/math/ general - Buddhabrot edition

this thread is for mathing

>what are you studying?
>any cool problems?
>any cool theorems or remarks?
>reference suggestions?
>???

Other urls found in this thread:

en.wikipedia.org/wiki/Mathematics_Subject_Classification
jmilne.org/math/xnotes/MOT.pdf
en.wikipedia.org/wiki/P-adic_quantum_mechanics
arxiv.org/pdf/1212.5975.pdf
arxiv.org/pdf/hep-th/0604151.pdf
web.math.princeton.edu/~nelson/books/1.pdf
twitter.com/NSFWRedditVideo

Why mathematics is more diverse than physics?

There is a clear pathway to learn physics: class. mechanics, electricity, thermo, waves, optics and quantum mechanics

Math is pretty much a mess, there is no logical pathway

Redpill yourself with Bourbaki.

It's a way to keep normies and brainlets away

I think it shows that math doesn't really intensify in difficulty past calculus it just gets more convoluted and unintuitive. In mathematics you pretty much just need to know the rules and be a passable problem solver.

>I think it shows that math doesn't really intensify in difficulty past calculus it just gets more convoluted and unintuitive.
if getting more convoluted and unintuitive isn't intensifying the difficulty then what would be?

And then wildpill yourself with MathFoundations.

this thread is sponsored by the mcchicken®

>I am a brainlet
We know.

>MathFoundations
>This channel aims to explain a lot of interesting mathematics to a broad audience
>a broader audience
i.e. a brainlet audience. Popsci is cancer and popmath is no exception.
K.i.l.l.y.o.u.r.s.e.l.f.

Concrete rebuttal right there

>for any axiomatic system whose axioms can be encoded in a LISP program N bits long, the provable complexity barrier has an upper bound [math] L \leq N+2359 [/math]

It's a serious video series building mathematics from first principles in a logically solid way unlike modern mathematics.

>I just remember how the proofs are done without understanding them.
wew, take a load of this guy

Physics usually means "pure physics." If we lumped things like material science or electrical engineering under the moniker "physics classes," it would look just as messy.

>MathFoundations
Just a convoluted appeal to "common sense". The entire series is an obfuscation of the regression of mathematics to a less rigorous framework.

>It's a serious video series building mathematics from first principles in a logically solid way unlike modern mathematics.
>MathFoundations16: Why infinite sets don't exist
>argument 1: appeal to authority
>argument 2: the paradoxes of naive set theory

>Math is pretty much a mess, there is no logical pathway
You mean to say, perhaps, that there is no classification of mathematics which you find intuitive.

Math is not "messy" and engineering isn't physics.

What do you math lads like to drink while proving things? Older thread started getting into this

A bit of rum while working on homework. Zaya, neat.

Might try a shot before a difficult exam and see if it helps the nerves like some people said

Knowing is understanding. Understanding doesn't mean wrestling with something that's called being a brainlet

>I think it shows that math doesn't really intensify in difficulty past calculus it just gets more convoluted and unintuitive.

If most of it doesn't seem intuitive then you don't understand it, just using physical intuition as a crutch gets you by on a metric fuck ton of mathematics, just look at any decent mathematical physics textbook and you'll see how. Even without physics though a lot of it is pretty intuitive in that most fields are developed and progress largely by intuition. Also the claim that the difficulty doesn't increase after calculus is demonstrably false, considering how many people breeze through calculus but get butt fucked by some simple looking nonlinear pde's or problems like the lonely runner conjecture show that things definitely do get more difficult. Hell, look at the entire field of combinatorics, nothing particularly convoluted about counting shit, yet even some basic questions are still left unanswered, even by the best problem solvers.

>In mathematics you pretty much just need to know the rules and be a passable problem solver.

Maybe if you want to be a scrub mathematician sure, but to be anything even remotely above that you need to be able to have/develop you're own idea and pursue various avenues possibly even crossing fields to find new connections.

...

>set theory without arithmetic
wew lad

lmfao what kind of brainlet made this?

>arrow from real analysis to point-set topology
>arrow from galois theory to representation theory

...

