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What is, objectively, the most complex level...
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What is, objectively, the most complex level of mathematics you can do?
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>>7633238
differential eq :D
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>>7633238
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>>7633250
they don't even teach that level of math at University. It's too complicated for most professors to understand.
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>>7633238
First off, complex is relative. I can solve a problem in graph theory that no one in my department would know how to start, but I still suck at elementary real analysis.

To answer your question though, interpreting basic results in the theory of modular forms is about as far as I get in terms of holy shit what the fuck am I doing complex.
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Complex Analysis
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>>7633272
during my degree I picked up a book on the subject, Numerical weight estimates of OPs mom: A first, second and third course".

first page is an intro into the Schwarzschild metric
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Honestly?

Multiplication.
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>>7633238
analytic differentiation (deriving Laurent's theorem etc)
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>>7633238
Vector calculus
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>>7633333
>have fully solved the construction that is noted by its pale comparison the integral

I'm impressed!
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>>7633280
>complex is relative...I still suck at elementary real analysis

Agreed. This is me. However, I can do some stuff with grothendieck topoi and its relation to "spatial logics" that most people in my (non-mathematics) field would have a hard time with (but wouldn't impress a mathematician by any means). I guess I'm pretty good at most stuff in comm algebra and logic applied to algebra, both from a traditional and categorical point of view.
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Integration
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>>7633238
Algebraic topology in manifolds.
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Me? Probably algebra
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testing to post here

and maybe compute some homology groups?
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Calc II
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>>7633238
>love
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triple integrations and 3d volumes crap
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>>7633378
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>>7633280
This^^^
I can do work w/ Lie groups and lie algebra, stuff in algebraic topology, and stuff in the type of algebraic geometry used in physics. But I have never done any type of real analysis and probably couldn't even prove if a basic function was Riemann integrable or not.
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i can show that tor is a balanced functor
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Integral calculus
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series calculus
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Interuniversal Teichmüller Theory
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Polymeric Falcighol Derivation
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>>7633238
Wavelet compression or finite elements
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>>7633238
>complex

definition needed
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Fourier Analysis
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>>7633238
philosophy of mathematics
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>>7633943
real with an imaginary part, noob
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>>7633238
Unironically inter-universal teichmüller theory.
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>>7634077
kek'd and check'd
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>>7633331
>first second and third course
kek
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>>7633238
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Maths guys tend to have difficulty with fermionic stuff, so things like spinors and supergeometry might be their choice.
Physics people, on the other hand, are very familiar with fermions on a rigorous and intuitive level, so they'd probably go for motivic homotopy.
There are mathematical physicists who might disagree completely.
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Re(s)=1/2. RH or die tryin'
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>>7633238
i been studying the reduction of polynomials of degree 2 to linear factors. Initially in Q, but I hope to expand into R by means of a formula, my professor says I am not ready for, but I've heard it involves something called the square root of the discriminant.
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>>7635585
I think OP is asking what is the highest level of math that you personally can do, not the highest level that exists.

Honestly it triggers me that you even attempted to label any specific field of mathematics as the "highest", senpai.
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>>7635585
damn this is a quality response I did not expect from /sci/
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Honestly?

Counting from 1 to 5.
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Quadratic equations. Hopefully soon this will change. I lately have taken more of an interest in math.
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>>7636338
Good to hear fellow
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>>7633238
Balance my checkbook.
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>>7636338
As long as it makes you happy, thats all that matters
Happy maths and god bless
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I also have a question. What is the most advanced mathematics ever performed to date?

>>7633238
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>>7633238
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>>7633238
That's a tricky question.

Completely objectively, the most complex level of mathematics that the particle-molecule-organelle-cell-tissue-organism-sociobiological cell system known as "me" can perform is staggering, with calculations and computations performed every second that can barely be described within the character limit.
Like, I can run a goddamned sapient construct without even trying.

Unfortunately, that construct can only consciously do simple calculus :/
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>>7636926

As someone majoring in molecular biology, I thoroughly enjoyed your response.

