/mg/ - Mathematics General

[Anonymous No.11909838]

Dynkin Edition

Previously >>11903921

[Anonymous No.11909842]

>>11909838
first for sucking cock

[Anonymous No.11909845]

second for elliptic functions

[Anonymous No.11909848]

second for elliptic functions

[Anonymous No.11909868]

Where is he?

[Anonymous No.11909888]

Why is E8 the secret to the universe?

[Anonymous No.11909889]

>Zariski topology

[Anonymous No.11909891]

>>11909838
fourth for the absolute state of your maths departments

[Anonymous No.11909893]

Burying myself with warm red sand, I internally reviewed the first manuscript I was to translate. It was on new discoveries in fluid dynamics, a paper on how a fluid field could be described by differential functionals of with certain internal tension forms. As I tried to string together mathematically coherent German sentences, I swirled the sand around me in slow-time, trying to observe the effects talked about in the paper. Feeling graphs slowly shifting over time helped, I believe, putting a geometry to my writing where one set of grammar was within the function and the other without – Die Funktion von W.
Language, though preserving most of its vocabulary and grammar, has been taking the course mathematics did in the 22nd century after the introduction of hypersymbolism by Feynman and then the string theorists in their equation-diagrams.

>what do you guys think of this math paragraph in my scifi story

[Anonymous No.11909895]

>>11909893
>differential functionals of with certain internal tension forms
check your grammar, but I liked it otherwise

[Anonymous No.11909897]

>>11909893
>of with

[Anonymous No.11909899]

>>11909891
do Americans really?

[Anonymous No.11909901]

Do the only automorphisms of k[X_1, ... , X_n] that fix k arise from linear substitutions?

[Anonymous No.11909905]

>>11909891
kek Harvardfags btfo

[Anonymous No.11909909]

What is the white man's field of maths, /mg/?

[Anonymous No.11909920]

>>11909909
Algebra

[Anonymous No.11909921]

>>11909909
Everything

[Anonymous No.11909932]

>>11909909
geometry and topology
and analysis if you want to count Jews as white, although that was mostly the 20th century and they're being rapidly replaced by the Chinese. At the moment the Chinese really only have a stranglehold on PDE groups though.

[Anonymous No.11909939]

>>11909909
Everything except the really autistic jewish stuff

[Anonymous No.11909949]

>>11909932
>rapidly replaced by the Chinese
Chinese papers are almost all boring and terrible.

[Anonymous No.11909992]

>>11909901

[Anonymous No.11910008]

>>11909891
wtf this is a blue board

[Anonymous No.11910019]

bros...
why doing maths is so stressful...

[Anonymous No.11910027]

>>11909842
Are you offering?

[Anonymous No.11910028]

>>11910019
because it matters

[Anonymous No.11910029]

>>11910019
Why not? Stress is fun.

[Anonymous No.11910034]

i'll do the honours
>Elliptic curves

[Anonymous No.11910046]

>>11910034
why are elliptic curves so special?

[Anonymous No.11910051]

>>11909891
fuk

[Anonymous No.11910053]

>>11910046
>he thinks elliptic curves poster knows literally anything about them

[Anonymous No.11910055]

The elliptic curves Chad fears the abelian varieties gigachad

[Anonymous No.11910072]

>>11910053
the real elliptic curves poster isn't here yet, i just did it for him because he's late

[Anonymous No.11910073]

>>11909891
kys

[Anonymous No.11910075]

>>11909909
>pic
I can't wait until biology subsumes sociology and critical theorycels get the rope

[Anonymous No.11910083]

Threadly reminder to work with gender theorists.

[Anonymous No.11910093]

>>11910083
work on what

[Anonymous No.11910096]

>>11910093
On your whiteness and your preconceptions.

[Anonymous No.11910101]

>>11910093
here's one of the great unsolved problems of mathematical gender theory: what is the cardinality of the set of sexual orientations?

[Anonymous No.11910109]

>>11910101
define sexual orientations. You may not use oriented manifolds.

[Anonymous No.11910110]

>>11910101
am I allowed to use forcing or is that rape culture?

[Anonymous No.11910116]

>>11910101
Assume that there's a set of all genders:
That is literally fascism and imposing your disgusting preconceptions on the possibilities of trans people. Who are you to tell people what genders they can identify as, bigot?
Thus, there are only two genders, q.e.d.

[Anonymous No.11910132]

>>11909888

[Anonymous No.11910146]

Context: Sturm-Liouville stuff.
Did the author slip up with the [math]y^2(0)[/math] and it should be [math]y(0)^2[/math]? On one hand, [math]y(y(0))[/math] shouldn't necessarily exist, from the definitions until now. On the other, he kinda placed the exponents inconsistently, so I don't know.

[Anonymous No.11910179]

>>11910146
Writing [math]f^2(x)[/math] for [math]f(x)^2[/math] is a common notation in some fields, especially for older books and older people. It's still done with [math]\sin^2x[/math] instead of the ugly [math](\sin x)^2[/math], with logarithms and theta functions, and so on.
He didn't slip up, he just assumes the reader won't be that much of an autist to get too fucked up about it, and will know exactly what he means.

[Anonymous No.11910184]

>>11910101
Independent of ZFC

[Anonymous No.11910185]

>>11910019
I never deal properly with problems in my life so if I see a problem and I don't get the answer instantly in my head I go into a trance of brainlet self hatred. Which I might deserve, but it certainly doesn't help

[Anonymous No.11910192]

>>11910179
>He didn't slip up, he just assumes the reader won't be that much of an autist to get too fucked up about it, and will know exactly what he means.
I wouldn't get confused if he consistently used one of them, you ass.

[Anonymous No.11910196]

Yeah, I'm thinking I'm too dumb for algebraic topology.

[Anonymous No.11910201]

>>11909891
Plz dont kil her =(

[Anonymous No.11910218]

i was thinking about the problem of which is bigger out of 2^300 and 3^200, which can be solved by just seeing that 2^3<3^2, but is there a general solution to this, where is x^kx bigger than (kx)^x? and what about (x+k)^x and x^(x+k)? i looked on wolframalpha and where k=1, x^(x+k)>(x+k)^x for x>=2.29317 but why is that? what processes do you use to find the solutions to x^kx=(kx)^x and (x+k)^x=x^(x+k)

[Anonymous No.11910224]

>>11910218
take logarithms

[Anonymous No.11910226]

>>11910192
kek

[Anonymous No.11910227]

>>11909891
Bitches name is Milena D, fyi. It was irking me

[Anonymous No.11910254]

>>11909891
state of this shitboard

[Anonymous No.11910294]

If I have something like [math]\sqrt{a^2 + b^2 - 2ab\cos {\beta}}[/math], any idea on how to simplify it?

