/mg/

[Mult No.12715244]

Math, in general
>a shape of algebra
Talk mass

FrÜher: >>12692234

[Anonymous No.12715301]

you all have girlfriends right? math is sexy r-right guys?

[Mult No.12715351]

>>12715301
I got a hippie chick fascinated with math but she wouoldnt sex me, sadly. Im working ona psychoapathic programmer girl rn

[Anonymous No.12716343]

>>12715244
Stop fucking making the OP while namefagging and posting in german. Are you genuinely trying to kill these threads?

[Anonymous No.12716815]

>>12715301
I've had chicks interested in me, but I just ignore them
math is my waifu uwu

[Anonymous No.12716819]

>>12716343
just filter that faggot

[Anonymous No.12716881]

>>12715244
Nice sandpile fractal, those are great.

[Anonymous No.12716924]

>tfw children are better at Abstract Algebra than you
https://youtube.com/watch?v=XMu1O0OnStI

[Anonymous No.12716935]

How I C Mathematics:

[Anonymous No.12716944]

>>12715301
Im Here, bro.

[Anonymous No.12717093]

Graduating from a decent school with a 3.7 major GPA (used to be a 3.9, had a terrible year with some important classes.) Two research projects that went nowhere, and two more from an unrelated (Computer Engineering) major. Where do I stand as a grad school applicant?

I want to do math, but I don't think I can teach that well. Are there any career options for people like me?

[Anonymous No.12717141]

>>12717093
Responded to you in /sqt/. I should also mention that it does depend on what fields of math you like. I was highlighting stuff that uses numerical analysis and linear algebra, but if you like shit like algebraic topology or something you might have a tougher time making those CompEng experiences sound meaningful.

[Anonymous No.12717200]

>>12717141
Thanks anon! I responded in /sqt/.

[Anonymous No.12717611]

>finish math problem
>think to myself the result is beautiful
I think I caught the autism.

[Anonymous No.12717630]

>>12716924
Who does he remind me of?

[Anonymous No.12717656]

>>12717630
It might be this but I'm not sure.
https://www.youtube.com/watch?v=hz_gOFRwTcg
>>12717611
What was the result?

[Anonymous No.12717823]

(ab)(ab) = a^2 + 2ab + b^2

[Anonymous No.12718085]

>>12717611
I feel ya lad
especially when the whole thing is typeset cleanly in Latex

[Anonymous No.12718095]

>>12717823

[Anonymous No.12718200]

anyone know some cool inequalities?

[Anonymous No.12718214]

>>12718200
OP ∈ Fag
For every possible OP

[Anonymous No.12718267]

>>12718200
x = i
where is your order now

[Anonymous No.12718276]

>>12718200
n=1 or x=0.

[Anonymous No.12718277]

>>12718200
It's not even true for n=1

[Anonymous No.12718307]

>>12718200
Shouldn't the inequality be greater than or equal to, n is natural number, x>=0

[Anonymous No.12718319]

>>12715301
some of us become girlfriends like >>12718276 did

[Anonymous No.12718329]

>>12718214
>>12718267
>>12718276
>>12718277
>>12718307
aw jeez fellas. give me a break

[Anonymous No.12718485]

>>12718329
It's ok anon. I'd rather /mg/ get a bump than those stupid self fellating IQ threads or motherfuckers that wont shut the fuck up about memevirus

[Anonymous No.12718503]

/lit/'s making fun of us again >>17574139

[Anonymous No.12718511]

>>12718503
Sigh.
>>>/lit/17574139

[Anonymous No.12718514]

>>12718511
Thank you. I don't think I've ever made a cross general link. You're a bro.

[Anonymous No.12718521]

>>12718514
You can also link to rules but I don't remember the way.

[Multi No.12718523]

>>12718085
I dont like latex!

[Anonymous No.12718574]

Anyone have an updated link to the Verbitsky pasta? The old pastebin got deleted.

[Anonymous No.12718818]

>>12718574
Remiliafag fucked off and deleted it on his way out, yeah.
Here: >>/sci/thread/S11354444#p11354448

[Multi No.12718945]

Sentient diagrams. The diagram on washing machine once I considered the axiom that a human gave it logic. The axiom that there is a solution aids the thought process. How universal is this axiom?

[Anonymous No.12719004]

if p is a permutation representation of some group G, what does it mean to say
p={G_1,G_2,...,G_n}
where each G_i is a subgroup of G

[Anonymous No.12719054]

>>12719004
It is a group of every subgroup, isn't it?
What do you mean?

[Anonymous No.12719071]

>>12719054
p is supposed to represent G, also it’s not every subgroup, it is supposed to be a subset of the set of subgroups

[Anonymous No.12719075]

>>12719054
and i’m assuming that somehow, your choice of subgroups will determine what p is, but I don’t understand how

[Anonymous No.12719242]

A space [math] X[/math] is weak Hausdorff if [math] f(K)[/math] is closed for any compact [math] K[/math]. Does [math] K[/math] have to be a compact subspace of [math] X[/math] or can it be an arbitrary compact space?

[Anonymous No.12719301]

>>12715244
Hi frens,
/g/ here, trying to re-arrange: [math]y\ =\ \operatorname{mod}(t+(x/c),\ 1)*s[/math]
Around [math]x\ =[/math]
Does anyone know how to do inverse of modulo? Can't seem to find much online...
Thanks lads

[Anonymous No.12719354]

>>12719301
there is no true inverse of modulo, but you can get your set of solutions by writing it as kx+r. Also please use actual math notation I have no idea what the thing you wrote means

[Anonymous No.12719651]

I’ve been gone for so long... who is mult?

[Anonymous No.12719766]

Does the function [math]f(x)=\sgn(\cos(x))[/math] have a Fourier transform?

[Anonymous No.12719801]

>>12715301
Yes I do, we talk philosophy not math tho

[Anonymous No.12719810]

How many possible results are there if you roll 6 regular die at one?
My result is 6^6 but my book has 11C6 how the fuck? don't you have 6 possibilities of the second die for each result of the first one, that would 6*6 and then so on for all of them resulting in 6^6 possibilites?

[Anonymous No.12719811]

>>12715301
I would get a girlfriend, but grad school is too demanding. Too much math to be done.

[Anonymous No.12719838]

>>12719810
imagine rolling 6 dices at once, and you don't distinguish the dices

[Anonymous No.12719878]

>>12719838
Yes, I understand that you have kind of a 'bank' of possible results and you are going to have to divide to account for the permutations. If worked out the problem for the 2 dice case and I got 21 possible results by brute forcing it but I'm having trouble expressing that as a combinatorial number. Because I thought OK so I have 6 possible choices for the first number and then another 6 and then the possible permutations that I have to account for are 2! when the numbers are different but only 1 in the 6 cases that are the same, and I don't know how to express that. My best idea is to first count the cases where the numbers are not the same, which are (6*5)/2! = 15 and then add the extra 6 cases for a total of 21. Okay that is easy for my simplified case, but when I have 6? Pretty impossible to generalize my result, there is something I am not seeing

[Anonymous No.12719933]

>>12719651
It's just an idiot.
>>12719242
Arbitrary.

[Anonymous No.12719934]

>>12719651
I think he's just a random newfag, didn't see him here 3 weeks ago. Unless he didn't force that name before.

