/sci/ - Science & Math

>>10757660
>>10757661
>>10757670
>t. unemployed

>>10759244
Anyone going to IMO 2019? 14 days boys.

>>10759267
>being an olympiadshit
>being a high schooler
fuck off pseud, we do real math here. not "le frog jump on 3d grid of lilypads xD :3" math.

>>10759338
>fuck off pseud, we do real math here. not "le frog jump on 3d grid of lilypads xD :3" math.
Do you really need to swear?

>>10759244
Anyone has experience taking the entrance exams to Kyoto U?

>>10759244
So much virginity in that room. Why are maths people so ugly?

>>10759338
Wow, this is a kid-friendly thread man. Watch the language. Anyways, I'm not a high schooler. I'm not going there to compete, just to socialize and make sure our kids don't jump off a bridge or something. The fun part is talking to the other professors who attend.

>>10759338
>fuck off high schoolers discussing olympiad problems
>t. high schooler namedropping theorems from wikipedia

>in model theory we sometimes actually consider
Refer to >>>/lit/.

>>10759244
Is 24 too late to start learning math?

>>10759375
>people
I think you're mistaken. Those are "Japanese".

>>10759244
Someone redpill me on homotopy type theory. Specifically what are the advantages over plain inductive type theory for the purposes of computer formalizations of math?

>>10759482
>inductive type theory
>computer formalizations of math
Refer to >>>/lit/ and >>>/g/.

>>10759482
>redpill
Discuss "The Matrix" on >>>/tv/. We don't do that in this thread.

>>10759476
Yes and no.

>>10759494
>"Yes and no."
What did he mean by this?

>>10759515
That you can still go relatively far, but not too far.
In all honesty, I don't think anyone here is actually all that interested in the pedagogy of mathematics.

>>10759485
>>10759489
why is this board so useless? if you don't know the answer you don't have to respond

>>10759538
computers are really important, you are important for wanting to waste time caring about them thank you

>>10759359
No, but a bunch are available here: https://www.math.kyoto-u.ac.jp/en/past-exams
I can solve the entire 2018 one, and I'm retarded, so you should be fine.
I'd like to mention that question 4 is particularly kino for forcing you to prove both lower and upper semicontinuity, which is relatively rare for that stuff.

>>10759538
It's spam, ignore him

>>10759577
>no longer offering a foreign language version of the entrance exam in English as of 2020

Based and culturepilled

>>10759793
I wonder why they stopped.

>>10759476
It all depends on what background you have and your capacity for making connections between different topics ("mathematical maturity").
The hardest part is to get a good understanding of proofs and calculus on your own.

>>10759338
that shit is hard

>>10759515
mostly yes

Why Arent you picking yourselves? I'm behind mochi with a cheeky grin on

>>10759244
china masterrace

Is anyone a bit demotivated by the fact that their work on theory doesn't have immediate practical applications in real life?

Maybe it's just my depression, but lately it feels like I'm playing with adult toys rather then doing useful work.

>>10760296
>Is anyone a bit demotivated by the fact that their work on theory doesn't have immediate practical applications in real life?
No, I'm not subhuman.

Does /mg/ not know what nonlinear programming is?

>>10760351
I know. Are you doing optimization? How is that related to data science these days? Had data science eclipsed operation research?
Cause I'm researching this career path and it seems to me that today, everyone is a data science guy and there's nothing about operations research, even though the demand is obviously still there, so it seems to me that now data scientists do both. Is this the case?

>>10760390
It's both. The large-scale regression methods from ML are used to generate forecasts that get fed into the optimization solver. My job has me working on all kinds of different things, from signals processing to, to stats, to optimization, which definitely keeps it interesting. Basically I am the head applied mathematician at a major retail chain, so lots of different stuff comes across my desk. Pretty comfy desu.

>>10760425
Very interesting. I love logistics optimization. I don't know why. It's some innate autism.

I have one more question. How's your pay? Do you get paid better than the programmers?

>>10760351
> nonlinear programming
>>10759485

>>10760425
> muh meme learning
refer to >>10759485

>>10760438
Yes, I make about 50% more than their already inflated wages.

>>10760442
>>10760445
Stay jelly and unemployed, incels. Every day my math moves billions of dollars.

>>10760456
Do you have a Ph.d or just MS.c? Contemplating whether it is worth it to spend four years earning below median salary for that title. But I'm also scared that it would put me at a disadvantage or that I'll his a glass ceiling later on.

>>10760485
>Do you have a Ph.d or just MS.c?
No, although I did achieve some very impressive research results as an undergrad, which ultimately got me the job. They want demonstrable proof that you're competent more than certifications.

http://dec41.user.srcf.net/notes/

>>10760594
I too visit reddit

>>10760594
Do people actually study using someone else's notes?

>>10760456
>>10760485
>>10760537
Refer to >>>/biz/ and >>>/adv/.

>>10760627
Yes.
t. person who writes the lecture notes for his fellow student.

>>10759244

> tfw a lot of math programs I want to apply for at my university explicitly exclude white men

they justify it by mentioning "x% of math professors are white men"

>>10760718
Become trans?

>>10760673
A mathematician who never applies theory will be intellectually stunted cause dimensions of the space of the relevant theory will never occur to you out of nothing, but they can occur in nature as an application of theory to natural phenomena.
Nature acts as a sort of filter that only lets through interesting aspects of the theory.

That's why modern physics has managed to contribute so much to math.

-- Ed Witten's forged signature

>>10760722

xd

>>10760729
>natural phenomena
>modern physics
Refer to >>>/lit/ and >>>/toy/.