[Anonymous No.11910304]

>>11910294
nothing to simplify here

[Anonymous No.11910306]

>>11910294
plug it into wolframalpha?

[Anonymous No.11910308]

>>11910294
unless you're getting this from cosine law on some triangle, in which case it's just the other side, there's nothing you can do in general

[Anonymous No.11910352]

>>11910218
https://www.youtube.com/watch?v=PI1NeGtJo7s

[Anonymous No.11910370]

>>11910101
depends if you are using axiom of gender choice

[Anonymous No.11910385]

>>11910101
say there are 4 billion people of sexual maturity on the planet, attraction to any subset of them defines a unique sexual orientation, therefore there are approximately [math]2^{4000000000}[math] possible sexual orientations.

[Anonymous No.11910388]

>>11910294
Write it as the magnitude of the vector [math]\mathbf{u}=(a,b)[/math] with [math]\beta[/math] the angle between [math]a[/math] and [math]b[/math]

[Anonymous No.11910456]

I will do my best to become 世界で一番強い数学者 (the world's strongest mathematician).

>>11909848
based, I'm going to read up on this and elliptic integrals soon

[Anonymous No.11910469]

>>11910456
>I will do my best to become 世界で一番強い数学者 (the world's strongest mathematician).
そ です か

[Anonymous No.11910470]

what are some good differential geometry textbooks?

[Anonymous No.11910472]

>>11910470
What level? Tapp's is good for a quick introduction.

[Anonymous No.11910480]

>>11910470
the existence of a good differential geometry book would imply that differential geometry is capable of being a good subject, which is a contradiction

[Anonymous No.11910482]

>>11909909
Number Theory

[Anonymous No.11910483]

>>11910470
do carmo
tu

[Anonymous No.11910491]

If I want to prove that F is a function (equivalent class) in a Sobolev space H^k, all I need to do is show that F is finite with respect to the H^k norm, right?

[Anonymous No.11910493]

>>11910483
>tu
What is this?

>>11910470
Besides Do Carmo's 2 books, I liked Theodor's Frankel: Geometry of Physics. It's covers everything in an adequate level of rigor. Physics is not necessary prerequisite.

[Anonymous No.11910494]

>>11910491
Yes.

[Anonymous No.11910507]

>>11910493
https://lmgtfy.com/?q=tu+differential+geometry&s=b

[Anonymous No.11910509]

>>11909891
based

[Anonymous No.11910510]

>>11910507
Based.

[Anonymous No.11910513]

>>11910470
lee smooth manifolds and riemannian manifolds

[Anonymous No.11910514]

>>11910507

I didn't realize it was a surname. I thought it was an acronym.

[Anonymous No.11910515]

>>11910513
Don't like it. Too terse and dry. Not good for a beginner imho.

[Anonymous No.11910519]

For which matrices is
[math] (Mu)^T\cdot v = v^T \cdot (Mu) [/math]
?

[Anonymous No.11910532]

I need a book with harder problems and solutions for linear algebra. Any recommendations?

[Anonymous No.11910536]

>>11910532
Halmos

[Anonymous No.11910538]

>>11910532
Proofs or computational?

[Anonymous No.11910555]

>>11910470

http://www.topology.org/tex/conc/differential_geometry_books.html

http://www.topology.org/tex/conc/dg.html

[Anonymous No.11910574]

Are there any explanations for why finite rings "lean" towards commutativity?
There's the classical example of finite division rings being full-on fields. There's also the thing with how if they have a one-sided identity they have a normal identity.

[Anonymous No.11910600]

>>11910574
maybe there's just few finite rings or they spill over, in their finite characteristic, to the unit too easily

[Anonymous No.11910623]

>>11910574
there are too few elements

[Anonymous No.11910646]

>>11910480
why do you think it's a bad subject?

[Anonymous No.11910656]

>>11910646
because I got pleb filtered

[Anonymous No.11910657]

>>11910370
Underrated.

[Anonymous No.11910662]

>>11910519
All matrices over a ring with commutative multiplication, assuming you have defined the dot product between a row and column vector without any messy operations like complex conjugates.

[Anonymous No.11910665]

>>11910574
¿The billion different proofs of Wedderburn's Little Theorem don't do it for you?

[Anonymous No.11910677]

Redpill me on complex multiplication.

[Anonymous No.11910679]

>>11910677
it's a multiplication
of complex numbers

[Anonymous No.11910680]

>>11910679
I really hope that's trolling.

[Anonymous No.11910681]

>>11910662
thx, thought so

[Anonymous No.11910684]

>>11910677
complex - it means not simple
multiplication - shit like three times four

[Anonymous No.11910687]

>>11910680
of course it is, its just real multiplications with a funky square root somewhere there

[Anonymous No.11910705]

>>11910677
When two complex numbers love each other very much, they look gently at each other and hold hands, and the end result is a beautiful baby complex number.
This is called complex multiplication.

[Anonymous No.11910708]

>>11910705
>the end result is a beautiful baby complex number.
your sense of beauty is skewed

[Anonymous No.11910709]

Do retards on /mg/ really not know what complex multiplication is? Are there only highschoolers and undergrads here?

[Anonymous No.11910715]

>>11910705
>>11910687
>>11910679
Wow anons youre all so funny! Any plans on becoming stand up comedians?

[Anonymous No.11910719]

>>11910715
nah, physics not my thing

[Anonymous No.11910721]

>>11910709
no one bothers to respond to low-quality dumb questions seriously
also, i'm pretty sure even highschoolers know complex numbers

[Anonymous No.11910730]

>>11910709
I don't know what complex multiplication is, but I don't really give a shit about algebraic geometry.

[Anonymous No.11910735]

>>11910721
>>11910730
The absolute state.

[Anonymous No.11910739]

>>11910709
Your question was dumb faggot. Learn to Google shit

[Anonymous No.11910756]

Hi mthematics generab!

I have a homework promleb from scjool and was wonderifn if you could helep me solve it?????