[Anonymous No.12719997]

>>12719810
You can prove this using power series:

We compute the coefficient of [math]x^6[/math] in the power series expansion of [math]f(x) = \frac{1}{(1-x)^6}[/math] at 0.
On the one hand, we have [eqn]\left(\frac{1}{1-x}\right)^6 = \left(\sum_{n \ge 0}x^n\right)^6 = \sum_{n_1, \dots,n_6 \ge 0} x^{n_1+\dots+n_6}[/eqn]
hence the coefficient of [math]x^6[/math] is the number of sextuplets [math](n_1,\dots,n_6) \in \mathbb Z_{\ge 0}[/math] such that [math]n_1+\dots+n_6 = 6[/math], that is the number of possible results of six simultaneous dice rolls.
On the other hand, the coefficient of [math]x^6[/math] is [eqn]\frac{f^{(6)}(0)}{6!} = \frac{(-1)^6 (-6)(-7)\dots(-11)}{6!} = {11 \choose 6}[/eqn]

[Anonymous No.12720035]

>>12719878
yeah you need a totally different method
read this https://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)

[Anonymous No.12720199]

When you are given Acos(3wt), does that automatically imply A(cos(3wt)+isin(3wt))???

[Anonymous No.12720484]

Say I have a square matrix [math]A[/math] over an integral domain [math]R[/math], then [math]\text{det}\, A = 0[/math] implies that there is a nontrivial [math]R[/math]-linear relation for the columns of [math]A[/math].
I think I proved it, but I'd like to see a different approach.

[Anonymous No.12720497]

>>12720484
Something something it's true over the field of fractions of R something something multiply all terms by the denominators to cancel them out.
>I'd like to see a different approach.
I doubt anyone's going to prove it in an even slightly different way.

[Anonymous No.12720524]

>>12720497
Oh right, kek
I was too fixated on the [math]R[/math]-module I had, which isn't trivially a vector space over the field of fractions.

[Anonymous No.12720527]

>>12720524
My disappointment is immeasurable.

[Anonymous No.12720535]

>>12715301
i have a wife who lets me ramble about math every now and then. she's a nurse, going to school to be a nurse practitioner. wish i had more people to talk math with other than /sci/

[Anonymous No.12720555]

>>12715301
>math is sexy r-right guys?
It is

[Anonymous No.12720558]

i dont get it. what do line integrals give? length of the line or the area within? why is the line integral of half this circle is 0? (f=xy for this matter).

[Anonymous No.12720591]

>>12720558
area under the line when f gives the 'height' of the line

[Anonymous No.12720597]

>>12720591
alright, so why is the area of half a circle is 0? ive calculated it and got 0, the website that has the exercise has an example of the solution which is also 0. how come its 0?

[Anonymous No.12720610]

>>12720597
Did you read the post and see the image you're replying to?

[Anonymous No.12720646]

Should I switch to mathematics? The problem is I am almost 22 years old and I only have 3 semesters left. But CS is a meme in our country (lacks rigor), and we are always doing group projects with 6-7 subjects per sem (I'm at a third-world shithole that's why I can't pick my schedule). I can't take it anymore since I'm not learning anything at all, I've reached the stage where I know more than the professors here.

Yet despite falling for the sunken-cost fallacy, I am compelled to stay and grind it out. Since the number of subjects that I'll be credited with is at most 4. I also don't want to take Calculus since I've already self-studied real analysis from Rudin.

[Anonymous No.12720682]

>>12720597
What? The area of half a circle is not zero. How is this related to line integrals? Green's theorem relates area integrals to line integrals, are you talking about that?

[Anonymous No.12720683]

>>12720646
what do you mean you can't pick your schedule. Surely you can pick up a math minor or something and use that as an excuse to take some harder math classes.

[Anonymous No.12720699]

>>12720683
> You can't pick your schedule
The faculty does this for us. I know it sounds retarded, but they've cluelessly shoved every elective up our ass. The worse part is, even the so-called professors are clueless about the field.

[Anonymous No.12720724]

>>12720699
well idk if it helps but I completed pretty much all my math undergrad courses in a year (lin alg, alg, anal 1/2, complex anal) so it depends on if you can do the same at your school. That being said, if you are forced to take calculus, it's absolutely NOT worth it.

[Anonymous No.12720726]

>>12720699
What country?

[Anonymous No.12720761]

>>12720724
The problem is, our classes are unbearably autistic. It's all inane group projects with some tedious, but not mentally challenging bullshit added in. I guess it's not worth switching either, I'm not allowed to test out Calculus since it is mandatory for math majors, even though I was the one tutoring those mathfags kek.

>>12720726
Somewhere in South East Asia.

[Anonymous No.12720832]

>>12719242
Suppose [math]K[/math] is any compact space and [math]f\colon K\to X[/math] is a compact subset. Conversely, if [math]K \subseteq X[/math] is compact, then it is the image of the inclusion [math]i \colon K\to X[/math]. Combining those, you see that a subset of [math]X[/math] is compact iff it is a continuous image of a compact space, so you can replace the condition with the requirement that compact sets are closed in your space. It is then easier to check whether your space is weak Hausdorff or not.

[Anonymous No.12720884]

>>12719004
https://doi.org/10.2307/2373739
Bumping with the paper where I saw the notation.

[Anonymous No.12720917]

>>12720884
https://arxiv.org/pdf/0705.4122.pdf
I believe it is the orbit decomposition of the group itself. See the beginning of section 2 in the linked paper.

[Anonymous No.12721058]

>>12720917
*gives you sloppy kiss on the cheek*

[Anonymous No.12721178]

>>12719651
A 12 year old namefag who announced himself in the most embarrassing way possible in a /mg/ a few weeks ago and posts horrible garbage. Too bad mods don't do their jobs...

[Anonymous No.12721223]

>>12721178
how’d he announce himself

[Anonymous No.12721332]

>>12721223
>>/sci/thread/S12668218#p12670973
That's his oldest post in /mg/ I can find in the catalog.
Although technically he might the lad who's been posting german in the OPs for a while now.

[Anonymous No.12723787]

>>12720917
Wait, do these sets {G_1, G_2,...,G_n} merely capture some of the properties of a given permutation, or can one construct a function which will map from it to a permutation.
I’m just confused because, if each subgroup there is the stabilizer group of a point for every orbit, your choice of point would influence what subgroup you get. And I don’t see how one could derive the permutation as a whole from this set, I only see a few key properties.

But the author of the paper I linked used the equals sign when talking about this, would that not mean that the correspondence is one to one? I stg reading this paper has made me run around my house punching the air

[Anonymous No.12724267]

>>12721223

[Anonymous No.12724279]

>>12724267
-_-

[Anonymous No.12725006]

>combinatorics was never my strong suit
>for some reason my research needs more and more of it
fugg:DD
Well at least I'm forced to learn something actually usefull desu.

[Anonymous No.12725822]

>>12719004
i mean it looks like the notation used for denoting the stabilizers on symbols 1 - n, assuming that this permutation group is acting on the first n integers. i dont know what the curly brackets are for. maybe that the group is generated by the set of all stabilizers?

[Anonymous No.12725908]

Is there a good book list to start from basic maths and work to the more advanced subjects? I want to build a better foundation

[Anonymous No.12725954]

>>12725822
It's a subset of the lattice of subgroups , but it is supposed to represent a permutation. The groups are chosen by choosing one element from each orbit, and taking the stabilizer of it. The only thing I'm confused about is, would there not be multiple different choices for a given permutation? And if given such a set of subgroups, how would one determine what the permutation is?

[Anonymous No.12726105]

>>12723787
No idea to be honest. I have never seen that before. That's just something that I found after googling minimal permutation representations. Sorry.

