What is your favorite branch of mathematics and why? Mine would

>>7705628
What qualifies as "Real Analysis"? Sequences, set theory, etc.?

Topologyyyyy

>>7705634
I would say sequences, limits, continuity smoothness, series, integration derivatives DEq...

Basically Calculus with all the theorems to construct it properly

>>7705638
omg this coffee mug has ONE hole, it's just like a hoolahoop I luv math xD

>>7705634
What >>7705642 said, done in R^n. That is, an n-dimensional space in R. It turns out this is isomorphic ("the same") as doing it any n-dimensional vector space, so it's really nice.

>>7705833

Hahaha if you give a topologist a coffee mug he'll eat it because he'll think it's a donut XDDDD I luv maths they are fun :).

>>7705833
>>7705875
>I actually watch numberphile (or is it vsauce? im forgetting the other one) and sperg out on what I see there

I love stochastics. It just fascinates me and it involves just so many other branches of math, in particular functional analysis, spectral theory, differential geometry, PDE, combinatorics, graph theory, algorithmics and many more. Also a lot of classical results can be proven more elegantly by stochastic methods. For example zeta(2) = pi^2/6 can be obtained from exit times of Brownian motion under holomorphic maps. There even is a stochastic proof of the Atiyah-Singer index theorem.

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The answer is computability theory. My dick is getting hard just thinking about it. Maybe combinatorics if you want something purer.

Complex Geometry (from both the analytic and algebraic viewpoints)

Non-Euclidean Geometry...

Ahhh I just love it :)

Just blows my fucking brains out sometimes

>>7705628
Mostly set theory and other discrete math in general. I dunno why, I just have lots of fun doing it.

>>7705628
Addition, subtraction, and multiplication.
A bit of division if I'm in the mood.

Category Theory, duh.

> Algebra
Linear Algebra

> Analysis
Functional Analysis

> Geometry
Hyperbolic Geometry

> Topology
Algebraic Topology

Ahhhh, I can't choose. Sorry bro.

Anyone likes any of these topics I mentioned?

>>7706390
for Algebra i would also choose Linear Algebra,

for some reason other branches of algebra have dissapointed me, loved linear algebra to

>>7705628
>"Hi and welcome to numberphile"
>camera zooms in on the face of some sperglord already covered in sweat
>"Today we are going to talk about the number five"
>sperglord smiles the smile of a thousand suns
>drops of sweat pouring from his forehead
>he writes the number five on a paper
>"The amazing thing about this number is that it is a part of you"
>camera zooms in on his hand that is soaked in sweat and shaking uncontrolably
>"As you can see my hand contains five fingers"
>a tear falls from his eye
>"I would not even know what to do with my self if not for five"
>looks at the camera like he is seeing god
>tears of joy raining down his cheek
>In a shaky voice he says:
>"Without five I couldn't even count to six!"
>begins to cry

>>7706390
Awesome. Yeah, it's fun to toy around with, and I only enjoy the contemporary/proofy side to it; not the applications.

Don't you ever get a knack out for proving it's 'linearity'? I do.

>>7706441
never thought I'd read a numberphile pasta

>>7706441
You need the picture. It's not funny without it.

>>7705628
Mine is multiplication

>>7705628
Dynamical systems desu

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>>7706441

>favorite
i have no idea lol

Teichmuller theory desu senpai

>>7706777
You stole my idea you faggot. Fuck your trips.

>>7705628
Fractal analysis and chaos theory

Calculating radius of your mom's ass. It doesn't appear to converge desu sempi.

>>7706209
Hah, my answer is combinatorics, but computability and complexity theory if you want something applied

>>7706209
>literally my two least favorite branches of math. imo, they both feel like tools for producing "negative" results (how complex? too complex.) and just landing on a pretty theorem that reaches outside of very particular circumstances seems rare. It just feels removed from the rest of mathematics except when you need to know if a word problem is solvable or more generally if you have some nice notion of completeness.

however, my fav branches are also pretty bland. I'd have to say comm algebra, lattices, and classical alg geom. I'm just getting into "spatial logic" (basic topos theory/geometric logic/pointless topology) and that shit is dope af. i got all these rings and logics and spaces lying around and it can eat that shit up no problem. plus there's something satisfying about primality.

>>7707027
i guess i take that back for combinatorics. but it also seems to connect to other fields mainly insofar as you need to organize "case by case" facts or some such thing