>pic related

[Anonymous No.11910764]

>>11910721
Highschoolers are taught about complex numbers, but I wouldn't say they have any sort of meaningful intuition regarding them.

[Anonymous No.11910785]

>>11910764
especially regarding elliptic curves

[Anonymous No.11910799]

>>11910709
Its the induced multiplication on the quotient ring of R[x] / (x^2 + 1)
what answer were you expecting

[Anonymous No.11910802]

>>11910709
Let a and b be complex numbers. Let c=ab. The magnitude of c with be the product of the magnitudes of a and b and the angle of c will be the sum of the angles of a and b.

[Anonymous No.11910803]

>>11910799
I don't know, stuff about points and curves I guess

[Anonymous No.11910812]

>>11910799
[math]\mathbb{R}[x]/\langle x^2+1\rangle \cong \mathbb{C}[/math]

[Anonymous No.11910816]

>>11910785
Based.

[Anonymous No.11910819]

>>11910735
A lot of people can criticize me for my tastes in fields, but not algebraic geometers, in particular algebraic geometer frogposters, go to hell.

[Anonymous No.11910824]

So nobody here actually knows anything about elliptic curves? Despite talking about it in literally every single thread?

[Anonymous No.11910825]

>>11910819
what do you do that's so great then mr. fancy pants?

[Anonymous No.11910828]

Why don't you stop shitposting RIGHT NOW and solve this simple exercise:
[eqn]\int_0^{+\infty} sin(x^2) dx = ? [/eqn]

[Anonymous No.11910829]

>>11910825
I fuck your mother.

[Anonymous No.11910831]

>>11910824
Anything in particular you want to know?

[Anonymous No.11910833]

>>11910831
Yes, complex multiplication. Recommend me books or stuff about it.

[Anonymous No.11910834]

>>11910828
Sure thing bub.
https://www.wolframalpha.com/input/?i=integral%20of%20sin%28x%5E2%29%20from%200%20to%20infinity

[Anonymous No.11910838]

>>11910834
beat me to it

[Anonymous No.11910840]

>>11910828
[math]\sqrt{\frac{\pi}{8}}[/math]

[Anonymous No.11910843]

>>11910834
>>11910838
The absolute state.

[Anonymous No.11910846]

>>11910833
http://swc.math.arizona.edu/aws/1999/99RubinCM.pdf

[Anonymous No.11910848]

>>11910843
why would I waste my time on something a machine can do for me?
Best quality of a mathematician is laziness

[Anonymous No.11910850]

>>11910846
Thanks fren

[Anonymous No.11910855]

>>11910848
>It is beneath the dignity of excellent men to waste their time in calculation when any peasant could do the work just as accurately with the aid of a machine.

[Anonymous No.11910856]

>>11910848
just making sure you are an unskilled mathematician who couldn't solve it by hand ;)

[Anonymous No.11910861]

>>11910856
integrals arent math

[Anonymous No.11910862]

>>11910856
I can
No need to though

[Anonymous No.11910871]

>>11910843

[Anonymous No.11910872]

>>11910861
sorry, wanted to post something easy, but i guess it's still too hard for you
maybe this problem will be more suited to your level:
123 + 456 = ?

[Anonymous No.11910877]

>>11910828
[eqn] -\infty < \int_0^\infty \sin(x^2)dx<\infty [/eqn]

[Anonymous No.11910880]

>>11910872
789

[Anonymous No.11910883]

>>11910880
utterly based

[Anonymous No.11910884]

>>11910872
>more suited to your level
>a literal calc baby

[Anonymous No.11910893]

>>11910861
They are.
[math]\int _{-\infty} ^ {\infty} e^{-x^2}dx=\sqrt{\pi}[/math] is one of the coolest proofs in mathematics.

[Anonymous No.11910892]

>>11910884
Couple weeks into calculus 1 now, doing well, already past the chain rule and beyond. Quotient rule was a joke. Product rule remains my specialty.

I ask my professor his thoughts on quantum mechanics and partial derivatives. He's impressed i know about the subject. We converse after class for some time, sharing mathematical insights; i can keep up. He tells me of great things ahead like series and laplacians. I tell him i already read about series on wikipedia. He is yet again impressed at my enthusiasm. What a joy it is to have your professor visibly brighten when he learns of your talents.

And now I sit here wondering what it must be like to be a brainlet, unable to engage your professor as an intellectual peer.

All of the deep conversations you people must miss out on because you aren't able to overcome the intellectual IQ barrier that stands in the way of your academic success... it's so sad.

My professor and I know each other on first name basis now, but i call him Dr. out of respect.

And yet here you brainlets sit, probably havent even made eye contact with yours out of fear that they will gauge your brainlet IQ levels.

A true shame, but just know it is because i was born special that i am special. I can't help being a genius, nor can my professor.

Two of a kind is two flocks in a bush.

[Anonymous No.11910899]

>>11910880
Peak mental performance.
>>11910893
t. statiscian who's never seen a kino proof in his life.

[Anonymous No.11910902]

>>11910892
Holy shit you stupid fucking undergrad. You do realize that calculus 1 is so fucking elementary even a child could learn it? In fact children do learn calculus because calculus is for idiot children. Undoubtedly you are taking some shit, remedial college class at a noname college - you think lemmas are a fucking fruit from Lord of the Rings (I'm doing quite well at a top 20 graduate programme and have passed all of my qual's with flying colours, so don't bullshit me).

Your professor does NOT want to talk with you snivelling child. He DOESN'T CARE ABOUT YOU. I'm sure he was holding back his laughter when you raised the topics and you may have just seen him rub his left arm after experiencing symptoms of an oncoming heart attack induced purely by the cringe of you skimming Wikipedia pages after jacking off to Brady on Numberphile.

You are not special and clearly will never make it past trivial proof courses before you 'drop out' and 'transition' to your preferred field of study - drooling, smooth brain comp. sci. Seen the same with your types dozens of times as a TA and it's always the same. Bright young kid with a big attitude from a small part of town moves to the big boy pond and can't cope. Horizons too narrow. Goes back to the baby pond with newfound superiority complex over the urchins and engineers that tremble in your mathematically superior presence.

Many. Such. Cases.

[Anonymous No.11910916]

>>11910902
haha yess my pasta is back

[Anonymous No.11910931]

>>11910799
The right one, about automorphisms of elliptic curves.

[Anonymous No.11910944]

>cannot do basic integrals
>runs away into category theory or other bullshit gay field
why does this happen so often?