[Anonymous No.12726142]

>>12725954
this is pretty confusing to me as well, but im only just beginning to study permutation groups and group actions on sets.
I tried perusing some of my books on permutation groups and didn't find anything useful.

[Anonymous No.12726159]

>>12726105
It’s ok, thanks for the paper at least. Maybe it’s possible that no matter what element of an orbit you choose, the subgroup that results from it, while being possibly different, will be isomorphic. Then, maybe it’s also possible that this can only be used to write minimal permutations. Just thinking it through in my head, if I have any permutation group, I could simply add an element which doesn’t go anywhere, then there would only be one choice in that specific orbit, and it’s stabilizer group would be G. But then of course, if you add some other new elements in that fashion, you couldn’t possibly get another copy of G, because it’s just another set.

[Anonymous No.12726224]

>>12717823
Is this supposed to show some order? How does foil come about? I can see 2 A's, 2 B's, and two sets of ab. I guess that's it.

[Multimorph No.12726301]

>This collection, having the the basic properties of physical one or near-one dimensional segments, such as violin strings or subatomic strings, is referred to as the G-string for its generality.(27)
L-lewd

[Anonymous No.12726356]

>>12726159
And I just realised that the orbit interpretation seems quite wrong. Suppose we have the whole group [math]G[/math] act on itself, and that there were [math]x, y\in G, Gx \neq Gy[/math]. As this, at least according to the intro of either your or my paper, is the usual [math](g, x) \mapsto gx[/math], now we could choose [math]g = yx^{-1}[/math] to ruin everything and have [math]Gx = Gy[/math]...

[Anonymous No.12726366]

>>12726356
hmm quite strange indeed. I guess I’ll just go pervert mode on the author of mine and hope maybe he wrote a paper with but a crumb of definitions. There was also another paper I read which used seemingly a closely related fact and simply said “it is a part of the folklore that...” with no source

[Multimorph No.12726405]

>>12726366
It is part of the folklore that what

[Anonymous No.12726444]

>>12726366
Good luck! He had the energy to write the notation there but not explain it in any way. Folklore is nice when it's about trolls living in the woods or ancient wizards singing people into the swamps, but not when the result you need happens to be folklore.

>>12726405
https://en.wikipedia.org/wiki/Fornj%C3%B3t

[Anonymous No.12726447]

>>12726405
It is part of the folklore that the least value of [math]\sum_{i=0}^t|G;H_i|[/math] where [math]H_i[/math] are subsets is the degree of the minimal permutation representation.

[Anonymous No.12726451]

Why does -5 + -1 = 4? I know it's a stupid question, but I have to refresh on my math for college.

[Anonymous No.12726468]

>>12726451
that’s not just -5, that’s -(-5). What you’re actually looking at is 5-1 which does indeed equal 4

[Anonymous No.12726471]

>>12726451
Bait

[Anonymous No.12726472]

>>12726444
I don’t have any тянoчки to hug you back with but i’ll do my best

[Anonymous No.12726481]

>>12726468
So if it's in parenthesis and a negative number, it'll be a positive instead?

Alternatively, what should I be reading up on to make sure I don't get confused by this again.

[Multimorph No.12726508]

>>12726444
https://en.wikipedia.org/wiki/%C3%9E%C3%B6kk

>>12726447
Because no one has ever found a counteraxample and it seems obvious? Why dont they just prove it then?

[Multimorph No.12726511]

>>12726481
Read up on pemdas and negative symbols, but really you dont need to read, you just need to practice and think it through a few times, the information is probably already in your rom

[Multimorph No.12726515]

>>12726511
Sorry not rom, just M, but not ram, because its writeable to

[Anonymous No.12726539]

>>12726511
>pemdas
Oh right, that's what I was looking for all along. Thanks anon.

[Multimorph No.12726594]

What is the definition of a mathematical object, as opposed to a non mathematical object?

[Anonymous No.12726633]

>>12726594
...

[Anonymous No.12727104]

Im gonna turn namefag off when I use this general, mg is too pure for it. However you can catch M branded posts elsewhere on sci and 4chan and one day the internet

[Anonymous No.12727159]

>analysis test in 3 hours
lets fucking go boys

[Anonymous No.12727207]

>>12727159
Good luck anon, remember to analyse

[Anonymous No.12727254]

>ring theory exam in three seconds
>not even married

[Anonymous No.12727260]

>>12727159
take this brother may it serve you well

[Anonymous No.12727262]

Brainlet high school dropout here. If you divide an odd number by another odd number, do you always get an odd number as a result?

[Anonymous No.12727319]

>>12727262
yes, and you can prove it pretty easily if you think about the prime factorization of odd numbers.
an odd number never has a 2 in its prime factorization and dividing that odd number by another odd number wont change that.

[Anonymous No.12727322]

>>12727319
even more straightforwardly, if you got an even number, then even x odd(divisor) would = odd, which doesnt make sense

[Anonymous No.12727337]

>>12727319
>>12727322
Thanks my guy.

[Anonymous No.12727651]

>[math]R^3[/math]

[Anonymous No.12727663]

>[math]\mathbb{R}^2[/math]

[Anonymous No.12727705]

>>12726481
minus a negative number is plus the corresponding positive number. it has nothing to do with the parenthesis.

[Anonymous No.12727759]

>R = E

[Anonymous No.12727820]

>>12727262
No, 7 divided by 3 is not a whole number

>>12727260
Weird, proof?

[Anonymous No.12728006]

What is [math]\mathbb{P}^3[/math]?

[Anonymous No.12728070]

>>12728006
Usually tridimensional projective space.

[Anonymous No.12728484]

Has anything happened in univalent function theory after the Bieberbach conjecture was proven? Is the field dead?

[Anonymous No.12728584]

>>12715301
I do
But I'm an engineering student lmao

[Anonymous No.12728731]

Is there any way that Thales theorem can be modified to work on the surface of a sphere? I was thinking that the diameter on a circle constraint could be modified to two antipodal points on a sphere, but that doesn't seem to work in all cases.

[Anonymous No.12729204]

if a | bc does it automatically mean that a | ppcm(b,c)?

[Anonymous No.12729324]

>>12729204
french moment
12| 12, but 12 doesn’t divide least common multiple of 2 and 6

[Anonymous No.12729343]

>plug and chug

[Anonymous No.12729382]

I've already taken a differential geometry course, I know about tensors, connections, curvature, metrics, differential forms, integration (not an expert here but still), etc. I was diving through wikipedia today and found shit like this
>Cartan connection
>Solder form
>Connection forms
>Spin forms
>Klein geometries
>Absolute parallelism
>Principal bundles
Then I got to Ehresmann connections and gave up. While I feel like I have the basic knowledge to understand what all this shit is if I read the article over and over, I feel like I would be better off reading a book that introduces this stuff properly. Any recommendations for this?
Pic unrelated

[Anonymous No.12729431]

>>12729324
Much appreciated.

[Anonymous No.12729538]

anybody know of an alternative to khan academy when it comes to self-learning math on the internet? khan's test taking system makes me want to blow my fucking brains out every time I use it.

[Anonymous No.12729566]

>>12729538
books

[Anonymous No.12729577]

>>12729382
Kobayashi&Nomizu for bundles
Sharpe for Klein and Cartan stuff

[Anonymous No.12729663]

>>12729538
spam /mg/ with questions

[Anonymous No.12729673]

>>12729577
This one?

[Anonymous No.12729677]

>>12729673
Yup.
>(corrected)
$10 says it's not lol.