>>10760729
>applies theory
Mathematicians constantly apply theory. They just do it to their subject itself. Now go to some other board to discuss "modern physics".

>>10760729
> mathematician who applies theory
A mathematician is one who conjectures and proofs theorems. A mathematician is not a scientist or an engineer. By definition application is not a part of mathematics, meth is a purely theoretical subject. One who applies meth might still be a mathematician if he is "proving or conjecturing theorems" but he is not while doing application.
For application refer to >>>/sci/eng/ or /g/.
Now leave this thread meme learning code monkey tards, physishits and toddlerneers.

>>10760768
>>10760782
>>10760831
Incoherent babble as expected from retarded asspie mathemashitstains.

>>10760718
i imagine there is some sort of legal issue there

>>10760840
>mathemashitstains
Ooh I'm stealing this

>>10760840
Refer to >>>/sci/medical/ and/or >>>/sci/eng/ and/or >>>/toy/.
>>10760845
Refer to >>>/law/.
>>10760846
>stealing
See the above text.

>>10759244
>altmath

>>10760840
>asspie
I feel you. It's tough being a neurotypical in any even remotely demanding field. That's not an excuse to vent your rage here though.

Is there something like compactification but with connectedness instead?

>>10760896
What exactly do you want in the end?
Something like the convex Hull?

>>10760896
so you want a dense embedding of your space into a connected space?
just pop some points in and glue the connected components together are the points or something. glue one component to a point, then the other to the same point. make some sort of transfinite chain this way.

>>10760905
a connected space from a space that is already metrizable and compact
but first I'm mostly interested if you can simply build a connected space from a disconnected one without needing to keep those properties
>>10760925
uh, sure, I will try that

>>10760933
>metrizable and compact
yikers

>>10760845

Maybe but I can't do shit about it

Is the Lax-Milgram theorem (https://en.m.wikipedia.org/wiki/Weak_formulation)) just Riesz-Frechet with a different norm? I mean, using the notation in the article, you could define a new inner product <v, w> = a(v, w). Both norms are equivalent, so they define the same topology so I guess you could just apply the Riesz theorem with the new norm.

>>10760982
>Both norms are equivalent
By this I'm referring to the norms induced by the original and new inner products

Hey guys, I've failed a mathphysics exam (more like I didn't even show up heh ;_;) and now have all summer left to catch up. Any suggestions of lit for beginners? We had like eh.. Sobolev spaces I think.

>>10760896
Depends what you want. I guess the easiest way is to take every connected component [math]U_i[/math] of your space and select a point [math]x_i\in U_i[/math] in each component to get a (totally disconnected pointed cover) [math]\{(U_i,x_i)\}_{i\in I}[/math], indexed over all components [math]I[/math]. You can show that if your space [math]X[/math] has such a cover, then in particular there is a canonical homeomorphism [math]X\approx \coprod_{i\in I} U_i[/math], where the latter is the disjoint union over all components. Then you can identify all the selected points, so as to glue the components together, [math]\coprod_{i\in I} U_i /\sim[/math] where [math]x_i\sim x_j[/math] for any [math]i,j\in I[/math]. Basically, this is the wedge sum over all components.

>>10760925
way to make it overcomplicated, see this
>>10761008

>>10760982
Oh shit I'm a retard. Just noticed that the form isn't actually skew/symmetric so it won't give me an inner product.

>>10761017
>>10760982
You are kinda right though. Riesz is pretty much the relevant point of the proof (at least it is one possibility), as you can "symmetrize" by looking at <v,w>+<w,v>, an actual inner product, and can get a a contradiction to "unsolvability".

>>10760845
Not everywhere is some shithole, where people are let into positions based on merit:
https://twitter.com/TUeindhoven/status/1140953221822853120

>>10760995
>mathphysics
Refer to >>>/toy/.

If [math]X := \mathbb{A}^2-(0,0)[/math], it would seem that [math]K[X] = K[x,y][/math] because [math]K[X] = K[x,y,\frac{1}{x}]\cap K[x,y,\frac{1}{y}][/math].

But if [math]Y = \mathbb{A^2},\ K[Y]=K[x,y].[/math] So, I'm going to assume they exclude the trivial isomorphism of X to [math]\mathbb{A}^2[/math].

Then, all that's left is to say "Any affine variety has a coordinate ring which is a proper ideal of K[X], therefore they can't be isomorphic."

This is my best proof of the "exercise 3 of 4.5" they refer to. My question is:

Where do I start to prove that [math]\mathbb{A}^2-x[/math] is not isomorphic to any projective variety?

>>10761117
>implying there isn't a mathphysics course in literally any math degree.

>>10761124
Stop feeding the troll, retard.

>>10761125
Jesus why is this happening on /sci/ of all places? I could've never left /a/ is I wanted to mindlessly shitpost like this.

>>10761133
>Jesus why is this happening on /sci/ of all places?
/mg/ is LITERALLY the most autistic place on all of 4chan.

>>10761124
>>10761117
What is mathphysics? I didn't have any such thing because I double majored in physics so I just took the normal physics classes.

>>10761138
Basically just advanced PDE's pure math pretty much.

>>10761145
>Basically just advanced PDE's
Not him, but ... why not have a PDE class, at least thats how it is here...

>>10761152
Well we had both. First semester (of masters) PDE as preparation then second - mathphysics. It was all focused on https://en.wikipedia.org/wiki/Sobolev_space but not like I know the details, I already said I failed it. Really nothing is as boring and tiresome as PDE.

>>10761160
Well, first Master Semester I had a PDE course about the classical theory and now, in my second Semester one about the non-classical, but I wouldn't know why either had deserved the name mathphysics.

