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/sci/ - Science & Math

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7482721 No.7482721 [Reply] [Original]

Post the hardest or most advanced maths you know.

Here's mine. It's how to graph and solve the value of x of quadratic and polynomial equations via factorizing and expansion.

>> No.7482723

How to get the gradient of a point on a curve

>> No.7482848

in b4 triple integrals

>> No.7483049

>hard
HAHAHAHAHAH

>> No.7483096

Permutation groups and proving some trivial things about bounded sets. Essentially babby Abstract Algebra and Analysis. Hopefully one day I'll be OHP tier.

>> No.7483244

Finding extremals of functionals (a function of a function) using the Euler-Lagrange equation.

Or finding the optimum point of a function in n-dimensional space using the method of steepest descents or the conjugate gradient method.

I fucking love maths

>> No.7483246

>>7482848
no kidding they suck

i can ask mathematica to do shit for me that i cant compute

>> No.7483255

>>7482721
Sheaf Cohomology

>> No.7483342

One time pad decryption.

>> No.7483388
File: 66 KB, 2000x1758, how to integral.png [View same] [iqdb] [saucenao] [google]
7483388

I have no shame, this is my current mathematical education.

>> No.7483399

Early Calc II material.

Coolest application I know is finding the volume created by rotating the area between two functions around the x or y axis. Also, finding the length of a curved line.

>> No.7483435

>>7482721
Everything I've learned so far is trivial. I'll just list something which uses the most knowledge to do. I'm going with substitution to solve double integrals. It requires knowledge of double integrals, jacobians, and vectors.

>> No.7483462

Calculating the Flux of a vectorfield / rotation via stokes/gauss etc.

It's amazing how things like simple integrals, gradients, dot and cross product can calculate really cool shit.

Am I the only one who's becoming less into vidya and more into maths/physics etc.

>> No.7483472

Finding the probability distribution of the transformation of several probability distributions.

Yeah.. Not exactly hard and advanced but I haven't done maths in years so I'm glad I'm still able to teach myself this kind of stuff

>> No.7483499

Certain complex analysis and ODE techniques, which is where my undergrad education topped-out. "Know" is always fuzzy here since I'd need to open my books back up.

>> No.7483524

>>7483388
Figuring out why integrals actually work is pretty cool although its not difficult in the slightest.

>> No.7483534

nothing is hard as long as you have a solutions manual nearby

>> No.7483579

I dropped out of high school in 10th grade

Unless you faggots are pursuing STEM degrees you have no business learning this useless shit

>> No.7484561

>>7483246
Yep they suck. I used Maxima when undergrad

>> No.7484564

>>7483096
What's a OHP?

>> No.7484568

I guess some neat theorems of Arhangels'kii, Alan Dao, Grothendieck, etc

>> No.7484571

I know field theory, a bit of algebraic topology and how to prove the fundamental theorem of tropical geometry

>> No.7484572

>>7484564
A legendary Math grad student who may sometimes be spotted on /sci/.

>> No.7484654

I'm taking calc I over again, because I got a D in the summer session. Gonna do it with honors.

The damn professor is an official abstract algebraist, and skips steps arbitrarily, to see if students understand what he did in-between, and asks "is everybody there?"

For the most part it's because he knows everybody is so slow that they can't keep up with him, nor do the steps in their head, so he's looking for somebody to ask questions, which is usually me, go figure..

Anyways, I know how to do basic integrals poorly. That is the hardest maths I know.

>> No.7484679

>>7482721

>>do you even calculus?

Go to bed kid you got school starting soon

>> No.7484682

>>7483462
EE master race?

>> No.7484691

>>7484654
Good luck anon, frankly I won't blame a prof for being fast, I'd just raise my hand and ask if it really is a problem for me. And you might enjoy Algebra one day, although getting started in it is one of the least enjoyable parts.

>> No.7484927

i came across a particularly troublesome integral on a test today

<div class="math">\int_{0}^{\infty}\!\!\!\frac{\sqrt{x}}{x^2+1} dx</div>

>> No.7484952

>>7484682
Nah, Earth And Space Physics And Engineering

New degree in Denmark

>> No.7484957

>>7484927
(1/2)*Pi*sqrt(2)?

>> No.7485042

>>7484927

I feel like its piss easy if u split it into two seperate integral for num/denominator but i can't remember by arctan etc shit very well.

>> No.7485070

i was looking at some random unsolved math problems and in trying to solve one of them i created the product integral and proved it was equal to exp(dln(f(x))/dx)
i was so excited with my findings that i thought it had to have been found before so i started googling and found this

https://en.wikipedia.org/wiki/Product_integralhttps://en.wikipedia.org/wiki/Product_integral

:(
type 1 is what I found, one of the most conceptually difficult things i've come across in a while since i'm no longer in any math courses
unfortunately it wasn't what i needed to solve the unsolved problem
interesting stuff though

>> No.7485073

>>7485070
oops
I proved the product derivative was equal to exp(dln(f(x))/dx)
product integral = exp(integral of ln(f(x)))

>> No.7485101
File: 34 KB, 800x498, 1429312690435.cached.jpg [View same] [iqdb] [saucenao] [google]
7485101

>>7482721
this is some good bait.