Funny thing is there's still a shit ton of a mathematics left out, some more interesting connections are that of the langlands programs which connects harmonic analysis, number theory, and geometry, combinatorics being equivalent to functional analysis over the "field with one element" and various well established connections, same with combinatorics, dynamical systems, number theory, and harmonic analysis coming together in ergodic theory which has also made deep connections with hodge theory and the theory of riemann surfaces. There's also the application of algebraic geometry to problems in pde's Let's also not forget how intimately connected math and physics are. I could go on but I think the point has been made.

Next time you might want to use a more sensible taxonomy, e.g. en.wikipedia.org/wiki/Mathematics_Subject_Classification

>leaving out the single most applied field of math

>Not including Measure Theory in Analysis
>Not realizing algebra is as important to modern physics as analysis

>convoluted and unintuitive
I can agree with the first, but not the second part. I remember, as a freshman, wondering how the hell most of the calculus was actually derived. Yes, there were explanations, but they didn't satisfy me. Then, after two years of real analysis and abstract algebra and measure theory, I finally understood the inner workings of mathematics, making the whole of maths quite a lot more intuitive.

>leaving out probability
confirmed moron

Trying to solve this bonus question but I can't find anything in my text book about rotation of regular languages.
I have to prove that ROT(ROT(A)) = ROT(A).

I was bored so I tried to create an improvement on this (so I can post it to every thread that comes up every single day)

opinions? am I missing something important?

>opinions?
it's blatantly obvious you don't know anything about most of the subjects in the picture

i have at least 100 books downloaded in my computer about all of those subjects, bro

>i have at least 100 books downloaded in my computer about all of those subjects, bro
my point stands

There's a clear pathway for physics because there's the "real world" that we can make reference to and prepare curricula based on what's accepted at the time. Physics doesn't become diverse until grad school, and even then it still more or less follows one or two major theories in the individual fields. Meanwhile for maths there is no "real world" grounding, which means that there are so many crazy fantasies going on that a student can easily chose one to specialize in early on.
Basically math without any applications to physics is pure wank.

wtf are motives

>Birch is 85
>Swinnerton-Dyer is 89
>BSD conjecture is still only proven for the lowest ranks in one direction
:(

jmilne.org/math/xnotes/MOT.pdf

I posted in the other thread but this seems to be the right one.

Looking for a recc for a subject to learn. It will be through self-study, so any texts would also be welcome.

I know the basics of algebra, analysis & topology, with a little more depth in commutative algebra and algebraic number theory.
(i.e. taken pretty much all the typical "undergrad" courses)

What should I check out next?
I'm taking an alg. geometry class next semester so I figure I may as well just wait to learn that.

Funny how that "pure wank" turns out to be followed by followed by all sorts of phenomena and patterns in nature. It's almost as if the universe is conspiring with mathematicians.

You should study some probability theory, even though you don't seem inclined to go in that direction. Radically elementary probability theory by Edward Nelson is a good quick overview.

Not funny at all. Number theory is pure wank and it still haven't found itself an application to physics.
Also some fields of mathematics are starting to be inspired by physics (i.e. TQFT and quantum algebra); mathematicians will be doing physics before they know it.

"Intuition" is often faulty.
Many fields of mathematics have been inspired by "natural philosophy" (physis in Greek) broadly put. It's not surprising how you get maths out of modelling nature mathematically.
Mathematicians have been doing physics since ancient Greece. The more mathematical a science, the more successful it is in describing nature. But this could be a simple consequence of being a tool designed for the task, if not for the fact that previously thought purely mathematical constructs seem to have found their usefulness in the study of nature.
Number theory is not my favourite subject either, but considering how, for example, abstract algebra is a thing mainly because of needs in number theory, I wouldn't be so quick to diss it as "pure wank".

I dont like linear algebra. Orthogonality, proofs, RSVD/SVD/QLambdaQ^T/SLambdaS^-1/QR/LDU blah blah jesus christ when does it end

>Number theory is pure wank and it still haven't found itself an application to physics.
b-but p-adic quantum mechanics
en.wikipedia.org/wiki/P-adic_quantum_mechanics
a-and Langlands reciprocity connected to automorphic black hole entropy
arxiv.org/pdf/1212.5975.pdf
a-and geometric Langlands connected to electric-magnetic duality
arxiv.org/pdf/hep-th/0604151.pdf

>gotta abstract the "number" part away from number theory to have it be useful
YOU CAN'T MAKE THIS SHIT UP LMFAO

Actually already have taken 2 semesters of probability theory / statistics, but thanks

Geometric Langlands dumbass avatarfag.

you better get used to it. linear algebra is used in almost every other field of math.