>Really nothing is as boring and tiresome as PDE.
???
I mean, Sobolev spaces can be a bit dry, but that isn't really the point.
The classical theory, in itself, was pretty nice and Sobolev spaces only become interesting if you see how they relate to actual PDE's.

>>10761118
The inclusion X into A^2 induces an isomorphism of the affine coordinate rings, but the latter implies an isomorphism of varieties, which is not the case since it is a proper inclusion. Hence X is not affine.

Suppose X is a projective variety, and consider any irreducible component. Then any regular map from such a component to A^2 is constant (Corollary 1.2 of section 5 Chapter 1 in Shafarevich). But the inclusion considered above provides you with a contradiction.

Is there a nice characterisation of ideals in subrings of a ring?

For example, we know that an ideal in a ring R/I is in correspondence to an ideal in R containing I. There is another correspondence theorem for subrings in the same vein. However, I am speaking about a correspondence of ideals between a ring and its subring.

Or does it go crazy? What about in a local ring?

>>10761165
I don't know. I honestly believed it's called mathphysics everywhere, maybe it's just a thing in Russian universities. Sobolev spaces were not the only thing in the course obviously. We had some equations of thermal conductivity and such. Maybe that's the reason. Also you said you also had this, right? Could you maybe suggest me some materials on this topic?

>>10760729
this is why you are ridiculed in your own department

>>10761180
>Could you maybe suggest me some materials on this topic?
I could name-drop some books my Professor mentioned, but as I am studying mostly by my lecture notes I really can't vouch for them.
Namely, Adams-Fournier, Sobolev spaces and Gilbarg-Trudinger, Elliptic Partial Differential Equations of Second Order.

>>10761174
Btw I'm asking because I have a local ring [math]R[/math] and a subring [math]S\subset R[/math], and I want to show that the latter is local.

Let [math]\mathfrak m_R[/math] be the local ring of [math]R[/math], and consider the prime ideal [math]\mathfrak m_S=\mathfrak m_R\cap S[/math]. I want to show that this is local - if [math]R\hookrightarrow S[/math] was integral, this would be automatic.

I also have this further condition: [math]S[/math] is the subring [math]R^G[/math] of automorphisms from the action of some group [math]G[/math]. Now, if the group was finite, then [math]R[/math] would be integral over [math]S[/math], but my group is not necessarily finite. Can we still conclude it?

I was thinking some argument like, let [math]u\in S\setminus \mathfrak m_S[/math]. Then [math]u[/math] is a unit in [math]R[/math], so let [math]vu=1[/math]. Acting with [math]g\in G[/math], we get on the one hand [math](gu)v = uv=1[/math], and on the other, we get [math](gv)u= g\cdot 1=1[/math], hence [math]gv=v[/math], and so [math]u [/math] is a unit in [math]S[/math].

This seems a little too easy. Is this right?

>>10761218
Wow I got the words all jumbled...

>Let [math]\mathfrak m_R[/math] be the maximal ideal of the local ring [math]R[/math]***

> I want to show that this is maximal

>>10761214
Thanks, friend.

>>10761167

>The inclusion X into A^2 induces an isomorphism of the affine coordinate rings, but the latter implies an isomorphism of varieties, which is not the case since it is a proper inclusion. Hence X is not affine.

What are you referring to when you say "the latter?"

>>10759485
>>10759489
>>10759470
>>10760673
>>10760768
>>10760871
>>10761117
stop linking to other boards plaease . your posts have nothing to do with math and you contribute nothing to this general . talk math as op has said

>>10761240
well, there's the equivalence of categories between varieties (closed affine algebraic sets) and finitely generated k algebras. So if you have an isomorphism of k-algebras, you have an isomorphism of varieties. If the inclusion [math]i:X\hookrightarrow \mathbb A^2[/math] was a morphism of affine algebraic sets, if you check, [math]k[X]=k[x,y][/math] as you said, therefore the inclusion induces an isomorphism of coordinate rings [math]i^*:k[\mathbb A^s]\to k[X][/math], but then the inclusion was an isomorphism of affine varieties to begin with, which is not true since it is a proper inclusion.

>>10761255
just dont reply to the spammer, he will go away with time

>>10761255
Stop feeding the fucking troll you fucking idiot.

Filter posts that link to other boards, but stop replying to him.

>>10761255
>your posts have nothing to do with math and you contribute nothing to this general
Oh, the irony.

What if space is 1 dimensional and time is 2 dimensional (like a circle). Where there is no real present, just what has happened and what can be. And every outcome leads to a different universe. But sometimes the universes are so similar- with only a single particle being in a different spot, that the multiverse fuses them together. And that single particle now acts as a wave. And every particle is like this.

>>10761013
i essentially said the same exact thing but with extra points you fucking troglodyte

>>10761137
not nearly as bad as /jp/

>>10761546
Why dont you go ask the relevant thread? Isn't there a /ppg/ up right now?
>>10761160
>PDEs
>boring and tiresome
Lmao amazing cope

>>10761546
>a circle is 2 dimensional
Oh no
Oh no no no
Please refer to >>>/x/ or >>>/lit/

>>10761546
ignoring the other retarded shit you said, circles are best seen as a one-dimensional object (ie it looks 1 dimensional if you zoom in close enough - this is the same reasoning as the earth being globally round but locally flat). That would make it plausible even - we are in a time loop but it is too big for us to notice that it is anything but 'flat'.

>>10761652
>we are in a time loop
>earth being globally round
Cool fiction. I think you know the proper place to discuss this.