Also, it seems like a minor feat but we should be proud of being able to do calculus. I would estimate that at least 80% of people on earth don't even know what an integral is. And I think i'm probably being generous.
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>>7633238
College Algebra
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>>7636955
Anyone who finished highschool in Europe or in Asia (including China and India which make up 1/3 of the world population alone) knows Calculus.
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Learned how to understand and solve shit like
[eqn]\oint_{\partial\Omega}\mathbf{E}\cdot \textup{d}\mathbf{S}=\frac{1}{\varepsilon_o}\iint_{\Omega}\rho\;\textup{dA}[/eqn]
but I'm still in sixth form so the most I do there is shit like
[eqn]\frac{f(x)}{g(x)}=\frac{g(x)f'(x)-f(x)g'(x)}{g(x)^2}[/eqn]
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>>7636960
Calculus is not required in highschool in the US. Most people do take Calc AB which is a joke.
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>>7636971
I didn't know that the US is in Europe or Asia.
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>>7636960
Not true.
Maths (at least here in the UK) isn't compulsory for the last two years of school so a lot of people drop it. Which is the two years in which you are first taught calculus. I'd wager that anon is right, go up to anyone in the street and ask them to solve

[eqn]\int_{0}^{3}2x^2\;dx[/eqn]

And I bet at least 80% of people will look at it in complete confusion.
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>>7633280
If you have k copies of a complete graph of k vertices, and you join them all together such that any two graphs share at most one vertex, is is possible to color the vertices of the resulting union with k colors?
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>>7633916
Most likely this
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Very basic functional analysis, probably.
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the first chapter of pre-algebra
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There is no "objectively", but whatever
Computation-wise, I can solve some beginner PDE's (not just method of separation of variables though)
Proof/logic-wise, I'm pretty far along in linear algebra and abstract algebra

Who hates analysis as much as I do? It's so mundane and sloppy
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>>7637073
>analysis
>sloppy

You're not doing it right
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>>7637076
I mean sloppy in the sense that it doesn't offer many concrete, perfect answers like algebra does
Analysis deals a lot with "we'll take this number to be very very very small and then predict what happens as it gets closer to 0", for example
Whereas in algebra everything follows very strict rules and people didn't have to come up with stupid fucking definitions
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For me personally, I think the most complex is homotopy theory in arbitrary model categories, including some with additional structure with which I want my constructions and results to play well (cohesive settings in particular).
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>>7637086
I recommend studying "synthetic" non-standard analysis, which you will probably find more algebraically oriented, but which is equivalent to classical analysis.
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>>7636985
I'd up that to 95% m8
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>>7637117
That actually looks like something I would enjoy a lot more, thanks
I'm booked up with work and school currently but I'll definitely take a look into it over winter break. Any books or other resources you could recommend?
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>>7636054
underrated post
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>>7637168
Nelson's Internal Set Theory is the classic textbook recommendation. I haven't studied any of it formally, but I am familiar with parts if the theory. This textbook was recommended to me. Good luck!
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>>7636054
Kek
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No idea what the title of any of it is, 2nd year uni mechanical engineering in the UK level
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>>7633331
I would think it would go into limits, types of infinity et all
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>>7633333
Nobody checking these quints?!
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>>7633238
Algebraic Topology

Honestly what the fuck professor how was I supposed to come up with that covering space on my own
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>>7637086
But there are rules in analysis. Sure there is a certain amount of heuristics involved (as in all math) but, in order to prove anything, you write a careful argument (again, as in all math).
I mean, analysis isn't even my thing but I think this is a strange thing to complain about.
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>>7633356
Double Integration
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>>7638874
triple integration with spherical coordinates fuck me in the ass
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>>7633238
It's always possible to invent arbitrarily convoluted operations, there is not most complex level.
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>>7636990
Yes.

Trivial.
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>>7638891
Not even hard.

It's really just a matter of choosing the right coordinates for your surface.
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>>7633238
Analytic and Algebraic Topology of Locally Euclidean Metrization of Infinitely Differentiable Riemannian Manifold.

I wrote a paper on it once but some fucker in Russia somehow got his hands on it.
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>>7638998
triple integrals are a joke lol
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Calc II, but it will be Calc III soon

STEM (mech eng) masterrace
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>>7633238
Calculus 1 Linear Algebra and Discreete Math
1st semester :(