[Anonymous No.12729680]

>>12729382
>Spin forms
Weird term, where did you see this? I'm imagining that's what I'd usually call a spinor-valued form.

[Anonymous No.12729684]

>>12729680
Meant spin connection, my bad

[Anonymous No.12729697]

>>12729684
Oh, I see.

[Anonymous No.12730663]

is anyone doing putnam tomorrow

[Anonymous No.12730949]

>>12716815
based

[Anonymous No.12730962]

>>12729566
this unironically
generally books are fucking great sources for higher level knowledge, I struggled for months with my digital circuits study listening to pajeets on youtube untill I just picked up a fucking book and read it carefully, really eye opening

[Anonymous No.12731019]

Which courses should I take emgee? I need to pick three.
https://maths.anu.edu.au/study/courses/math-3349-math-4349-math-6209-special-topics-mathematics
>Toric Varieties and Combinatorial Methods in Algebraic Geometry
>Three-Manifolds (the best manifolds)
>Dirac Operators and the Atiyah-Singer Index Theorem
>Randomised Numerical Algorithms and Applications to Data Science
>Symplectic Geometry
>Mathematics and Climate
>Equivariant Stable Homotopy
>Riemann surfaces
>Mathematical Aspects of Gauge Theory
>Introduction to Integrable Models and Knot Theory
Normal courses:
>Fractal Geometry & Chaotic Dynamics
>Probability Modelling & Applications
>Foundations of Mathematics
>Differential Geometry

[Anonymous No.12731031]

>>12731019
>Symplectic Geometry
>Riemann surfaces
>Mathematical Aspects of Gauge Theory
Might want to replace Riemann Surfaces by Differential Geometry if it covers basic shit that you don't know.

[Anonymous No.12731042]

https://www.planetary.org/space-policy/cost-of-perseverance

mars rover budget: $2.7 billion

materials: $2.3 billion

STAY IN SCHOOl

[Anonymous No.12731502]

Riddle me this, mathfags
Why the fuck do mathcucks go on about gabriel's horn.
>muh infinite SA
>muh finite volume
Yeah, stop saying that shit to normies because finite is not "finite," colloquially.
If you say the volume is 2 or some shit I'd be like, wow that's insane I can't believe it. No, it's pi.
Pi goes on for fucking ever so can we stop with this "fill the horn with cum" line because you'd only approach pi but never reach it lest you exceed volume capacity. I don't give a shit about ass-simp-totes.
>muh closer you get to a wall it's like an ass simp tote but you can still touch the wall but always be approaching it
fuck off with your pilpul god damn
Fucking mathfags I swear.

[Anonymous No.12731658]

>>12731042
>NASA tries to justify its billion budget
>can only come up with a dried up planet
>shill this mars crap for decades
>all the drones support those bureaucrats spending tax payer money on a pile of dust

te atheist republic is a huge mistake

I love how atheists are still upset by having not found a luxurious planet like Earth so they try to cope with hyping a crappy planet

[Anonymous No.12731664]

>>12731042
>NASA tries to justify its billion budget
>can only come up with a dried up planet
>shill this mars crap for decades
>all the drones support those bureaucrats spending tax payer money on a pile of dust


I love how atheists are still upset by having not found a luxurious planet like Earth so they try to cope with hyping a crappy planet

the atheist republic is a huge mistake

[Anonymous No.12731692]

>>12731664
based christianfag

[Anonymous No.12731791]

>>12731502
This is pretty bad bait and finitism is a scuffed meme but I'll bite. I can simple scale the equation so that the volume is 2, what do you think of that?

[Anonymous No.12731823]

>>12729577
I'm looking at sharpe, and wtf, is this a memebook? the guy is quoting guenon

[Anonymous No.12731825]

>>12731823

[Anonymous No.12731927]

>>12720558

[Anonymous No.12732046]

>>12731791
Then you would have 2/pi in the equation
Yet another infinite quantity
The horn can therefore never be realized

[Anonymous No.12732509]

What's the name for when a smooth curve of points on a surface under a different family of smooth curves all have the same holonomy? I've been trying to find or remember the name of it for twenty minutes.

[Anonymous No.12732733]

>>12732046
What about black holes bro? Perfect radial force distribution , perfect circle?

[Anonymous No.12732739]

>>12732733
Technically not in the quantum model, then only perfect in limiting case which either requires infinite time or infinite universes

So maybe irratinals are a bit whack. But math is about imagining infinity.

[Anonymous No.12733161]

>>12732509
if you cant find a name, name it yourself

[Anonymous No.12733193]

>>12715351
Did the stacy you were stalking on KikeBook block you again eh, jugdish.

[Anonymous No.12733311]

>>12731502
You’re saying a circle of radius one doesn’t have a finite circumference with this logic

[Anonymous No.12733768]

Let's define 'ndx' as 'roll x-sided dice n times'.
What's got higher expected value: (1d4)d4 or 1d(4d4) ?

[Anonymous No.12733868]

>>12733768
Define (ndx)y nd(mdx) first.

[Anonymous No.12734095]

>>12733768
probably the second one

[Anonymous No.12734667]

Numerology also known as applied number theory

[Anonymous No.12734824]

>>12733768
>(1d4)d4:
1, 2, 3, 4
2, 4, 6, 8
3, 6, 9,12
4, 8,12,16
Mean is 5.625
>1d(4d4)
4, 8,12,16
8,16,24,32
12,24,36,48
16,32,48,64
Mean is 22.5

[Anonymous No.12734837]

Can anyone recommend me a book on Real Analysis where I could self-study in it? I have some experience writing proofs (from linear algebra and discrete math) and I would like to study Real Analysis before I take a course on it next year.

[Anonymous No.12734844]

>>12734837
rudin

[Anonymous No.12734859]

>>12715301
Women can be like peat bogs

[Anonymous No.12735823]

any book recs in abstract algebra?

[Anonymous No.12735838]

>>12735823
Dummit & Foote

[Anonymous No.12735982]

>>12734837
There's Gaughan's Introduction to Analysis that I really enjoyed. A downside I guess is that it only goes through single variable calculus, and doesn't touch on multivariable calculus at all.

[Anonymous No.12736305]

I just proved that 4/[x(4-x)]>=1 if 0<x<4 using calculus. I have never used calculus in order to do anything except for pass a test. I feel like I have been lied to by my university and all my math teachers. Math is actually interesting and useful.

[Anonymous No.12736443]

>>12736305
This book is actually helping me think for myself mathematically, which is seemingly never taught in American schools because it is all news to me.

I hope I can make it all the way through to the top. My dream is to finish 1 book for every category in hbpms.blogspot.com.

[Anonymous No.12736478]

>>12736443
I don't think the full hbpms list is necessary or even the best list, but you are automatically better than most posters here for having a passion to actually learn and do math

[Anonymous No.12736502]

>>12736305
>>12736443
>>12736478
Nothing has ever satisfied my autistic yearning for absolution than math. What do you think is a better list than HBPMS? I know it is outdated but I appreciate its breadth.

[Anonymous No.12736531]

Hey guys, I'm a freshman and haven't so much as touched group theory yet. Is there a name for the shortest combination of transformations that would take the object the group operates on through every possible permutation of it if repeated indefinitely?
I was thinking about how there are algorithms for Rubik's cube and looking at the simplest algorithm for seeing every possible permutation of the cube but I'm not interested in Rubik's cubes as much as I am in the group stuff underlying it.

