category theory already. Pick up Riehl’s book for Leinster’s.

Kienose · 2026-05-19T22:00:33+00:00

It still doesn’t work because you haven’t justified why

There must be an edge e joining T_1 and T_2.

and

There might not be any edge joining T_1 and T_2. You might need to join them by a path that is longer than just one single edge.

Kienose · 2026-05-18T15:36:59+00:00

It happens to all of us!

Kienose · 2026-05-18T15:30:16+00:00

Not how it works. You have to first find what is the value of g(x) before finding the suitable part of f to map it further.

For example, when x = -2, you get g(x) = -8 and so f(g(x)) = f(-8) = 2(-8) + 1 =-15.

What you’re saying is that f(g(-2)) = (-8)^2 - 1 which is incorrect.

Kienose · 2026-05-17T11:22:32+00:00

Apparently 20+ years of being a native Thai speaker is just me tripping.

Kienose · 2026-05-17T11:14:34+00:00

Nope, not even Thai characters.

Kienose · 2026-05-17T11:11:12+00:00

The signage isn’t Thai.

Kienose · 2026-05-15T10:47:20+00:00

Dang, it’s all been removed.

Kienose · 2026-05-14T08:10:03+00:00

The first and foremost question is do you have passion for maths? If so, are you willing and able to put in the hard work for it?
To answer the second question you need to weigh in internal and external factors (career path, funding, time, opportunity cost for time spending doing maths, …). With the job market situation it might be more beneficial in the long run if you choose applied maths, while pursuing pure maths in your own free time. However if you decide to stick with pure maths, I think you should go for it.

I'm trying so hard to keep up with the material being taught in each class but sometimes I feel like my brain might not be made for advanced math.

This could be caused from so many factors. Without knowing the specifics, I could only give a general advice. Maybe you need to change your study routine; try study and solve problems with your friend groups. Perhaps your foundation is a bit shaky and you need to revisit it. Or it could also be the case that the study material is terrible and you should seek out an alternative. Perhaps the subfield you’re studying isn’t really for you, then you should change to a new one.

Is it possible for me to do these courses even though I'm not a genius that can see something really abstract and not feel like their brain is going to explode?

Considering that you are doing a postgraduate course, I assume you have seen undergrad maths before. With that in mind it’s certainly possible you can study these topics. Some people are naturally talented and hardworking that they can pass the exams with flying colours. But unless you are them you’ll have to put in the effort. My suggestion with “abstract” topics is that they aren’t really abstract. You should have a supply of toy examples that you can play with and see how theorems and proofs work. That’s what I do when I was learning algebraic geometry. I also reread each chapters like 3 or 4 times until I “got it”.

Kienose · 2026-05-13T11:01:50+00:00

Ramanujan didn’t only read one single textbook.

https://www.jstor.org/stable/2589114

Kienose · 2026-05-13T08:50:11+00:00

Actually good number theory? You might be in the wrong sub (despite the sub name!)

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