[Anonymous No.11910969]

What is the exact relationship between function spaces L^infinity and L^p for p finite?

If f is in L^infinity it is in L^p right?
But doesn't the opposite also hold?

[Anonymous No.11910974]

>>11910944
because integrals are useless, so they do something more worthwhile

[Anonymous No.11910980]

>>11910969
I dunno anon, is [math]f(x) = 1[/math] in [math]L^p (\Omega)[/math] for an arbitrary domain [math]\Omega[/math]?

[Anonymous No.11910988]

>>11910969
no relationship in general
if the measure is finite, then you can work out some inclusions

[Anonymous No.11911014]

>>11910893
Which proof do you know?

[Anonymous No.11911020]

>>11911014
The one that involves squaring the integrand and converting to polar coordinates.

[Anonymous No.11911134]

>>11909891
Fucking hell, I wish I could cure my obsessive thinking.

[Anonymous No.11911142]

>>11910899
>never seen a kino proof in his life.
not him, but please post kino proofs

[Anonymous No.11911152]

The entirety of mathematics, but specifically Differential Equations and Dynamical Systems, concepts non-whites are utterly incapable of understanding hence the lack of technological ingenuity.
>>11909939
algebra and number theory are both white dominated historically, Jews have contributed more to analysis (Faustian) than any other field of math.

[Anonymous No.11911155]

>>11911142
Mochis proof of abc

[Anonymous No.11911158]

>>11911142
the proof of the classification of semi-simple Lie algebras.

[Anonymous No.11911171]

>>11911155
brother, don't tell me you understand it

[Anonymous No.11911185]

>didn't research PHY homework and just plugged shit on mathway and was done with it and proceeded to go program video games because that's more fun
>cramming because I have mid-terms in two days
>its literally just convoluted right triangles and three formulas which one is literally just adding the other two.
>got 100% on the midterm review

college and physics are a joke.

[Anonymous No.11911189]

>>11911171
Only the important parts

[Anonymous No.11911199]

>>11911185
>on the midterm review
So, is this distinct from the midterm and you are presumably doing online examinations without a proctor correct? Two distinct questions, please answer both of them thanks.

[Anonymous No.11911239]

>>11911199
I suppose the professor is not such a dick that will make a mid-term review that doesn't cover everything that the test will not cover.
Also, no, our college is paying for online proctors and I honestly don't want to risk it and cheat.
But the normal weekly quizzes and homework are not proctored.

[Anonymous No.11911286]

>>11911189
I love her....

[Anonymous No.11911311]

>>11911239
Wait until you take the exam before basking in your own intellectual supremacy. Feedback is important to update your model of your own abilities. This is freshman physics right? That shit is just a filter for non-majors and the innumerates. Wait until, presuming you're going into physics, you get to the upper division courses.

[Anonymous No.11911313]

>decent at writing proofs and dealing with objects in the abstract
>fall apart or fuck up whenever presented with a computational problem
How do I remedy this?

[Anonymous No.11911316]

>>11911311
how hard can it be? lol.

can't wait to see how I pass the next two PHY classes and get these ez A's and never ever having to take PHY again.

[Anonymous No.11911319]

>>11911316
Significantly harder than anything you will see in freshman physics by an order of magnitude. Since you aren't going to be taking more classes beyond your gen ed requirements you won't have to worry about that.

[Anonymous No.11911325]

>>11911313
>>fall apart or fuck up whenever presented with a computational problem
Literraly how? Is it low working memory and you just forget shit, or is your handwriting just that bad? Whichever of those that is your problem, just fix that

[Anonymous No.11911328]

>>11911313
Same, but I'm in undergrad, so not confident enough to say I'm decent at proving.
I think I just hate solving computational problems so much that I never gave it the time, maybe that's your case too?

[Anonymous No.11911337]

>>11909909
Chinks own applied maths. Whitey dominates the rest. 100% that's going to change in a few decades as western schooling focuses on framing every subject as the oppression Olympics whilst eastern schooling leaves its part loyalty shit to history and civics.

[Anonymous No.11911343]

>>11911313
give an example of a computational problem you cant do

[Anonymous No.11911346]

>>11911337
So doing phd in china with focus on applied math is a good idea?

[Anonymous No.11911349]

>>11911343
>>11910828

[Anonymous No.11911350]

>>11911325
Guarantee its bad working memory as that seems vital to computational tasks and would explain why asians excel at these things so effortlessly. See also >>11911337 though they don't "own applied maths" they're just unusually good at it.

[Anonymous No.11911357]

Does anybody know something about the SISSA PhD school (Trieste, Italy)?

What do you think of it? Is it a good place to pursue a PhD? (Pure maths)

[Anonymous No.11911359]

>>11911349
Have you tried copying the trick used for [math]\exp(-x^2)[/math]?
Because I'm pretty sure you either do that or you exploit what [math]z^2[/math] looks line in polar coordinates with Cauchy-Goursat.

[Anonymous No.11911384]

>Frobenii

[Anonymous No.11911386]

>>11911343
Show that [math]17\cdot7=119[/math] without performing any multiplications

[Anonymous No.11911388]

>>11911384
post 10 examples where this happened

[Anonymous No.11911389]

>>11911386
17+17+17+17+17+17+17=119

[Anonymous No.11911390]

>>11911389
A brilliant trick!

[Anonymous No.11911391]

>>11911389
Shit he's fast.

[Anonymous No.11911393]

>>11911389
but that is by definition, multiplication

[Anonymous No.11911397]

Can someone enlighten me please.
the question is:
>A cubic box with an edge of exactly 2cm has a volume of (in meters)
So what I did was (2cm)^3 = 8cm^3 and then converted to meters so my answer was 8x10^-6 m^3.
How was it wrong and why is the answer 2x10^-6 m^3?
Am I low IQ?

[Anonymous No.11911400]

>>11911393
Is it, though?

[Anonymous No.11911403]

>>11910828
How bad should I feel about myself for not being able to solve this on my own

[Anonymous No.11911411]

>>11911403
depends.
high school: not bad
freshman: not that bad
anything after freshman: bad
you have a degree: get the vodka out

[Anonymous No.11911414]

[math]17\cdot 7=(12+5)(12-5)=12^2-5^2=144-25=119[/math], using the well-known results from the literature, that [math]12^2=144,5^2=25[/math], and [math]a^2-b^2=(a-b)(a+b)[/math].