[Anonymous No.12736644]

>>12736531
superpermutations is the closest thing I could think of to what you’re looking for, but I already know it’s quite right.
Always remember that the elements of your group aren’t analogous to the single face turns of the rubik’s cube, in reality a scramble as a whole is a single element.
For instance, if you want to get permutations a,b,c,..., you could just do
a(a^{-1}b)(b^{-1}c)...
and from a group theoretic standpoint, each term inside the parenthesis is a single move.
A closer question to what you’re asking would be to say, if {x,y,...} is a subset of G, which generates G, how can I factor a given element of G into these generators

[Anonymous No.12736669]

>>12734837
I took a proof based calc course that used apostol vol 1&2 and it was actually really nice preparation for baby rudin. Maybe consider doing that. Or else just jump to rudin.

[Anonymous No.12736677]

Have we considered putting some pasta at top of these threads with the basic book recommendations?

[Anonymous No.12736682]

Is there any technical term for 'norm that was derived from inner product'?

[Anonymous No.12736702]

>>12736682
if there’s an inner product, the norm has to coincide with it. So maybe just inner product space

[Anonymous No.12736788]

>>12736682
Norm induced by inner product

[Anonymous No.12737189]

>>12736677
No. Bad idea. Bad anon. Bad.
Do not go out of your way to encourage undergrads, high schoolers and neets to come post here. They're already 95% of this thread.

[Anonymous No.12737191]

>>12736677
Yes we have. We don't.

[Anonymous No.12737205]

>>12729382
Always work out explicit examples when learning a new concept. Even the most alien ones (at least in DG) will make quite a lot more sense if you proceed that way.

[Anonymous No.12737207]

>>12731019
Diffgeo is a prerequisite for Gauge Theory and Symplectic Geometry. So answering your question is kind of impossible without knowing what you already know. Anyway, Toric Varieties is nice imo.

[Anonymous No.12737364]

>map, plane, vector, tensor, matrix
wtf do all these mean???? in highschool i learned that vectors are just direction and size and matrices just modify vectors but now they are saying this is wrong???? i am not dumb for not understanding this right?

[Anonymous No.12737369]

>>12737364
maps are elements of map spaces
planes are elements of plane spaces
vectors are elements of vector spaces
tensors are elements of tensor spaces
matrices are elements of matrix spaces

[Anonymous No.12737599]

>>12736677
/sqt/ has the lists, not that people check

[Anonymous No.12737672]

I graduated with my bachelors in math this december. I was starting grad classes my last 2 semesters, but I'm not going to online grad school cause fuck that. Also I'm poor, so now I need a job to pay the bills so that I can spend all my free time just self studying, and maybe in the future enter a grad program when shit goes back in person.
I thought teaching would be perfect for this, but instead I just spend my days yelling at minorities and nights doing paperwork for all their fake retardations stemming from not having dads. I also make chump change.
What is a good /mg/ career path after undergrad to save up for a nice grad school?

[Anonymous No.12737715]

>>12737672
teaching rich kids privately and not paying taxes

[Anonymous No.12737843]

>>12734844
>>12735982
>>12736669
Thank you, anons. I will see if I can do Rudin first and if not, I'll do the other books you guys suggested.

[Anonymous No.12738162]

>>12737715
What is the best way to get these clients?

[Anonymous No.12738489]

ктo-нибyдь зaхoдит в oбщeмaтимaтичecкoм тpeдe нa двaчe?

[Anonymous No.12738512]

ктo-нибyдь зaхoдит в oбщeмaтимaтичecкий тpeд нa двaчe?

[Anonymous No.12738853]

I’ve been looking at a few groups and some of their more interesting group actions, and it seems like if you’re given {G_1,G_2,...}, I as a human can work out what the action is by logicing it out, but I still don’t see a function which maps from these subsets of the subgroup lattice to permutation representations
>>12726356
I think the problem with this logic is that the number of orbits/whatever other property isn’t invariant under choice of group action. If you define a group action by having the group act on itself, you’re always going to get a transitive and free action, which more often than not means it’s inefficient. (one situation where it wouldn’t be inefficient would be dedekind groups, if you look at the properties in the first paper I linked, if the core is nontrivial, then the representation won’t be faithful; therefore the group action of the quaternions group acting on itself is minimal).
Would anybody here like to try to prove the properties given in the paper I linked?
Of course I’ve been using those properties to go from these subset representations to permutation representations, so we’d have to actually reverse engineer a definition from what we know before we can prove anything.

[Anonymous No.12738960]

>>12737672
Why not do online grad school? It's not going to be forever (hopefully) and you can start knocking classes out and at least grab a master's degree.

[Anonymous No.12739004]

>>12738853
Also it would be nice to figure out if this way of representing permutations works for infinite groups, obviously the papers here only talk about finite ones so minimal is defined

[Anonymous No.12739308]

based

[Anonymous No.12739336]

Dude I love math but I've always been such a terrible student. When I was a sophomore in High School I self-taught calculus and got a 5 on the BC Calc exam just because I was that into math. That year I failed like 3 classes and got a D in my actual math class. My last semester of HS I got straight F's before dropping out and testing out. Now I'm working a pretty good wagie job with A decent career ahead but I will never be able to study and learn math to its fullest. Its kind of absurd how little I know about math compared to someone with a PhD. I wish I could be a textbook author or lecturer but there's no way in hell I could ever self-teach to the point where I could ever effectively do either of those things. I will also probably never make any kind of meaningful contribution to math ever I'll always be a passive observer with less knowledge than the average undergrad.

[Anonymous No.12739344]

>>12730663
I took the Putnam. Others must have as well. Is there not a thread for it?
I thought some of the problems were fun. I really enjoyed B3.

[Anonymous No.12739393]

>>12739344
what was B3 again?
I was only able to do 2.5 problems but I’ve been told that’s decent for my first time

[Anonymous No.12739594]

>>12739336
>I will also probably never make any kind of meaningful contribution to math ever
Why not? A guy managed to slf-study in prison until he actually made a new contribution in combinatorics, all while in jail. The question should be: Do you really, really want it? Enough?

[Anonymous No.12740143]

>>12737364
Unironically vectors just mean ordered lists of numbers, they can be directions if each index refers to a spatial dimension, nut they can refer to other kinds of dimensions like color or frequency. Then there are a few rules to add them, and if you add them differently, you can think of them as other kinds of vectors or vectors in a different domain of algebra. Maps matrixes and tensors are all kinda the same thing, just formulas to change your vectors, as if you were rotating a plane or stretching it. The plane is just a bunch of points/vectors (points and vectors are interchangeable). It can be drawn as a 2d plane on a paper, or drawn other ways, or represented purely algebraically with a pair of vectors that are linearly independent, aka dont go in the same direction, and those vectorses combinations

>>12737369
I hope for your sake you are just joking

[Anonymous No.12740170]

my math teacher once told me "if it smells like fish, eat all you wish. if it smells like cologne, leave it alone."

[Anonymous No.12740172]

>>12740170
Is he talking about pussy?

[Anonymous No.12740178]

>>12740143
>Unironically vectors just mean ordered lists of numbers
Wrong.

[Anonymous No.12740208]

>>12740178
W..what..

[Anonymous No.12740210]

>>12740208
When you write a vector as an ordered list of numbers, it is understood that said list is subordinate to a specific basis. The vector itself is a member of the vector space and as such exists independently of the chosen basis and indeed it may be the case that a finite basis might not even exist, thus your definition loses all meaning.

[Anonymous No.12740214]

>>12740210
Okay, but if you happen to have a basis, then you have the vector as a list of numbers. And if you dont have a single basis, how are you gonna do anything on that space anyway?

