Why does topology suck?

Why does topology suck?

Because you is a brainlet

take that back... >_>

Algebra is more better and topology sucks balls

because it's an abstraction of a useful concept (open sets) taken to the extreme, where there are people studying set theoretical topology which has nothing to do with anything relevant to any practical applications, ever

I guess my rage is more directed against set theory and logic-circlejerks instead of topology, tho. topology can be fun and useful as well, but set theory cannot

at some point (when you're not an undergrad anymore basically) your problems will branch into various mathematical problem fields.

algebra, as well as topology, gives you a toolbox to work on problems. saying one tool is superior to the other when sometimes you simply need both is just silly

You use algebra to solve problems in topology, and not conversely, which shows algebra is better

You can use topology (the fundamental group) to prove the fundamental theorem of calculus. You can use covering spaces and the fundamental group to prove things in group theory.

Calculus is not algebra m8

>conveniently ignores the algebra example

kek

>where there are people studying set theoretical topology which has nothing to do with anything relevant to any practical applications, ever
Except as the basis (ha) for algebraic and differential topology, which do have applications all over the place, from string theory to robotics!

also the fundamental theorem of algebra

Topology is actually so nice?
It has a beautiful simple definition.
It has beautiful compatibility with the concept of continuous function.
You actually can go from continuous function to topology or from topology to continuous function.
It's amazing that that simple definition has extremely useful properties and implications.

...

I think topology is super neat. I like it/geometry and analysis for some reason, while algebra does almost nothing for me.

They should all be interrelated in a lot of ways, so I don't know why I feel that way. It seems to be an aesthetic thing for the most part.

Math gets fun when you build up enough knowledge to the point where you can start combining a bunch of random stuff from all over the board. General topology can be tedious, but it pays off when you start doing algebraic and differential topology or differential geometry where you can start pulling theorems out from all over the place and apply it to the problem you're working on.

What this relates to? t: brainlet

>Algebra is more better and topology sucks
t. undergrad who is currently having his ass kicked by a topology course, and who understands some entry level shit like basic group theory and now thinks that he can make a career in algebra without touching anything else

set theory is the "basis" of all modern math. doesnt mean it makes sense to study it in isolation.

give a single example of a theorem of set-theoretical topology being relevant outside of set-theoretical topology

image of a compact set in a continuous map is compact

>set theory is the "basis" of all modern math.
Sweetie....

Because you haven't derived graph theory from field theory and type theory.

dumb frog poster

There is literally no point in studying math unless you're autistic.

How will learning abstract mathematics help me learn actually cool, practical shit?

>he doesn't have aesthetic sensibilities
>will never be able to prove the strong law of large numbers, will never have a measure-theoretic background, won't even work with a lim sup lmaooo

fuck off and enjoy ending your math studies with calc 1

>calc 1
Umm, honey, I know how to triple integrate, thank you very much.

>graph theory
Stupid shit for cs monkeys

Is triple integration calc 3?

If you want to learn how to solve cool, practical problems then just learn operational research.

until you realise that lots of problems require PDE, and most optimisation problems require functional analysis and modern calculus of variations, and advanced problems with uncertainty require measure theory , and every real world problem requires numerical analysis to discretise and and implement it.

>HURR MUH CS MONKEYS
Come back when you're over tbe age of 18

no, it's an advanced postdoc research topic

What are the problems in triple integration other than Barnett identity?

topology is hard

Good luck trying to understand basic real analysis or measure theory without any topology.

Topology is literally revolutionizing neuroscience.

Topology is widely used in finance and managing healthcare systems, and the company Ayasdi was founded by a topology professor and it's basically BTFOing every other data cience firm in the fucking world.

When I do topology I'm the one who's hard

How do I learn topology as a biofag? I've taken calculus and linear algebra.

I think it's sort of interesting. Struggling through it myself, but my geometric intuition is just shit.