[Anonymous No.11911419]

>>11911386
divide both sides by 7

[Anonymous No.11911421]

>>11911414
how is that computational?

[Anonymous No.11911425]

>>11911411
Should I be able to solve this after calculus?

[Anonymous No.11911427]

>>11911403
its an integral, you shouldnt even care about it to begin with

[Anonymous No.11911434]

>Textbook uses both [math]\xi[/math] and [math]\zeta[/math] for indices

[Anonymous No.11911445]

>>11911425
https://en.wikipedia.org/wiki/Fresnel_integral

[Anonymous No.11911454]

>>11911427
The classic "I will vehemently insist that everything I suck at doesn't matter anyway" cope

[Anonymous No.11911457]

>>11911454
kiss my wolfram link, you filthy undergrad

[Anonymous No.11911461]

>>11909838
>Dynkin Edition
How can F4 be 52-dimensional yet have rank 4?

[Anonymous No.11911466]

>>11911454
Refer to >>11910855. The person who developed integration even agrees that it's a waste of time to be done by humans.

[Anonymous No.11911471]

>>11911461
Please go read the definition of "rank"
then go read the definition of "dimension"
after you do those two things, the answer will be clear

[Anonymous No.11911476]

>>11911471
Based.

[Anonymous No.11911480]

>>11911466
Integration was just infidel mathematicians making twofold mistakes that arrived at the truth until long after Leibniz died.

[Anonymous No.11911481]

>>11911466
>The person who developed integration even agrees that it's a waste of time to be done by humans.
And the person who developed modern algebraic geometry said that his work was an abomination and that all copies of it should be destroyed. What's your point?

[Anonymous No.11911485]

>>11911481
I hope you're not implying that Grothendieck was wrong.

[Anonymous No.11911488]

>>11911481
And he was right.

[Anonymous No.11911495]

>>11911471
>Please go read the definition of "rank"
What is Cartan subgroup? What is transcendence degree?

[Anonymous No.11911499]

>>11911495
read.
the.
definitions.

[Anonymous No.11911502]

>>11911346
Absolutely not - all the best Chinese academics wind up in the US.

[Anonymous No.11911505]

>>11910388
He said simplify it, not move it into a different field of mathematics.

[Anonymous No.11911506]

>>11911502
Most of the mediocre ones end up in the USA too. Mainland China is a dystopian hellhole, anyone with any ability to do so escapes as soon as they can.

[Anonymous No.11911507]

>>11911499
>read.
>the.
>definitions.

>In mathematics, a Cartan subalgebra, often abbreviated as CSA, is a nilpotent subalgebra {\displaystyle {\mathfrak {h}}}{\mathfrak {h}} of a Lie algebra {\displaystyle {\mathfrak {g}}}{\mathfrak {g}} that is self-normalising...

ELI5?

[Anonymous No.11911514]

>>11911507
Why do you find it confusing that a Lie group can have more than one property? Rank and dimension are different things. I don't understand why this would confuse you. It's like asking how a box can have width 4 yet volume 64.

[Anonymous No.11911521]

>>11911397
pls tell me if im retraded

[Anonymous No.11911527]

>>11911506
I have met one person who wanted to go back to China. She was not born there and has only visited. While tutoring her in trigonometry over the summer, she explained to me that she preferred the way people were there and the way the culture and country is. She especially liked the social credit system, which lets people move beyond their class. She then told me about how elites have figured out how to abuse the social credit system to their benefit, which holds other people back. She then asked me if I knew of an indoor water park nearby. I asked her why it had to be indoor, and she told me it was because there are so many top-level performers vying for jobs in China that they decide who gets better positions based on things like beauty standards. Since darker skin is viewed as less attractive, she didn't want to have her skin any darker than it already was. She then told me about how she wished she lived in a community with an HOA so she could get the people who wouldn't mow frequently evicted from next to her.

Maybe it's just my white culture and attitude coming through, but nothing she said sounded good to me.

[Anonymous No.11911529]

>>11911521
>>>/sci/sqt
>>>/wsr/

[Anonymous No.11911532]

I came to tell lyou you are nice!!

>>11911397
The ansrrer tself is wrong.

[Anonymous No.11911535]

>>11911532
Thanks, lad.

[Anonymous No.11911536]

>>11911397
>>11911521
cm to m is itself a conversion factor. You have to cube the conversion factor, not just the magnitude.

[Anonymous No.11911541]

>>11911527
>an actual bug person

[Anonymous No.11911626]

>>11909891
nigger

[Anonymous No.11911635]

>>11909891
Sneed

[Anonymous No.11911666]

>>11911532
>>11911536
>>11911529
thx I was eating my head because everywhere I searched online said I was correct.

[Anonymous No.11911731]

>>11911666
BEHOLD
https://www.wolframalpha.com/input/?i=cube+with+side+2+cm%2C+what+is+its+volume+in+meters%3F

[Anonymous No.11911769]

>>11911731
Is there any computational problem Wolfram can't do?

[Anonymous No.11911823]

>>11910470
Godinho-Natario is basically doCarmo's but better.

[Anonymous No.11911845]

>>11911823
how does it compare to Lee's book on Riemannian Geometry?

[Anonymous No.11911859]

>>11911845
it's a meme

[Anonymous No.11911865]

Based or cringe?

http://www.topology.org/tex/conc/mathlearn.html

[Anonymous No.11911877]

>>11911865

[Anonymous No.11911880]

>>11911845
I haven't checked Lee but from reading its table of contents on Springer I'd say it's different. Natario starts out with smooth manifolds and it adds structure as it advances, and it's not completely focused on Riemannian manifolds since you don't need a metric to define connections for example.

[Anonymous No.11911923]

>>11911865
500 Pages for foundations
pretty based

[Anonymous No.11912054]

>>11909891
epic

[Anonymous No.11912062]

>>11911865
V cringe because of this:
Louis Auslander, Robert Earl MacKenzie
Introduction to differentiable manifolds
1963
ISBN 978-0-486-47172-3
224 pages = 106 A4 pages
My review.
My Amazon review.
This book shows how differential geometry was starting to be overtaken by an unfortunate trend towards algebraic abstraction in the 1960s, which has continued to pervade DG until the present time. They present germs on pages 10–15 and 39–42, which is a pointless abstraction of differentiation that attempts to pretend that differentiation is a topic in algebra. In many other ways, this is an unpleasant book, in too many ways to mention. Chapter 3 on Projective spaces and projective algebraic varieties is particularly pointless and painful. This book shows clearly the way DG was splitting into two subjects, the more abstract algebraic/topological pure mathematical approach (concerned with global topology) and the more applications-oriented approach (concerned with physics and engineering). The one thing I really like about this book is the fibre bundle chapter, which helps to explain how the modern incomprehensible fibre bundle concepts came into being. The last chapter on tensors and multilinear algebra seems to be disconnected from the rest of the book.