[Anonymous No.12740215]

>>12740214
>Okay, but if you happen to have a basis, then you have the vector as a list of numbers.
That's a representation of the vector, not the vector itself.
>And if you dont have a single basis, how are you gonna do anything on that space anyway?
Are you on highschool? Honest question.

[Anonymous No.12740225]

>>12740215
>latter
Eh fuck it you can do things I just meant things regarding specific vectors, for whom representation isnt that different to actuality anyway, and no Im not in HS or college either

[Anonymous No.12740230]

>>12740225
Have you ever taken a functional analysis course? Or a PDE course?

[Anonymous No.12740248]

>>12740230
No

[Anonymous No.12740250]

>>12740178
Darling, everything is just an array of numbers.

>>12739308
Good heavens, based!

>>12738853
>the number of orbits/whatever other property isn’t invariant under choice of group action
Obviously not. If you take the usual left action, then there is only one orbit, but the trivial action makes every orbit a singleton. One thing I thought of quickly was to ask which subgroups would stay fixed under this action. Say you knew that all normal subgroups are precisely your fixed subgroups. This would mean that your action should be conjugation. Similarly, having no fixed subgroups other than the group itself would suggest translation, every subgroup the trivial action and so on. Maybe up to some equivalence relation, these would let you map your set of fixed subgroups to the (class represented by) the action that would keep precisely those fixed. However, this could fail if you could find a set of subgroups that would not correspond to any action at all, and I'm only thinking about finite groups. Just some random and quick ideas, maybe (probably) total rubbish.

[Anonymous No.12740263]

>>12740248
Infinite dimensional vector spaces are extremely useful in a variety of fields. In measure theory for example you can define the spaces of p-integrable functions, which are infinite dimensional when viewed as a vector space over the real numbers. Nobody ever writes the functions in said spaces as a "list of numbers" because
1. It's impossible. Even though a (Hamel) basis exists, it is uncountable. Thus your list would have uncountably many zeros.
2. It's not needed. You've certainly written down a function and you didn't bother writing it as a list of numbers.

While it can be argued that some functions can be written down in terms of a Schauder basis, that's not always the case.

[Anonymous No.12740367]

can anyone help me with my home work it says i'm supposed to add 1/4 + 1/6 but i thought it was theoretically impossible to do this unless the bottom numbers are the same

[Anonymous No.12740391]

>>12726224
Are you 12 or something?
Binomial expansion mate.

[Anonymous No.12740469]

>>12740367
It’s probably a typo, that’s impossible

[Anonymous No.12740483]

>>12740367
1+1=2
4+6=10

2/10

[Anonymous No.12740494]

>>12719997
>!
we can latex in this forum?

$\Sum_{nigga}$

[Anonymous No.12740501]

>>12740494
>forum
[math]
newfag
[/math]

[Anonymous No.12740637]

>>12740143
>points and vectors are interchangeable
ISHYGDDT

[Anonymous No.12740699]

>>12740494
newfags cant [math]\LaTeX[/math]

[Anonymous No.12740759]

>>12740367
What if 1/4 and 1/6 are both equal to some other fractions which have the same denominator, a denominator that has 4 and 6 as a factor, such as 24?

[Anonymous No.12740761]

>>12740637
For linear algebra, why not? Physical forces the arrow intuition is good though

[Anonymous No.12740769]

>>12740761
vector spaces and affine spaces are totally different structures. not for technical reasons, they're supposed to capture different concepts. the only reason they seem interchangeable is because R^3 happens to be both.

[Anonymous No.12740874]

>>12740210
>When you write a vector as an ordered list of numbers, it is understood that said list is subordinate to a specific basis
So a vector is a pair of an array of numbers and a reference basis, and since an array of numbers without a specified reference basis has a natural choice of basis, you only need to specify the basis when it strays from the natural one.
>infinite dimensional
A stream of numbers with a Schauder basis, with the natural choice of basis.

[Anonymous No.12740879]

>>12740874
>natural basis
no such thing, except is very special cases such as R^n

[Anonymous No.12740884]

>>12740874
>and since an array of numbers without a specified reference basis has a natural choice of basis
Not all of them do.
>Schauder basis, with the natural choice of basis
See my second post. Also there's no such thing as a natural choice in the same way as in R^n, you can have multiple Schauder bases that are "natural" in different contexts.

I don't know if a Schauder basis always exists, and even if they did they only make sense if you have a topology on your vector space to define convergence and thus series. That excludes purely algebraic vector spaces that don't have additional structure.

[Anonymous No.12740894]

>>12740769
Points on a plane assuming you have an origin scheint vector

[Anonymous No.12740938]

Are there any known problems that are independent from V=L?

[Anonymous No.12740959]

>>12740938
existence of most large cardinals

[Anonymous No.12741383]

>>12739393
Yes, that's well above average. I only did 3 (1 + 1 + 0.5 + 0.5) and this is my fourth time taking it.
Good work.
B3 was the expected value of the number of times you need to pick x_n from [0, x_{n-1}] with x_0 = 1 in order to get below some fixed delta between 0 and 1.
Big multiple integral which collapses nicely.

[Anonymous No.12741404]

>>12740263
actually, one might suggest that every function is a list of numbers (indexed by the domain) and since we describe almost everywhere equivalence classes of functions in L^p by choosing a representative, such vectors are not much more than lists of numbers (with properties).
in fact, the main thing you can take issue with here is the picking a equivalence class representative, not the function thing. people represent linear operators on function spaces by infinite dimensional matrices all the time.

[Anonymous No.12741439]

Bros is it possible to do vector/multivariable calculus in one semester (4 months)? I am not having a hard time in Calc I/II and I have a decent foundation in linear algebra.

[Anonymous No.12741496]

>>12741439
I would hazard that 4 months is the typical amount of time. Multi was easier to me than calc 2, it's just "do the thing you know how to do, but now do it 3 times" or stuff like that.

[Anonymous No.12741539]

>>12740938
Any large cardinal with consistency strength less than 0^sharp will be independent of V=L. Besides some obvious ones like Con(ZFC+V=L) I can't think of any really combinatorial statements. L is super regular almost everything you want to be decided in set theory is decided. Whether it is decided in the way you want is the annoying thing. You've got a Delta_2^1 WO of the reals, so all regularity properties of reals fail right above the complexity of analytic sets. L is technical tool for higher recursion theorists though, where you want to construct various objects through various definable forcings. That is the shit L is really good at.

[Anonymous No.12741784]

>>12741496
thank you anon

[Anonymous No.12741911]

why are big numbers so fucking scary?
https://youtu.be/0X9DYRLmTNY

[Anonymous No.12741934]

>>12738162
Well, being an intelligent person with a degree from an elite school (ivy league, MIT or Caltech) is usually the best bet for getting such wealthy connections. This is what those websites you read about colleges in high school meant when they said that elite schools have better networking opportunities. Outside of that, I can't think of a deterministic process of getting yourself into such a circle of people with no luck involved.

[Anonymous No.12742669]

if f_n -> 0 uniformly and the f_n are bounded, doesn't the integral
[math]
\int_{0}^{\infty} f_n(x) dx
[/math]
also converge to zero?

[Anonymous No.12742680]

>>12742669
oops, I mean the limit as n tends to infinity of that integral.

[Anonymous No.12742690]

>>12742669
No.
Consider something like [math]f_n = \dfrac{\chi _{[0, n]}}{n}[/math]

[Anonymous No.12742707]

>>12742690
Oh, right. Thanks anon, been a while since I last studied this.