Don't bother with shitposters. Just report the avatarfagging brainlet's posts.

gorilla and 2hu permaban when?

who is he avatarfagging as?

Why do hate them so much? They are cool, and you are just evil. Be friendly and kind, and you will see how wonderful our world is. I hope that you said it not seriously, just a bad mood.

When you actually start talking about math.

what even counts as avatarfagging, can one avatarfag as a mcchicken?

For me it's the best fast food sandwich.

>Holo avatarfag defends fellow avatarfags
You fags are the reason why /math/ is shit.

I saw these at the grocery store near me, you think they're any good?

>You fags are the reason why /math/ is shit.
which math-related posts are yours in this thread?

Get the tar tar sauce desu big mac sauce is gross

is that you on the left or you on the right?

Both rofl

yukari from 2hu. when hes not posting yukari, hes posting some other 2hu girl.

>yukari from 2hu. when hes not posting yukari, hes posting some other 2hu girl.
sorry weeb, i have no idea what these words mean

good night /math/

Good night senpai.

web.math.princeton.edu/~nelson/books/1.pdf

Pretty cool for just 26 pages.

[math] \text{if} \ U\ \text{and}\ V\ \text{are unitary}\ n\times n \ \text{matrices, show that the commutator}\ [U,V]=UVU^{-1}V^{-1}\ \text{obeys the inequality}\ \| [U,V]-I\|_{op} \leq 2\| U-I\|_{op}\|V-I\|_{op} [/math]

why aren't there many good math quotes?

>implying there are good quotes
Say something wise yourself and leave other people alone with their words.

Cauchy-Schwarz????

>Cauchy-Schwarz?
No.

>/mg/ is spread over two threads
This really triggers my autism. Can we please stick to one thread and move to the other one after this one reaches bump limit?

Is pi dimensionless?

[math][\pi ]=\frac{[\text{Perimeter}]}{[\text{diameter}]} = \frac{m}{m} = 1[/math]

Ye this proves that [math]\pi[/math] has dimension 1 so it's not dimensionless.

This.

Math noob here, why so many brackets? And what's the meaning of m?

dimension analysis, you take some quantity and you get its units, for example [F]=[ma^2]=[m][a]^2=kg(ms^-1)^2=kg*m^2*s^-2, and he used that the unit of diameter and perimeter is metre

What?

On wikipedia it says that when the unit is the same it's dimensionless tho.

This series of threads is a prime example of what is wrong with "generals".

I've been observing this for a while. We have a few tripfags/avatarfags circlejerking, often engaging in off-topic chitchat, and a few obligatory meme shitters posting intentionally retarded "troll" questions. Actual on-topic content is ignored, but due to the existence of a "general" it has become discouraged to post math related questions in separate threads, since they are immediately pointed to the "general". Thanks for destroying the board, faggots.

just got a B in my calc classs....
it was so fucking ez that i never studied for it.... should i feel bad?

have u guys ever gotten anything lower then an A and if so, what were the reasons behind it?

that's what [x]=1 means, x dimensionless

the vast majority of this board is garbage, I have every thread hidden except for /math/ and /sqt/

but where is the on-topic content you see getting ignored?

I posted in earlier versions of this general and never received a reply. Just rename the fucking thread to "avatarfag circlejerk".

>I posted in earlier versions of this general and never received a reply.
posted about what?

>p-pls respond!!
(You)

math

sounds like you make very uninteresting posts, i'm not surprised you got no reply

Let f : X --> Y be a dominant, generically finite morphism of finite type where X,Y integral. Show there is an open dense subset U of Y s.t. the induced morphism preim(U) --> U is finite.

If you consider math "uninteresting", then don't come to the math board. For anti-intellectuals we still have

i said your posts were uninteresting, not math

your reading comprehension is probably not high enough to do math anyway

Define your terms and give reasons for why these those properties are interesting. Low effort posts like these are the ones killing /math/, nothing else.

>these those
Fug

Someone who doesn't already know what those terms mean won't be able to help me.

Oh didn't know you were asking for help on your homework.

Not homework, but is that type of problem.