What is the subject that gets you the most dead tired?
Personally homo algebra tbqhwyf.

>>10761838

why the homophobia?

>>10761180
Evans is one of the standard textbooks

what does he do now that he's done with mathematics? is he seeking spirituality?

>>10761922
he's not done, he's just started.

>>10761922
He's catching up on his anime backlog.

>>10761262
>Filter posts that link to other boards, but stop replying to him.
I'm not a "him".

>>10760982
Well if you have the intuition for Riesz on Hilbert spaces like [math]L^2[/math] then some of that intuition might not carry over to the more general weak version. For instance, consider the Lagrandian density [math]\mathcal{L} \in \Omega^n(J^\infty E)[/math] on the jet bundle [math]J^\infty E[/math] of a vector bundle [math]E\rightarrow M[/math] whose sections [math]\Gamma(M)[/math] forms a Banach space (like [math]L^p[/math] for some [math]0 \leq p \leq \infty[/math]). Formally taking a functional derivative along the direction [math]v \in T_u(\Gamma(M))[/math] at [math]u \in \Gamma(M)[/math] yields [math]\delta_v \mathcal{L}[u][/math], whence optimization gives the strong Euler-Lagrange equation [math]\delta_v \mathcal{L}[u] = 0[/math] for all [math]v \in T_u(\Gamma(E))[/math].
Now by fibre integration along the jet bundle we can form the action [math]S = \int_M \mathcal{L}[/math] and obtain the weak EL equations [math]d_vS[u][/math]. In this case, if we wish to apply Lax-Milgram to [math]dS[/math], we need to be able to identify [math]T^*(\Gamma(M))[/math] with [math]\Gamma^*(M)[/math] (which can be done locally by regular Riesz in case [math]\Gamma(M)[/math] is Hilbert) so that we can define the bilinear form [math]a(u,v) = d_vS[u][/math] on [math]\Gamma(M) \otimes \Gamma^*(M)[/math], or at least in the neighborhood of a solution [math]u[/math] of the weak EL equation: [math]d_vS[u] = 0[/math] for all [math]v \in \Gamma(M)[/math]. This means that we need to identify [math]T_u^*(\Gamma(M))[/math] with [math]\operatorname{ker}\mathcal{L}[/math] as a functional operator, which in general is not true if [math]\mathcal{L}[/math] is not sufficiently regular, and Lax-Milgrim cannot be applied to yield a solution.

>>10762163
Refer to >>>/lgbt/.

>>10762228
Which books do I have to read to understand what the fuck this post is saying?

>>10762277
https://en.wikipedia.org/wiki/Babu%C5%A1ka%E2%80%93Lax%E2%80%93Milgram_theorem

One of the progenitors of the theorem wrote a book on Functional Analysis and another on Linear Algebra which you might want to check out

>>10762228
>Lagrandian
Lagrangian*

>>10762322
I already know linear algebra and functional analysis, I just don't understand the differential geometry wank going on in there.

>>10762328
>I just don't understand
>wank
Maybe you're the wank then? Ever considered that?

>>10761090
I thought of symmetrizing it after posting >>10761017 but didn't think much about it after that. Looking back, a proof using the new norm seems to work but it takes more or less the same amount of work as the standard proof (that I know).

>>10762228
I barely understand any of this lol. But how could you identify [math] T^*(\Gamma(M)) [/math] with [math] \Gamma^*(M) [/math]? It seems to me that one would have "double" the dimension of the other.

Thanks for the replies anyway

What do I need to learn to begin to understand the statement of the Hodge Conjecture? I've become interested in at least understanding what this problem is about.

>>10762707
hurr

>>10761922
He looks like a normal human being in that picture

>>10762803
At least algebraic topology at the level of Hatcher, and algebraic geometry at the level of Hartshorne.

>>10762805
Was that supposed to be an intelligent response?

>>10762839
He is. A bunch of libshits in western countries started laughing at him because he isn't a hedonistic consumerist retard, as if there is anything wrong with doing math and taking care of your aging mother!

are mathematicians ok?

>>10763387
no

>>10763519

from what part of france is that surname again?

>>10762328
you can always check the sticky
>>10762969
you deserved the response entirely

>>10763541
The german part.

>>10761922

>Perelman is quoted in an article in The New Yorker saying that he is disappointed with the ethical standards of the field of mathematics. The article implies that Perelman refers particularly to the efforts of Fields medalist Shing-Tung Yau to downplay Perelman's role in the proof and play up the work of Cao and Zhu. Perelman added, "I can't say I'm outraged. Other people do worse. Of course, there are many mathematicians who are more or less honest. But almost all of them are conformists. They are more or less honest, but they tolerate those who are not honest."[21] He has also said that "It is not people who break ethical standards who are regarded as aliens. It is people like me who are isolated."
This, combined with the possibility of being awarded a Fields medal, led him to quit professional mathematics. He has said that "As long as I was not conspicuous, I had a choice. Either to make some ugly thing or, if I didn't do this kind of thing, to be treated as a pet. Now, when I become a very conspicuous person, I cannot stay a pet and say nothing. That is why I had to quit." (The New Yorker authors explained Perelman's reference to "some ugly thing" as "a fuss" on Perelman's part about the ethical breaches he perceived).[36]

>>10763573
Thing is, Yau is a cunt, but he's also really good.
Wasn't worth giving up Perelman, tho.

>>10763591

It's funny how genius can happen both at a principled fervent like grisha and a trickster like yau

>>10763387

>as you hike around the alps, you find Grothendieck's cabin
>piles and piles of notes in every room
>every good conjecture proven, Hodge, abc, RH, BSD, etc

wat do? do you upload them for everyone to see or do you slowly siphon them and claim them as yours?