[Anonymous No.12743054]

>>12720646
Exact same thing happened, switch from CS to math at 21 years old, professors are shit but way better than boring CS courses.

[Anonymous No.12743203]

Urysohn a cute, a cute!

[Anonymous No.12743205]

When solving matrices equation, can i do something like this?
[math]\begin{equation} B = CA \end{equation}[/math]
[math]\begin{equation} C^{-1}B = A \end{equation}[/math]
Like, multiply to the left or to the right.

[Anonymous No.12743254]

>>12743205
I'm pretty sure you can do it iff the matrix is full-rank
the same as you're allowed to do it with numbers other than 0

[Anonymous No.12743509]

>>12743254
im assuming C is square and invertible as C^-1 is defined
then associativity of matrices IA = (C^-1 C)A = C^-1(CA) = C^-1 B

[Anonymous No.12743515]

>>12743254
>>12743509
of yeah nvm, just realised A,B must be square also
otherwise C^-1 B might not be defined i.e. inconsistent dimensions

[Anonymous No.12743626]

>>12743515
If C is nxn then B must have n rows so C^-1 * B is always defined

[Anonymous No.12743883]

>>12715301
yeah, but she is an ultra normie so I don't talk about math with her, also I like math but I'm not autistically in love with it.

[Anonymous No.12744081]

>>12741404
>the main thing you can take issue with here is the picking a equivalence class representative
That's a pretty big issue, considering you literally can't consider it as a list of numbers even in the naive way you propose.
>not the function thing.
That was just an example.

[Anonymous No.12744086]

>>12731019
>anu
Wtf why do you guys get so many special topics courses

[Anonymous No.12744110]

"Logical Level" concept presupposes a priori its conceptualization.
Self-contradiction if irrevocability is a given.

[Anonymous No.12744501]

>>12743054
"""CS""" courses here are just us building meme software in group projects. I honestly am dying inside each year here, but I have no choice. On another note, what field of pure maths is the most useful for CS? I'm doing Linear Algebra rn. I will probably do it alongside Combinatorics. I already know enough Analysis from Rudin btw.

[Anonymous No.12744570]

>>12731019
>>Dirac Operators and the Atiyah-Singer Index Theorem
>>12731019
>>Mathematical Aspects of Gauge Theory
>>12731019
>>Differential Geometry
>>12731019
>>Foundations of Mathematics


the last one is the redpill one, npc hates it

[Anonymous No.12744638]

Poopoo and peepee

[Anonymous No.12745038]

Postdoctoral Position in HoTT at the University of San Diego
Posted by Mike Shulman
MathML-enabled post (click for more details).

The University of San Diego invites applications for a postdoctoral research fellowship in homotopy type theory beginning Fall 2021, or earlier if desired. This is intended as a two-year position with potential extension to a third year, funded by the second AFOSR MURI grant for HoTT, entitled “Synthetic and Constructive Mathematics of Higher Structures in Homotopy Type Theory”.


https://golem.ph.utexas.edu/category/2021/01/postdoctoral_position_in_hott_1.html#more

[Anonymous No.12745042]

>>12745038
This is the same grant that’s funding Emily’s postdoc, but my bureaucrats took longer to get their ducks in a row, with the result that I won’t be able to make an offer before the AMS coordinated postdoc response deadline of February 1. Indeed, February 1 is only the priority submission deadline for the application, less than 2 weeks away. However, I’ll do my best to make a quick turnaround, and if you’re interested in the position but have other offers requiring a response, please let me know before giving up. As with Emily’s position, you must at least be able to obtain a visa to come and work physically in the U.S.; I’m still working on the details of visa sponsorship, but it should be possible.

Applications are encouraged from candidates working in any area related to homotopy type theory, broadly construed. If your background is in a related area but you’re interested in getting into the field, don’t let that deter you. Please include in your cover letter a discussion of your background and future research goals as they relate specifically to homotopy type theory, as well as any specific interests you may have in collaborating with the team for the grant, which in addition to myself includes Steve Awodey, Bob Harper, Favonia, Dan Licata, and Emily Riehl, and their students and postdocs. This is especially important if you’re new to the field and HoTT doesn’t figure prominently in your CV and past research.

[Anonymous No.12745045]

The University of San Diego (not to be confused with the University of California, San Diego) is a relatively small private Catholic university. Although the university includes a few graduate schools, the mathematics department is in the College of Arts and Sciences, which is purely an undergraduate liberal arts college. We have no graduate students, and this will be the first postdoc ever in the math department. So you should be aware what you’re getting into; but on the other hand, if you have any interest in eventually becoming faculty at a liberal-arts college, this could be a good opportunity to get a feel for what such a department is like. Although I can’t make any promises, the postdoc may have the opportunity to help supervise undergraduate research students and/or to teach undergraduate courses if they are interested (though this is not required, and will be decided later).

Applications should be submitted through the University of San Diego recruitment system. Please email to alert me of your application, as well as with any questions you have!

USD is an Equal Opportunity employer, and is especially interested in candidates who can contribute to the diversity and excellence of the academic community.

[Anonymous No.12745082]

Does one apply to student loans before or after getting accepted into a college? How about in germany, if anyone knows? Bildungskredit in particular

[Anonymous No.12745114]

>>12745082
At least in Fingolia one applies for the student support stuff (monthly money and loan) after acceptance. Of course, it could be a conditional OK for student loans in Germany, and then proof of acceptance would actualise it, but that would lead to a lot of unnecessary bureaucracy. I would assume it is after in most places.

>>12745045
>Catholic university
Probably Roman Catholics and not based Greek ones.

[Anonymous No.12745174]

X is a Banach space S is the unit sphere N⊂ S and is its ε-nets.
Prove the sphere or radius 1-ε is contained in the closed convex covering of N

[Anonymous No.12745482]

Hey guys. I'm solving a problem but having trouble. I've finished the question but I dont understand one thing;

The problem is basically just find the volume of half a sphere, where the cords of xyz are all in the origin, radius of the sphere is 1. The instructions say that integrating both x and y will result in 0 so there's no point, hence I have to integrate in spherical cords around z. Why is that? Why will it be zero? I understand the symmetry but it's a spherical shape, how will its volume ever end up zero?

[Anonymous No.12745615]

>>12745482
Double integral... Scattering o heights over xy coords... You give bounds for the first one, equations for the second, sum up the height. Just plug the function z = sqrt (x2+y2) into a double integral of x from -1 to 1 and y from the lower circle bound to upper circle bound

>>12745114
My german friend said to this effect yes. What math do you recommend for practical anxiety?
https://www.youtube.com/watch?v=MPVq30bPq6I

[Anonymous No.12745643]

>>12745482
You certainly won't get zero if you do it right. I could see there being something deceptive that makes it look that way.
The issue is that integrating sqrt(1- x^2 - y^2) on x^2 + y^2 < 1 is obnoxious and tedious, and it's much easier to do it in polar.

[Anonymous No.12746252]

>>12715244
Are there any names for the numbers in the hundreds places like there are for the tens place?
Are there any languages that don't have silly naming conventions for the teen numbers?
If you were going to make up a number name for the hundreds place, what would the syntax be? (twendred, thirdred?)

[Anonymous No.12746266]

Neet here, want start learning math from the scratch
Should I start with a mind for numbers as a total beginner mathlet?
Also how do I focus for longer periods of time

[Anonymous No.12746481]

/lit/ here

Are there any good biographies on great mathematicians, or just any mathematicians with really exciting lives to read about?