[Anonymous No.11912091]

>>11912062
This book is unusually clear and neat, although it is oriented towards pure mathematical geometric objectives rather than anything useful.
Like cmon bro that's the good stuff

[Anonymous No.11912135]

>>11912062
>hates algebrafags
I recall seeing this a few months ago, and in spite of the fact that his thoughts on this matter are indeed based and hygienic I was asking what you thought about his bizarre note taking prescription. I can’t imagine doing what he suggests is in any way efficient, his praise for rote learning is also quite alarming to me.

[Anonymous No.11912162]

>>11912135
The idea in principle is good, "practice what you don't understand, not what is already clear". That being said, I think lines 3-5 are a little overboard, I can learn fine by reading, thanks, and line 8 is just stupid. Quite often reading a little further on will help clear up an issue from earlier.

[Anonymous No.11912241]

Why do we care about Bernoulli numbers?

[Anonymous No.11912286]

/gmmg/

>>11911532
Phew, I remembered posting here but it wasn't worse than this.

>>11911357
>What do you think of it? Is it a good place to pursue a PhD? (Pure maths)
What do you want to work on? Does it have a big name in that field? Should the answer to the second question be "si", does this big name take students? If again "si", then go for it.

[Anonymous No.11912290]

>>11912286
Morning, lad.

[Anonymous No.11912293]

>>11912290
Based lad poster. I hope you have a good day or night depending on your time zone. Working on anything cool?

[Anonymous No.11912296]

>>11912293
Just finished my algebra homework. Probably going to sleep soon.

[Anonymous No.11912302]

>>11912296
What did you have to do?

[Anonymous No.11912313]

>>11912302
Mostly field/Galois theory related stuff.

[Anonymous No.11912320]

>>11912062
>>This book shows how differential geometry was starting to be overtaken by an unfortunate trend towards algebraic abstraction in the 1960s, which has continued to pervade DG until the present time. They present germs on pages 10–15 and 39–42, which is a pointless abstraction of differentiation that attempts to pretend that differentiation is a topic in algebra.
Holy based.

[Anonymous No.11912326]

>>11909893
Either that last paragraph is a gateway in to the thinking of a genius or you need to puncuate it more.

[Anonymous No.11912327]

>>11912313
Gotcha. Sleep tight!

[Anonymous No.11912545]

>>11909891
kek, the quality of /mg/ just keeps improving

[Anonymous No.11912596]

Does anyone know if there is a text or book which summarize what is known about [math]Gal(\bar{\mathbb{Q}} /\mathbb{Q}) [/math]?

[Anonymous No.11912691]

>>11912596
it's a group

[Anonymous No.11912694]

>>11912062
>This book shows how differential geometry was starting to be overtaken by an unfortunate trend towards algebraic abstraction in the 1960s, which has continued to pervade DG until the present time. They present germs on pages 10–15 and 39–42, which is a pointless abstraction of differentiation that attempts to pretend that differentiation is a topic in algebra
He's completely right about this.

[Anonymous No.11912723]

>>11912694
he's a brainlet for rejecting a different approach without any particular reason
>every generic smooth map from a surface into R looks like a projection, a fold, or a cusp in a suitable coordinate system
a lot of stuff like that is proved by module theory applied to the ring of germs

[Anonymous No.11912728]

>>11911769
There isn't.

[Anonymous No.11912753]

I wish we could ban all undergrads from posting here.

[Anonymous No.11912774]

>>11912753
that would leave only highschoolers posting in /mg/

[Anonymous No.11912780]

>>11912728
Two hours of computation have been deposited into your Wolfram account.

[Anonymous No.11912782]

>>11912596
Absolutely not.

[Anonymous No.11912815]

linear algebra book for code monkeying 'computer scientist' that wants to get into machine learning research?

[Anonymous No.11912827]

>numerical analysis

[Anonymous No.11912831]

>>11909891
fk u

[Anonymous No.11912858]

>>11911769
It can't do integrals.
https://www.wolframalpha.com/input/?i=integrate+1%2F(sqrt(1-x^2)+sqrt(1-y^2)+sqrt(1-(x%2By)^2))%2C+{x%2C+-1%2C+1}%2C+{y%2C+-x%2C+1}

[Anonymous No.11912873]

>>11912780
BASED Wolfram rewarding me GENEROUSLY for saying the TRUTH.
>>11912858
Did you Try again with pro computation time?

[Anonymous No.11912886]

>>11911769
Innumerably many.

[Anonymous No.11912912]

When you want to prove that [math]d[/math] is a metric, either it's trivial, [math]d(x, y) \neq 0[/math] if [math]x \neq y[/math] is a pain in the ass, or the triangle inequality is a pain in the ass, (I don't think I've ever seen a case where both of the last two are simultaneously hard, since if proving the non-zero thing is hard the definition usually involves some sort of suprema or infima, and this makes triangle easy).
Have any of you ever seen a metric where proving reflexivity is actually the hardest part?

[Anonymous No.11912929]

>>11910872
456 + 123
addition is commutative.

[Anonymous No.11912955]

>>11912912
reflexivity is usually very obvious and the definitions of metrics are almost always symmetric
the only exception i know is levy-prokhorov metric

[Anonymous No.11913023]

What are /mg/'s favorite examples of combinatorial arguments in calculus/topology?

I'll give two examples to get you going:
1.) The Bolzano-Weierstrass theorem is easily proved by iteratively applying the pigeonhole principle (a Ramsey-style argument).
2.) There's a lovely combinatorial proof of Brouwer's fixed point theorem that's based on Sperner's lemma (actually the two are equivalent).