>> No.7485102

I did multivariable and vector calc like 2 years ago. line integrals and green's, stoke's and divergence theorem feel like they're still the highest level stuff i've learned

>> No.7485414

>>7484691
You're right. I think his honors project is going to be hard as shit, considering that his tests are difficult to do, even for the professors who work in the math lab, yet he can do them quickly, and with a cheery, nonchalant wit to boot.

He showed me before the end of summer session one of his projects for Calc II would be to prove the relationship between two hyperbolic and trigonometric functions.

He's renowned in the state though, so I'm hoping I can get his req when I transfer.

>> No.7485422

Applied Math: Noether's Theorem provides a way for us to construct conservation laws of PDE's by finding variational symmetries of the lagrangian representing the system.

Pure Math: The nth singular homology group of a compact surface counts how many n-dim holes or cavities the surface has. Also how to construct a complex torus as a Riemann Surface by taking C mod the normal subgroup generated by two complex numbers in C that are linearly independent over R.

>> No.7485430

I suppose the proofs of the simplex algorithm and Bland's cycling rule in particular were among the more complicated stuff I've encountered.

>> No.7485441

>>7484927
I found <span class="math">\sqrt{2}\pi[/spoiler]. Not as easy as I thought.

>> No.7485443

>>7485422
hey that torus trick is neat

>> No.7485446

>>7483244

pls be bait

>> No.7485454

Show <span class="math">\mathds{E}(r(X)s(Y)|X) = r(X)\mathds{E}(s(Y)|X)[/spoiler]

>> No.7485882

>>7483096
Permutation groups are pretty nifty, but I want to know algebraic groups

>> No.7485889

>>7483244
My babby level gradients are pointing your way and they're telling me this is bait.

>> No.7486078

>>7482721
I've proven that a determinant of an upper triangle matrix is equal to the product of it's trace.

I can probably prove the chain theorem in any R^n.

>> No.7486402

>>7486078
wow. look at you. big guy over here with his wittle intro matrix theory

>> No.7486432

The hardest proof I can do is the proof of the generating function for the fibonacci sequence

I can only do it because i memorized it, I'm not smart enough to come up with shit like that.

inb4 babby tier
i'm okay with that

>> No.7486470

>>7482721
https://www.youtube.com/playlist?list=PLpW0M9zJ2RQ4lylhZq9LaiOcv0sAF0EiH

This is probably the hardest math I have ever studied. Although that is relative.

>> No.7486471

I can prove .999...= 1

>> No.7486473

>>7486078
>"I've proven"
>I know how to regurgitate a 200 year old proof
Great achievement bro

>> No.7486486

>>7483399
Literally the worst part of Calc II

>> No.7486489

>>7486486
>tfw passed calc II with a c

I should just drop out tbh
Linear algebra starts tomorrow

>> No.7486494

>>7486489
>linear algebra starts tomorrow
It's not the same as Calc really, you don't even need much if not any Calc material to do Linear Algebra, but I hope you work harder and do well for it. All the best anon.

>> No.7486500

>>7486494
I'll try. I only have 13 hours this semester so the extra time off will go into that. It's my last math course.

>> No.7486604

>>7484927
Real easy with contour integration.

>> No.7486621

Well, I'm currently working finding solutions describing a black hole interior containing a non-abelian (yang mills) gauge field with loop quantum gravity corrections. If the problem doesn't end up intractable (like almost everything in LQG is) that'll probably be my most advanced mathematical achievement.

>> No.7486635

>>7484564
Overhead press, do you even lift, faggot?

>> No.7486646

Right now I'm pretty good at investigating the structure of linear operators over the reals and complex numbers (diagonalization, Jordan form, direct sum decompositions, etc.) Hopefully I will learn more about other subjects the near future.

>> No.7486810

>>7482721
the solution to the poincare conjecture

>> No.7486818

Currently studying Galois theory of groups in prep for my class on it for my second year. Aswell as some number theory. Mostly just proving theorems such as, that the order of the Galois group G(K/F) for some finite extension K divides the degree of the extension [K:F[ as we can show that the order of the Galois group is equal to the degree of [F^G:F] were F^G is our fixed field, the set of elements who are fixed under the automorphisms of G in which case it is simple for one to see F is a subfield of F^G and so we can show it divides it,by seeing [K:F]=[K:F^G][F^G:F] where [K:F] is the dimension of K as a vector space over F. But the fact that the order of G(K/F) is equal to [F^G:F] is a little more elusive to prove but follows from the fixed field theorem.

>> No.7487320

>>7482721
Emm, I have a fairly advanced knowledge of statistics, compared to most people that study maths anyway, but I know that anyone doing an degree in stats is well past me.

Hmm, the two-sample t test? Maybe? That's probably the most advanced stats I know.

>> No.7488697

>>7486810
>the solution to the poincare conjecture
I'm slightly scared that you actually might be telling the truth.

>> No.7488787

>>7482721
I wonder how skilled /sci/ is, here's a problem from the 17th century.
"Find four numbers the difference of any two being a perfect square, in addition the sum of the first three numbers being a perfect square. "

>> No.7488820

>>7488787
0, 0, 0, 0

>> No.7489651

>>7484564
overhead projector