>>10763643

>implying h*mans deserve it

I tare all the papers apart and commit suicide by hypothermia

>>10763643
I just read them and feel euphoric from how superior my own proofs of these conjectures are.

what the fuck guys, did you know Erdish collaborated with Oiler? based

>>10763607
Only one of them is a genius, and it sure isn't the homeless-looking hack.

>>10763706
>Erdish
>Oiler
Never heard of such mathematicians.

>>10763717

>he never heard of the amphetamines math man and funny hat math man

yuropoors are such hacks

>>10763727
>amphetamines "math man"
Wasn't that a theoretical engineer?
>funny hat "math man"
Wasn't that a physical engineer?

>>10763727
>yuropoors
We are not European.

>>10763732
>theoretical engineer
Refer to >>>/lit/.
>physical engineer
Refer to >>>/toy/.

>>10763727
>amphetamines math man
Literally every single prof at our geometry department.

>tfw conference spam mails address you as a professor

>>10763821

>Literally every single prof at our geometry department.

This. Analysts are too busy hitting on women from the engineerings.

Collatz Conjecture thread >>10763838

>>10763573
Not hating on him, but if he had better social skills he might have managed to fight back and put Yau in his place. Instead he is just disappointed that the conformists didn't speak up for him, but did he even try to get their support?

>>10763862

Ah I remember when I was in 10th grade

why do people first learn proofs with geometry when introductory number theory is much comfier?

>>10764122
People first learn proofs with geometry?

>>10764206
No, usually Calc 1 and Linear Algebra.
Exceptions usually learn it in algebra (the high school kind) or euclidean.
I personally learned in high school with the last two.
>>10763643
I look around for a will, obviously.

Does anyone here prefer chalkboard to whiteboard, and why?

>>10764283
i do. whiteboards get smudged easier and chalkboards last longer and chalk is more reliable.

Is it normal to forget proofs of theorems? If you asked me I probably could prove to the fundamental theorem of calculus to you, even though it's rather simple. I tend to forget most proofs, is this normal? I have no trouble understanding them, and easier theorems I can often prove on the fly if asked to, but more "creative" stuff I have issues with.

>book gives the definition of a sheaf
>examples of sheaves:
>the constant sheaf
Truly an enlightening example.
>>10764402
I forget evaluations extremely easily, but proofs stick like glue.

>>10764434
What do you mean by evaluations?

>>10764443
[math]\Sigma (1/x^2) = \pi /2[/math], homotopy groups of spaces, etc.

>>10764446
[math]\pi ^2/6[/math] actually, mixed it up with the Dirichlet integral.

>>10759244
that picture reminds me of the 3 grad schools that rejected my PhD applications :( all were literally 80% asian males lol

Not sure about other people's experience, but almost all the asian's in my math graduate classes cheated off each other and were not at all qualified for grad school

>>10764475
Aren't asians mostly chinese basically scientific mafia that blow their h-index citing each other and selling quotations?

I once got rejected from a master's program because one guy didn't liked how I wrote my proofs lmao.

>>10764479
the asians I encountered in general were:
> chinese/japanese/korean - if they were americanized (born in US), usually on par with average-above average students, those who knew no english were always poor students in my experience
> indian/phillipinos - always rampant cheating in my classes, they all needed calc 2 and 3 for some pharmacy program at my university, so literally 30 hindus in a class of 35, all you'd hear all class was them cheating during tests, quizzes, anything.

>>10764496
How is cheating so rampant during exams in the US? How is it so common, and organized? I'm not from the US, so I don't know how tests are organized there, but at my uni we are placed around 10 feet from other desks when writing, so you couldn't peek even if you wanted to. Notes/phone/etc get you suspended from all higher education and fined/jail time.

>>10764529
>jail time
How do you do, my fellow huebro?

>>10764529
>and fined/jail time.
Wait what? You could get to jail for cheating at the exam? Where the hell do you live?

>>10764536
Not Brazilian, I'm Swedish. Jail time is rare, but there was a recent example of cheating on college entrance exams where the participants got jail time.

>>10764536
>>10764539
wow.. wtf

>>10764539
Sweden actually gives you jail time for cheating on exams?
Huh, I was pretty sure that was something only emergent countries would actually do.

>>10762774
Sorry, there was a typo, it should be [math]T_u(\Gamma(M))[/math], where [math]v[/math] lives.

>>10764538
Yes? It's rare, fines are more common, basically happen on every case, along with suspension. You can also be required to pay back any and all subsidies you received during the period you studied, which could be around $40,000. Any student loans also get bumped up to regular loans, increasing interest from below 1% to around 5%.

>>10764554
Sounds horrible.

>>10764564
t. cheating chink.

>>10764574
Enjoy your jail-time and student loans

>>10764564
Part of it is because when writing exams you sign your name on "honour and conscience", which in Sweden is a legal term that you're being honest, same thing you sign on when giving witness to a crime, applying for unemployment subsidies, etc. Lying after signing that is an offence under the same law, so exam cheating gets "captured" by it; the same law would apply to giving false witness, but with harsher punishment of course.

>>10764579
>implying I cheat
>implying it'd even make a difference if I cheated
>implying I don't live in Brazil and go to a public uni

>>10764582
wow that was really a revelation. I never could've thought this kind of extreme stupidity is actually implemented anywhere. And to go to such extremes as jail, I'm actually mind blown. Sorry for the offtopic btw.
>>10764586
Whatever hue, you do your thing.

d-do I really need to learn all the finite simple groups? I just want to specialize in Lie theory damnit(probably).