[Anonymous No.11913030]

Did you know that the German formalism/intuitionism dispute was racially loaded? Many advocates of intuitionism were nazis who detested modern math for being "too jewish". For example Brouwer who presented himself as a "champion of aryan germanness" complained that "Ostjuden" were writing for Mathematische Annalen. Bieberbach viewed modern algebra, set theory and others as way too abstract "franco-jewish" inferior math fields and advocated a more "aryan" type of math that doesn't rely so heavily on axiomatics like formalism

[Anonymous No.11913067]

>>11913023
https://www.impan.pl/~tkoch/COMB_lecturenotes/cbst_lecture_6.pdf

[Anonymous No.11913163]

>>11911769
At the very least the Halting Problem, and any problem that it can be reduced to.

[Anonymous No.11913186]

>>11913163
that's not computational though

[Anonymous No.11913191]

>>11913186
>In computability theory, the halting problem is...

[Anonymous No.11913194]

>>11913186
"find if any program halts" not "find a procedure to find if any program halts"

[Anonymous No.11913195]

>>11913191
>words cannot have multiple meanings

[Anonymous No.11913196]

>>11909891
lmfao

[Anonymous No.11913198]

>>11913194
and? Still not computational.

[Anonymous No.11913201]

>>11913198
how is it not computational

Here is a turing machine: does it halt

[Anonymous No.11913203]

>>11913201
It's as computational as saying
Here is a theorem: is it true

[Anonymous No.11913216]

>>11913203
well speaking of, you probably couldn't feed wolfram alpha something like "here is a formal proof of something, is the derivation valid," but I've never tried

[Anonymous No.11913249]

>>11909901
No, consider
X -> X + YX^2
Y -> Y

[Anonymous No.11913293]

https://en.wikipedia.org/wiki/Archimedes%27s_cattle_problem

[Anonymous No.11913312]

>>11909920
*stares in Al-Khwarizmi*

[Anonymous No.11913323]

>>11913312
Wrong kind of algebra.

[Anonymous No.11913356]

What is better: a very young advisor that comes from a postdoc with a Fields medallist or an older advisor who solved a conjecture when he was young and won some prizes?

[Anonymous No.11913368]

>>11913356
I had a young supervisor for my masters thesis and he was pretty shit at it, but he didnt have that good a background anyway

[Anonymous No.11913369]

>>11913356
The latter.

[Anonymous No.11913375]

>>11913356
The latter all the way.
The latter is easy mode, the former is hard mode.

[Anonymous No.11913398]

>>11913356
Always the older guy.
Young advisors are generally bad at advising; they have no practice actually advising people (it's hard, and it takes time to git gud), they don't know the field as well as somebody with 30 years of professorship in it, and most importantly they're far too busy furiously trying to advance their own fledgling careers to care much about yours.
There's also the issue that young profs almost never have enough clout to really help you out when you need connections, e.g. at job-hunting time. "Postdoc with a Fields medalist" isn't enough to carry that, it's not nearly as incredible as you seem to be implying it is unless he set himself up for the next batch of Fields medals during that postdoc.

[Anonymous No.11913399]

>>11913203
>It's as computational as saying
>Here is a theorem: is it true
This is a computational problem though.
What is your point LMAO?

[Anonymous No.11913406]

>>11910227
thanks anon, was about to ask

[Anonymous No.11913431]

>>11913203
There is no problem in this world that is not ultimately computational.
If you have a counter-example, I'm all ears.
If it's pic related (or something similar), you are a retard, though.

[Anonymous No.11913449]

>>11911142
https://arxiv.org/pdf/math/0403046v1.pdf

[Anonymous No.11913451]

>>11913398
>>11913368
>>11913369
>>11913375

the young guy seems very strong but I guess he is not Fields medal level himself (who knows though).

In general, one should always choose the older advisor then? (given he is not bad)
Is there any special case where one would be advised to choose the younger one?

[Anonymous No.11913464]

>>11913451
>Is there any special case where one would be advised to choose the younger one?
If it's Abel or Galois.

[Anonymous No.11913477]

>>11913451
The younger guy is more likely to post here.
He could also be physically attractive, if you like men.

[Anonymous No.11913483]

Hilbert's hat.

[Anonymous No.11913499]

>>11913483
Is a Panama hat.

[Anonymous No.11913504]

>>11913451
>Is there any special case where one would be advised to choose the younger one?
Of course there are endless special justifications you can make if you feel like it. Maybe the older guy is a sociopathic asshole. Maybe the younger guy is Peter Scholze. Maybe the younger guy is at Princeton and the older guy is at Wyoming State.
There are endless exceptions to any rule that general, but I don't know your exact life situation and I don't care to. It's up to you if you feel like you're in an exceptional case.

[Anonymous No.11913506]

>>11913477
>He could also be physically attractive, if you like men.
But older men are more attractive than middle aged men in many cases. It's sort of like the second puberty. Or that is my opinion, maybe someone finds it to be the other way around.

[Anonymous No.11913510]

>>11913504
Wyoming State > Princeton

[Anonymous No.11913527]

>>11912723
Seethe.
>>11912815
>>11912827
>>11913023
>>11913163
>>11913186
>>11913191
>>11913194
>>11913195
>>11913198
>>11913201
>>11913203
>>11913399
>>11913431
>>>/g/ >>>/out/ you stick out like sore thumbs, you will never be mathematicians, get out.

[Anonymous No.11913533]

>>11913527
how are my posts /g/ you fucking retard?

[Anonymous No.11913544]

>>11913533
off-topic posting is not allowed on /sci/, please respect the rules or go back to where you came from.

[Anonymous No.11913546]

>>11913527
Based.

[Anonymous No.11913548]

>>11913527
Consider taking your meds.

[Anonymous No.11913550]

>>11913544
computational problems are math you mouthbreathing retard.

[Anonymous No.11913552]

>>11913431
>There is no problem in this world that is not ultimately computational.
"What are the fundamental laws guiding reality"

[Anonymous No.11913561]

>>11913550
No they aren’t, and you are not and never will be a mathematician :^)

Seethe more

[Anonymous No.11913564]

>>11913561
>integrals aren't math
>(co)homology groups aren't math
>homotopy isn't math
>geometry isn't math

[Anonymous No.11913569]

>>11913561
>No they aren’t
The problem to derive a proof for a theorem is *literally* a computational problem.
There are *literally* computer programs which *literally* compute proofs.

[Anonymous No.11913571]

>>11913564

[Anonymous No.11913575]

>>11913571
Name a single thing which is math.