[Anonymous No.12746519]

>>12746481
"The Man Who Loved Only Numbers."
Also Simon Singh's book on Fermat's Last Theorem story if you're not much familiar with it.

[Anonymous No.12746525]

>>12745615
I recommend finite group theory for that. It kept me if not sane, then at least less insane two years ago. You get to do some induction and counting arguments and stuff, you have your Sylow and Hall subgroups, Frattini arguments and so on. I suggest you try that. It's sweet, you are sweet, I am sweet.
https://www.youtube.com/watch?v=PVHrZlCMVTE

[Anonymous No.12746532]

>>12746519
Thank you very much, these look really interesting :>

[Anonymous No.12746656]

>>12746525
Quick! Find me the normal subgroups of a group of order 2021.

[Anonymous No.12746662]

>>12746656
All of them?
2021 = 43*47.

[Anonymous No.12746717]

>>12746656
Trivial subgroup and the whole group [math]G[/math]. If there would be a normal 43-Sylow subgroup [math]S[/math] of [math]G[/math], then [math]G = N_G(S)[/math], so [math]n_{43} = |N_G(S) : S| = 47 \equiv 4 \mod 43[/math], contradicting Sylow's theorem. Similarly, there would be 43 normal 47-Sylows which seems quite awful considering the fact that there should only be one. I think those two are the only ones with a quick reasoning like this.

[Anonymous No.12746724]

>>12746525
>It kept me if not sane, then at least less insane two years ago
good wording as trannies are NEVER sane

[Anonymous No.12746732]

>>12746717
[math]\mathbb{Z}_{2021}[/math] has a ton of normal subgroups, what condition did you forget?

[Anonymous No.12746738]

>>12746724
Based.

>>12746732
Oops. I don't even know anymore. I forgot abelian groups exist, that's one thing.

[Anonymous No.12746815]

>>12746732
Oops I misremembered the normaliser thingy. Right. It wasn't the index of S in its normaliser, but the index of the normaliser in the whole group. But "tons of normal subgroups" seems wrong. It has 1, it has the whole thing and then you have the 43- and 47-Sylow. If we chose any subgroup, that would also be cyclic and its generator's order would have to divide 2021. It would then be 1 or divisible by at least one of 43 or 47. Suppose it was 43n with 1 < n < 47. Then the order of the 43rd power of the generator would be n, but does not divide the order (unless it is 43, but then the order of our subgroup would be 43*43 which is not OK), so the only possible values for n are 1 and 47. Similarly for the case in which the order of the subgroup is divisible by 47. Sorry, I'm retarded and can't even sleep anymore so my quality is even worse than it was a few months ago.

[Anonymous No.12746827]

>>12746815
Go to sleep then. No one's forcing you to stay up to shitpost.

[Anonymous No.12746953]

>>12746815
>which is not OK
logical contradictions are heckin cute and valid chud

[Anonymous No.12747123]

>>12746717
>not using \pmod
cringe

[Anonymous No.12747413]

What does nebenklassenzerlegung mean in english

[Anonymous No.12747422]

>>12747413
quotient group I think? sometimes people call it G mod H

[Anonymous No.12747445]

>>12747413
>nebenklassenzerlegung
ahahahahaahha

[Anonymous No.12747491]

>>12746481
Hilbert by Constance Reid
The Apprenticeship of a Mathematician by Andre Weil
Love and Math by Edward Frenkel

[Anonymous No.12747576]

>>12747413
Never mind, it means coset partition

[Anonymous No.12747713]

I'm blanking out on this pretty simple problem.
I basically need to know how much length of the side (580mm) changes when it is lowered by 100mm as shown in the image.

Lowering it changes all the angles afaik i can think and that's where my blank started. -_-

[Anonymous No.12747987]

>>12745482
>>12745643
yeah so i actually just went ahead and did this with a single trig sub and it's really painless. not sure why you wouldn't just do the sqrt(1 - x^2 - y^2) integral.

[Anonymous No.12748004]

Who here can draw a better integral by hand? Nobody.

[Anonymous No.12748022]

>>12748004
thats beautiful anon but im better.

[Anonymous No.12748043]

>>12748004
The pinnacle of autism.

[Anonymous No.12748048]

>>12748004
>bottom is curved while top is straight
Where is your symmetry, anon?

[Anonymous No.12748057]

>>12748048
cuz its not gay to fuck butt however its gay to get fucked in your butt

[Anonymous No.12748125]

>>12729538
Use mit opencourseware. Has everything you need. I cant believe I only found out about it this year

[Anonymous No.12748128]

>>12731825
You insult guenon?

[Anonymous No.12748283]

Is there a more comprehensive algebra text than Lang?

[Anonymous No.12748289]

>>12748283
You don't need anything more comprehensive than Lang or Dummit and Foote. Once you finish one of those you are ready to go onto specialized books on algebra topics.

[Anonymous No.12748348]

>>12747713
Figured it out on my own. Such a simple thing at the end, but with a brainfart it took me few episodes of anime to realize what to do.

[Anonymous No.12748691]

when does combinatorics become a hard subject?

[Anonymous No.12748874]

Are there any local-global principles relating finite and infinite groups

[Anonymous No.12749138]

Do you anons LaTeX your proofs or just leave them on the paper?

[Anonymous No.12749374]

>>12746481
Read Golden Years of Moscow Mathematics, it has lots of fun (and not so amusing) stories

[Anonymous No.12749379]

>>12731019
>Randomised Numerical Algorithms
>Fractal Geometry
>Probability Modelling

[Anonymous No.12749602]

>>12749138
Anyone has a pdf/djvu/whaterver for this? Sounds like an interesting reading.

[Anonymous No.12749666]

X and Y are banach spaces T:X Y is a continuous linear operator.T is a surjection and Y is separable.
How to prove there exists a separable Z⊂X such that T(Z)=Y?

[Anonymous No.12749689]

>>12749666
Think about what's the only certain set in X that you can construct from the separability of Y and the surjectivity of T.

[Anonymous No.12749698]

Suppose you have two cones such that their bases and points coincide but one is larger and completely covers the other. If you subtract the region occupied by the smaller cone from the larger cone, what shape do you get?

[Anonymous No.12749700]

>>12749689
T^-1 of the countable dense subset?

[Anonymous No.12749705]

>>12749698
Hey undergrad, this is for integrating a sphere or hemisphere, isn't it?

[Anonymous No.12750004]

im solving a bunch of problems for a calculus test but i just dont get it. the solutions always seem so random. its mainly volumes of 3d shapes, moment of inertia and mass. the integrated limits and even the integrated functions themselves seem to come out of nowhere in the solutions. is there some website that quickly covers everything on this?

[Anonymous No.12750046]

>>12719004
This is really weird. There is a lot missing here. We don't know the set it's acting on nor the group action. I have no idea what this is supposed to mean.

[Anonymous No.12750111]

>>12728070
>tridimensional
barf

[Anonymous No.12750744]

>>12750046
I’m the one who posted it, I figured it out, I’m just trying to prove some properties then I’ll make a full post of it, probably next thread.
If anyone’s curious, it’s almost like if you tried to define the quotient group but you don’t care whether or not the subgroup is normal

[Anonymous No.12752464]

>>12746815
what does it feel like to be a failure as a mathematician and a mentally ill faggot who thinks he can become an anime girl even though you will never be a woman? asking for a friend.

[Anonymous No.12752479]

>>12752464
at least she's not a scumbag retard like you, and to top it off I bet you suck compared to her

[Anonymous No.12752506]

>>12752479
>she
>her