I have a 20 hr flight and am looking for an introductory analysis book that reads like dummit and foote: i.e. many examples, no proofs left as exercises and comprehensive. Anyone has suggestions?

>>10759476
terry tao won a fields medal when he was only 16 years old

>>10764878
>terry tao won a fields medal when he was only 16 years old
scholze independently proved fermat's last theorem when he was only 8 years old

>>10764868
Zorich's thick 1100+ pages 2-volumes analysis books

>>10760296
You are.

>>10760296
Contemplating the abstract is good for the soul. If you keep your mind on the permanent things, you won’t be tossed and turned by the temporary distractions of this life. Don’t waste your ability. Some would kill to be able to think about half the things you can.

>>10764920
Thanks! I was browsing books and also settled exactly for that one so it must be the kind of book I wanted.

>>10764475
>but almost all the asian's in my math graduate classes cheated off each other
Don't you have oral exams?
Everything past the basic stuff (like Lin Algebra 1-2, Analysis 1-3) was examined in an oral exam and cheating there is basically impossible.

Brainlet here, can someone explain the difference between Jordan and Clifford algebras to me? At the basic level at least, it seems like they're talking about the same stuff from different perspectives (this whole anticommutation property). I'm sure they have a lot of different nuances to them, but what's their high level conceptual difference?

Is there something like "How to Prove It" for graduate school, a sort of methodology to deal with theorems that might that weeks to solve?

> I had not been able to discuss math with him at all. At one point, when I tried to make our conversation more detailed by writing on a piece of paper, he waved it away. But we spoke more than I had thought we might, and when he came back out of his house he presented me with a tomato and a packet of almond paste. The tomato was large and fresh and came from his garden – impressive for January– and he told me to eat it in good health. He also said I should remember that it was his friend; likely something was lost in translation. The packet of almond paste was very large. A kilo. I was not sure what to make of this generosity, and later, when I baked with it, it was good, though I realized that it had already expired when it was given to me. Almond paste has a very long shelf-life, so Grothendieck had likely had it for quite some time.

>>10765046

Dextroamphetamine and reading papers

What are your favorite linear algebra books?

I'm looking for something abstract and proof based, and also if possible one that covers the subject very similar to how group theory is covered, since I enjoy that topic very much and understand it pretty well

When did you guys first publish?
I'm 1st year in grad school and have not published yet and it's making me very self conscious.
I know most of my classmates are on the same boat but I feel like I have not yet proved myself.

>>10765274
I submitted my first paper when I was pretty much exactly one year into my phd. The quality of the paper/journal you publish in is much more important than the time of your first publication though.
Also a lot depends on the field as well I guess, I know that tons of people in graph theory for example publish an insane amount of papers (7 a year or so).

>>10765318

please don't say you're a published author cause it makes me gulity to shitpost on /mg/

>>10765257
maybe this can help https://4chan-science.fandom.com/wiki/Mathematics#Abstract_Algebra

>>10765046
https://4chan-science.fandom.com/wiki/Mathematics#Proofs_and_Mathematical_Reasoning

>>10764593
Actually it's not really extreme stupidity, because he's a swedecuck which means his school is paid for with tax money so cheating on tests is basically theft (stealing money that's supposed to go to schooling, not cheating) so yeah they deserve jail
If you cheat in a country like the US where college isn't free then there should be no legal punishment, just something like automatically failing the class or whatever

>>10765333
if you are working on something for a couple of months with some guidance from your supervisor, you will be able to prove something. From what I have seen the difficult step is from phd student/postdoc to getting a decent permanent position.

>>10765257
>understand it pretty well
lmao. not even group theorists ""understand group theory pretty well"".

>>10765257
Exactly at what level of linear algebra are you?

I'd say probably Hoffman/Kunze or Axler is good. Axler is a bit more modern.

applied math > pure math

>>10765505
based and truepilled
friendly reminder for all purefags that you will NEVER get a result as beautiful and profound as this guy who hated purefagging

>>10765505
>applied math > pure math
This is a meaningless notion.

Can anyone tell me some general but non trivial statements about the integers?
Something like the existence and uniqueness of prime decomposition, except it's supposed to require some more than basic commutative algebra to prove.

Are there any other impossibility proofs of the magnitude and significance, comparable to those of incommensurability (Greeks), unsolvability (Ruffini->Cauchy->Abel) and incompleteness (Godel) proofs?

>>10765585
Yeah, Matiyasevich.

>>10765593
Thanks.

>>10765585
>incommensurability (Greeks), unsolvability (Ruffini->Cauchy->Abel) and incompleteness (Godel)
>magnitude and significance
What?

>>10765585
>Are there any other impossibility proofs of the magnitude and significance, comparable to those of incommensurability (Greeks), unsolvability (Ruffini->Cauchy->Abel) and incompleteness (Godel) proofs?
Fermat's Last Theorem (Wiles)

>>10765633
>Fermat's Last Theorem
I prefer something more "true", like the Godel proofs. Do you have any examples of something like that?

>>10765652
First, don't pose as me, second

>>10765633
Did it have any aftermath at all and did it spawn any new mathematical methods - or simply compiled already existing?

>>10765656
>did it spawn any new mathematical methods
It did a whole fucking lot, but that was largely the modularity theorem, not exactly Fermat.

>>10765630
Whatever the initial incommensurability proof looked like, at the very least it spawned method of infinite descent, a variation of which is a method of mathematical induction.
Unsolvability proof spawned group theory.
Godel's theorems spawned computability theory.