[Anonymous No.11913578]

>>11913569
>implying checking is computing

[Anonymous No.11913580]

>>11913575
The proofs in his freshman courses

[Anonymous No.11913587]

>>11913578
Are you on drugs? Or just a retarded undergrad with a superiority complex?
What you say is nonsensical.

>>11913580
Proofs *are* a computational problem.

[Anonymous No.11913596]

>>11913575
Ramsey theory

[Anonymous No.11913598]

>>11913580
shouldnt it be "prooves"

[Anonymous No.11913600]

>>11913587
>redefining math so that CS is a superset over math in order to weasel your way into mathematics
Really makes you think

[Anonymous No.11913609]

>>11913596
Without a doubt questions in Ramsey theory can be brought down to computation.
As, again, proofs are a computational problem.

Also, you are an idiot, Ramsey theory is closely related to combinatorics, which is one of the areas where computational proof assistants are quite involved (see e.g. the four color theorem with its proof). At least say something like functional analysis where it isn't immediately obvious that you are wrong, although you still are...

Also, I highly doubt you know what "Ramesy theory" is, since you appear to be a retarded undergrad...

[Anonymous No.11913613]

>>11913600
>weasel your way into mathematics
I do Analysis and a bit of geometry. I have little interest in anything people in CS do, which doesn't make facts suddenly not true...

[Anonymous No.11913615]

What is hat of mathematicians?

[Anonymous No.11913627]

>>11913615
\land

[Anonymous No.11913672]

>>11913615
[math]\land[/math] and Hilbert's hat.

[Anonymous No.11913685]

>>11913600
CS is a subset of math, though.

[Anonymous No.11913696]

>>11913578
It literally is.
Most NP-hard problems arise from having to explicitly check too many fucking possible solutions.

[Anonymous No.11913698]

what sort of paper should i use for math homework?

[Anonymous No.11913701]

>>11913698
i use white a4 paper

[Anonymous No.11913706]

>>11913701
the only correct answer
doing math on lined paper is pig disgusting

[Anonymous No.11913708]

>>11913698
Lined notebook paper (8.5 x 11)

[Anonymous No.11913719]

>>11913609
>Without a doubt questions in Ramsey theory can be brought down to computation.
Erdos would disagree and use you as a meat shield against the aliens

[Anonymous No.11913725]

>>11913698
[math]\LaTeX[/math]

[Anonymous No.11913747]

>>11913719
Will we ever compute [math]R(6,6)[/math], bros?

[Anonymous No.11913761]

>>11913719
>>11913747
I am a little disappointed we still don't know what R(5,5) is, honestly. I feel like R(5,5) is probably a feasible goal if people actually cared (it's honestly one of the only few left that's a small enough range of small enough numbers to be feasible). When Erdos talked about it he seemed to think it was at least in theory plausible if you threw the entire planet's resources at it, and that was in 1990. The problem's been inched forward a bit since then, and our computing resources nowadays make the global arsenal from 1990 look like a Gameboy.
I guess it's just that computing numbers just for the sake of knowing what they are is Numberphile-tier stuff that people don't generally put too much effort into.

[Anonymous No.11913774]

I have some data that looks suspiciously circular when I use a logarithmic scale for the y-axis. Its density seems to be a reciprocal squared function from the center, and all data is in the first quadrant (+,+). There is a little extra compression between the y-axis and the center of "mass", but not enough to concern me if that kind of function/distribution is a lot more complicated.

What kind of standard or general form would this be? Is there a special type of distribution already documented for what I'm describing? I'm not deeply versed in statistics, and my math is certainly rusty.

[Anonymous No.11913783]

>>11913774
That picture would be a sufficient proof for a category theorist.

[Anonymous No.11913785]

>>11913761
Well, we know [math]R(5,5) \in [43,48][/math], so it's only a matter of time.

[Anonymous No.11913788]

>>11913783
Yeah, but it would't put bread on my table :/

[Anonymous No.11913796]

Anyone know what the underlined module is supposed to represent? M is a module over a ring here, and the x_i are elements of the ring

[Anonymous No.11913800]

>>11913774
One more thing:
I wanted to create a boundary line at a certain density to distinguish the enclosed area of arbitrary high density, and everything else outside. Bonus points if you can define a "ring" of density ranging from density-A to density-B.

[Anonymous No.11913834]

>>11913774
>>11913800
I threw this together in a couple minutes. Not familiar with the interface to make an axis logarithmic, but my inner-brainlet tells me it would be something akin to this:
https://www.desmos.com/calculator/pnhiy1b8z2

[Anonymous No.11913861]

>>11913796
Can you give any context?

[Anonymous No.11913917]

>>11913747
>>11913761
i browsed some surveys on ramsey numbers recently, here's a curious fact: the lower bound on R(6, 6) is 50 years old

[Anonymous No.11913929]

[math]R(3,3,3)=17[/math]

[Anonymous No.11914027]

>>11913929
speaking of other autistic computations, here's one i find interesting: number of posets on n elements, this has only been done up to n<=16 or something
https://en.wikipedia.org/wiki/Finite_topological_space#Number_of_topologies_on_a_finite_set

i'd like to find something obscure enough and compute some funny number myself

[Anonymous No.11914039]

>>11914027
>https://en.wikipedia.org/wiki/Finite_topological_space#Number_of_topologies_on_a_finite_set
That blows up fast.

[Anonymous No.11914091]

>>11914027
This one is interesting to me in a different way. One one hand the individual cases are less interesting, because they're just fucking huge; it's somehow much less satisfying to say "the answer is [bangs on number pad for 30 seconds]" than it is to say "the answer is 43"
On the other hand "the number of posets on an n-set" seems like an innocuous combinatorial thing that looks at first glance reasonably like it could have a generating function or at least a recurrence or SOME way of getting at it, yet it doesn't have anything at all.
Whereas he Ramsey numbers are one of those things where it's completely unreasonable to expect to be able to say anything useful about the general numbers, in fact (hot take incoming) it's probably more reasonable to expect somebody will prove some undecidability result about them.

[Anonymous No.11914160]

Is it common for you to also start doubting a theorem you already know the proof of and having to rework it to yourself? I feel like this is influence of this internet skepticism making me doubt everything

[Anonymous No.11914167]

>>11913929

now what's the algebraic interpretation of this picture

[Anonymous No.11914192]

>>11914167
spirograph 2.0

[Anonymous No.11914280]

>>11913564
Correct on all accounts.