Whats Veeky Forums's favorite area of math and why isn't it algebraic topology?

BA undergrad here. took a discrete mathematics class because I took a philosophy logical class (classical to first order).
I really enjoyed "Discrete Mathematics" especially set theory and combinatorics; the logic was basic classical logic and was just pretty MT and MP, that was it.

I like chaos and fractals.

On the subject of topology, the Hevea torus is pretty neat.

Are you me in the future? I'm taking Boundary Value Problems at the moment, but we are still stuck on ODE review.

Is there anything in particular that I need to look out for in PDE?

PDE theory uses a ton of delta-epsilons, real analysis, existence-uniqueness proofs, and topology, and its not even pure math in any way...

If you are a geometer, physicist or analyst, yes you are - its both beautiful and powerful.

it's spirals all the way down, kid.

Lolwut??? In my UK uni analysis starts with epsilons and deltas in the first week of first year.

How far through your degree can you get without taking any rigorous mathematical courses?

But I like algebraic topology.

>spend about 5 or 6 weeks on set theory
There is a reason set theory is its own course at lots of unis. I feel like he meme'd you.

>tfw no full set theory class at my school
>tfw basic set theory is bundled together in baby analysis and discrete math/intro to proofwriting
>ywn understand godel's incompleteness thm

study for yo SAT, kiddos, don't be a dope and go to state school

Category theory because of how elegant it is and it applies to everything.

Algebraic topology is cool when done right, i.e. with category theory. As you probably know, it gave birth to category theory (and n-category theory!), so it is cool in that sense. But I took one class on it where it was essentially about drawing pictures of universal covers. This is not my idea of a good time...

There's no such thing as "college algebra". It's just high school algebra for people who never learned it.

well basic group and ring theory could be called "college algebra"

I'm thinking he means abstract algebra. Groups rings and fields, etc.

>i don't give a fuck about neighborhoods
>i don't give a fuck about the existence of shit

In real PDE's, this is all you're thinking about. I kinda wish I was like you. I love pure math but I know its a stupid idea pursue it so I'm pursing applied math.

Because algebraic geometry is more elegant.

Also, mandatory pic related.

lol

I'm a calc 2 student who's enjoying math so far, would be advisable to study another field concurrently? A pure math sounds really interesting, but I have a feeling that to get into the meat of it I'd have to have the calculus series under my belt.

I was thinking of maybe just going back and reviewing trig, what do you think, anons?

another class? yes, definitely advisable. Get into proofs as soon as you can.

>bunch of shitty polynomials
>more elegant
Rofl

Chaos theory fascinates me

do you even lift?

What do you think?

Get into vector spaces (linear algebra), and then you can do modern algebra, modern geometry etc. Hilbert Space is also really good to learn.

Or just pick up an intro to proofs book. A lot of universities don't even require an intro to proofs course prior to taking a course like modern algebra real analysis etc. Books usually go over the set theory stuff in the first chapter.

If you want an intro to topology get Mendelson's for like $8 on Amazon. I'm sure there's a PDF too.

fuckin saved

D = 6.8E2EF6C62DLLLB

I thought it was, but either it isn't or OP is cheating!

>Category theory because of how elegant it is and it applies to everything.
The empty set is a subset of everything, but that doesn't make it the most interesting one

Triple integrals

Try orthotopology with its quadruple integrals on ultrafilters.

>be me, music major, need math for academic core
>several classes available for me, mostly for non-STEM students. Two of them say "Notice: This class is intended for students majoring in STEM, non-STEM should take these alternate classes etc etc"
>statistics and college algebra
>go with what sounds like fun
>it's fucking nothing
>end up hiding my perfect scores because I am just a music major

Did I make a mistake not going for statistics?

for you

As Grothendieck said, mathematics was held up for thousands of years for the lack of "trivial" concepts like zero. Can you imagine if someone had the idea of zero back in ancient times?

I took an Applied statistics course and an elementary statistics course and the only difference was there was multivariate Calculus in one chapter of the applied mathematics course. That and we got to regression lines in the elementary stats course. I think you're fine to be honest.

I have touched one of the print, looks nice.