>>10765656
>Did it have any aftermath at all
Not surprised that a non-mathematician would be asking questions like >>10765585

>>10765656
>Did it have any aftermath at all and did it spawn any new mathematical methods - or simply compiled already existing?

>>10765664
>computability theory
Refer to >>>/g/.

>Did it have any aftermath at all and did it spawn any new mathematical methods - or simply compiled already existing?

is hating on purechads just coping from people who read how to prove it books?

>>10760718
Sue them

>>10765925
I am not sure that the group it is coming from are just people who read how to prove it books, but it is definitely some serious coping.

>>10765554
The integers form a Dedekind domain.

Proof: Z is a PID so in particular Noetherian of dimension 1. Also every localisation at any non-zero prime is also a PID of dimension 1, hence equivalently, they're are discrete valuation rings. This is equivalent to Z being integrally closed, and as such, it is a Dedekind ring.

>>10765990
>more than basic commutative algebra to prove
>literally follows immediately from the fundamental theorem of arithmetic and the fact that the integers are a PID

>>10765554
Try rigorously showing the existence of integers. It's less trivial than it sounds.

>>10766005
>rigorously
Use >>>/lit/.

>>10766005
>try solving Hilbert's second problem
Ayy.

Has anyone ever found a method for proving consistency of a theory by associating a graph to it, and showing it's planar?
For some reason this is stuck in my head.

the eskimos have 100 words for snow

the mathematician has 1000 words for "function"

>>10766020
>method for proving consistency of a theory
Try asking at >>>/lit/.

>>10766030


can you redirect me to the board where I can find cheap amphetamines?

>>10766031
Use the "rap" threads on >>>/mu/.

>>10766030

>>>/o/k >>>/t/his >>>/i/s >>>/e/pic

>>10766020
>For some reason this is stuck in my head.
Mathematicians say "our", not "my".

>>10766028
>map
>morphism
>assignment
>correspondence
which else?

>>10766072
For example Operator, but you could also count specific functions, like Functionals, PDOs, etc.

>>10766072
Operator, mapping.
>>10766082
Functional isn't really a general term for function.

>>10766082
come on, that's just cheating.
You might as well have just said mathematicians have a million words for mathematical objects

>>10766086
>Functional isn't really a general term for function.
Please read my post before responding, thanks.

>>10766088
>come on, that's just cheating.
Well, firstly it wasn't me who made that Eskimo post, secondly their words for snow probably all have different slightly different meanings too.

>>10764966
Unironically, the only "possessions" I truly care about now, aside from essential things, is mathematical knowledge.

>>10759482
I believe the idea is create a set of axioms that can be used to deduce all of mathematics. If you had that you could build a computer proof system that could prove anything from first principles. For some reason these homotopy axioms are pretty good, but I don't know the particular advantages or whether they can do what they set out to do.

>>10766423
>I believe the idea is create a set of axioms that can be used to deduce all of mathematics.
Thanks for immediately showing that the rest of your post isn't even worth reading.

>>10765274
I helped with research as an undergrad and got my name on a paper

>>10765257
Hoffman-Kunze for undergrad level, Roman's Advanced Linear Algebra if it's for a second reading or if you want to learn more stuff (e.g. modules)

>>10766072

How much stuff is just a function?

Permutation, bijection, embedding, character, ____morphism, representation, action, transformation, coloring

>>10765554
Here a some very influential results about the integers in various directions with proofs that can be understood at the undergraduate level, so that you have some ideas what questions people might be asking themselves:
https://en.wikipedia.org/wiki/Quadratic_reciprocity
https://en.wikipedia.org/wiki/Dirichlet%27s_theorem_on_arithmetic_progressions
https://en.wikipedia.org/wiki/Prime_number_theorem
https://en.wikipedia.org/wiki/Hasse%E2%80%93Minkowski_theorem
https://en.wikipedia.org/wiki/Hasse%27s_theorem_on_elliptic_curves
https://en.wikipedia.org/wiki/Kronecker%E2%80%93Weber_theorem
https://en.wikipedia.org/wiki/Roth%27s_theorem
https://en.wikipedia.org/wiki/Lindemann–Weierstrass_theorem

Spivak or Courant?

>>10766924
for noobs the former

Best book for a first course on multivariable calculus? Going into second year of Uni and have a few years olympiad experience

I'm having a problem with the following question that should be relatively obvious:

>Let [math]X[/math] be a scheme, and let [math]f_0,\cdots,f_n\in\mathcal O_X(X)[/math] be such that their germ [math]f_{i,x}[/math] generate the unit ideal at the stalk [math]\mathcal O_{X,x}[/math] for every [math]x\in X[/math]. Show that the [math]X_{f_i}=\{x\in X\mid f_{i,x}\in\mathcal O_{X,x}^*\} [/math] form a cover of [math]X[/math].

Now, intuitively, we can think of glueing these locally unit sections to give a global unit, and therefore covering the space. However, I can't see how to work this out.

Say I have any point [math]x\in X[/math] in the scheme, and consider [math]\mathcal O_{X,x}=\langle f_{i,x}\rangle_i[/math], which is possible by assumption. Then it would be enough to show that at least one of the [math]f_{i,x}[/math] is a unit, but I don't see how I can conclude that - we only have a relation [math]1=\sum_i r_i f_{i,x}[/math] for elements [math]r_i\in\mathcal O_{X,x}[/math], but none of them are necessarily units, so I can't somehow factorise out some [math]f_{i,x}[/math] from the relation.