Omega = 18.CB105899A39211FBBF
Alpha = 7.8E2EF6C62DLLLBB
C = 8874 3AC3 C130 3119
R = 163 73B 795E B528111
Hydrogen Sqaure = 7.0471C42010AF6352BFFF

I solved Trig. God bless over The Truman vessel.

You took some bullshit auxiliary general math course in stats and algebra, did well and now you think you should have done statistics?

Let me tell you something. There is a reason even a disgusting music major like you was allowed to take that course. Because it is a bullshit easy grade freshman course.

I always find it funny when outsiders think they are good at math because I know from a friend that 'college algebra' is literally high school algebra 2.0. Just solve equations of real numbers.

That is NOTHING compared to the algebra courses I've taken in the math department. It is barely even related.

Sure you did well and maybe if you had not yet declared a major then I would tell you that probably you could do it but from the fact that you already made the decision to major in fucking art (music) I can just tell you this:

You are not smart enough for statistics.

Chaos and Game Theory. Otherwise known as the only real math.

>That is NOTHING compared to the algebra courses I've taken in the math department. It is barely even related.
Yes, I know, that's why my post is in reply to someone who said college algebra is just high school algebra for people who never learned it. My comment is in affirmation. I recommend classes in reading comprehension

>There is a reason even a disgusting music major like you was allowed to take that course. Because it is a bullshit easy grade freshman course.
>>several classes available for me
>>statistics and college algebra
So statistics is a bullshit easy grade freshman course as well? Then yeah, I guess I should have taken it, thanks for clearing that up.

>but from the fact that you already made the decision to major in fucking art (music)
I'm good enough at the cello to at the very least make it to the back of some minor professional orchestra, it would be an incredible waste not to hone it at a university level.

>but from the fact that you already made the decision to major in fucking art (music) I can just tell you this:
>You are not smart enough for statistics.

I hate this attitude more than anything. Your half of an engineering degree does not make you superior to those with different interests than you.

>tfw I could have gone to Harvard but I was too worried about "muh tuition"

>they aren't American

>they don't know Americans are actually so retarded they need to review basic high school algebra in college

You'll never get into Stanford.

Elementary arithmetic desu senpai

Because geometry is more useful.

>Algebraic topology is cool when done right, i.e. with category theory.
loled

underrated

One of my weaknesses is not knowing how to derive everything I use, especially in trig. Would going through a proofs book fill in that knowledge?

I memorized nearly everything in trig, deriving nothing, (therefore not actually understanding, just copy pasta) and would like to go back and fill in some missing knowledge.

There are two different approaches to analysis. One way is by introducing some basic topology notions such as neighborhoods, open sets, closed sets, etc.. The other way is by using delta-epsilon arguments.

Delta-epsilon arguments are older but more difficult. They are written in raw set theory/logic and many students struggle with them (the statements and the proofs). The topological approach is more modern and it generalizes to other topologies. In the case of the reals, it can be proven that the two approaches are equivalent.

Ultimately it sounds like the guy spared you and you should be grateful.

That said, I personally enjoy both approaches.

It probably won't cover the shit you blackboxed, but you'll benefit from it more immediately than reviewing trig.

You need to learn how to correctly ARGUE mathematics, an intro to proofs will help that.

Could you recommend any textbooks that use the topological approach? (preferably good for self-study)

Not only on reals but arbitrary metric space. What about general topological space, though? I think it stands, although I never understood proof of equivalence, it is only intuitive clear

that Q-A punchline made me literally kek

This is probably the best post I've ever read on sci. i think both algebraic topology and geometry suffer by teaching the subjects with their historical motivations. I think a class in modern AT starting at Lurie would be more worthwhile than starting with Munkres, and for that matter, beginning AG with representable functors and going straight into Artin stacks, rather than stupid varieties you could just review on your own.

>algebraic topology

algebraic geometry is better

Category theory does apply to (almost) everything, but liking it for that reason is like saying the dictionary is your favorite novel. The advantage of using category theory is that clearly distinguishes between deep results, and results that look deep but actually follow directly from "abstract nonsense". But since category theory is so general, it usually can't help to prove any non-trivial results in another subject. A good example of this is the Van Kampen theorem. The statement of this involving a pushout is no doubt more elegant than the usual formulation. However, formulating it in this way doesn't give any additional insight into the proof, and indeed, at some point you need to "get your hands dirty" with a topological argument.