>>10763858
can confirm

>>10767186
>unit ideal
>google it
>it's just the entire ring
Anyhow, did you try proving it for an affine scheme, and then glueing the proof for the remainder?

>>10765925
applied shits piss me off. I had a classmate that I occasionally used to read over assignments with when we had some classes together and his way of approaching the problems and his motivation really bothered me. I thought he was a straight up faggot.

>>10765674
this. comp-sci shit does not belong on /mg/

>>10767363
>wtf, stop applying things!! ;_;

>>10767361
how did he approach shit?

>>10767386
Exactly.

>>10767386
Do you have some kind of a handicap? comp-sci shit doesn't belong on /mg/ the same way biology shit doesn't. Use a dedicated thread to discuss your garbage.

the other day I had a nightmare where I discovered a new hereditarily unicoherent, indescomponible, planar continuum
then a physicist found about it and made tons of applications with it
I woke up sweating

>>10767492
>physicist
Refer to >>>/toy/.

>>10767509
but I'm not a physicist

I have three C's (two C+ and one C) on my transcript, should I give up on applying to top 20 grad schools?

I know this isn't the best place to ask but I don't know where else to go.

>>10767537
Could you at least write the country maybe?

>>10767560
My bad. USA.

>>10767569
Give up unless jewish.

>>10767572
Why is that?

>>10767576
Lol

>>10767537
depends on your recommendation letters, CV, and undergrad research exp

>>10767589
>recommendation letters
working on those
>CV
ive ta'd for many classes, might sign up for tutoring this year. nothing much other than that
>and undergrad research exp
only research experience so far is for my other major

is there anything you'd recommend doing apart from more research?

>>10767392
he has a disdain for anything that is not motivated by a real world problem. He constantly scoffs at whatever isnt a differential equation. He also tries to patronize me and convince me to study applied maths.
>>10767386
see>>10767426
computer science topics have no business on /mg/

>>10767522
Don't respond to the spammer

>>10767186
>but I don't see how I can conclude that
Recall that [math]\mathcal O_{X,x}[/math] is local..

>>10767492
>>>/x/

yo im tryna learn algebra but im a visual learner. how does one graph a group? how about a ring?

>>10767386
kys brainlet

>>10768010
>graph a ring
>im a visual learner
No, you're just a brainlet. A true visual learner can intuit visual properties of rings without needing bullshit like "graphs".

>>10767975
good point....

>>10768010
>group
Cayley graphs
>commutative ring
affine schemes
>noncommutative ring
probably something like matrices n shit

Imagine being so steeped in your own imaginary, self-referential autistic world, that you get angry when someone uses it to do something useful.

>>10768403
>Imagine being so steeped in your own imaginary, self-referential autistic world, that you get angry when someone uses it to do something useful.
what are you referring to

>>10768069
>No, you're just a brainlet. A true visual learner can intuit visual properties of rings without needing bullshit like "graphs".
Rings are non-visual objects.

>>10768430
Ask how I know you don't have intuitive understanding of rings. Do you know why a ring is called a ring?

>>10768432
>Do you know why a ring is called a ring?
Here, have a read: https://en.wikipedia.org/wiki/Ring_(mathematics)#History

>>10768432
Do you actually picture a ring as a ring?

>>10768440
>Do you actually picture a ring as a ring?
Rings are non-visual objects.

>>10768434
Read it again.

>>10768010
Imagine some keys dangling from a key ring. To apply a key to the opposite side of the dangling keys, you have apply the inverse operation of removing it from the side that you are taking it from. You have to take away a key on the left side of the key ring to apply it to the right side of the dangling keys.

This thread is full of pretentious pseuds.

>>10768447
>Imagine some keys dangling from a key ring. To apply a key to the opposite side of the dangling keys, you have apply the inverse operation of removing it from the side that you are taking it from. You have to take away a key on the left side of the key ring to apply it to the right side of the dangling keys.
This is the thought process of someone calling others "pretentious pseuds".

>>10768447
>Read it again.
Here, have a read: https://en.wikipedia.org/wiki/Ring_(mathematics)#History

>>10768450
As opposed to flaming newcomers asking for an intuitive explanation.

>>10768460
A ring is an algebraic object that admits zero divisors. You genuinely shouldn't visualize it in general, although you can in quite a few cases.

>>10768440
>>10768450
>>10768456
>>10768467
>wtf, stop understanding things!! ;_;

>>10768481
>>wtf, stop understanding things!! ;_;
Who are you quoting?

>>10768481
>wtf, stop correcting my misinterpretations of a subject and trying to help gain a better grasp of it!!

>>10768403
imagine being so angry because all the work you do is the low hanging fruit of mathematics. I have no sympathy for appliedfags, you people are like rabid retarded dogs that need to be put down.

Think about it logically. Being a pure mathematician makes you the ultimate cuck. You literally are proving a theorem to make it better at being applied. All that time making sure its true sufficient and necessary and consistent is literally just improving how easily it can get at being applied by engineers, physicists and applied mathematicians. All that time making it important and groundbreaking, who benifits. Only the people who do applications, the applied mathematicians.

>>10759244
Studying for a mathematical statistics exam. The parts on inference, confidence intervals, p-values, estimation of parameters I find a bit confusing. Any recommended resources?

>>10768668
Cohn's Measure Theory.

>>10768430
>Rings are non-visual objects.
Undergrad with zero intuition detected.

>>10768668
>mathematical statistics
>Any recommended resources?
>>>/sci/eng/ would be one. Refer to that.

>>10768641
>Think about it logically.
Refer to >>>/lit/.

>>10768764
>>10768784
>eltism in order to compensate for ignorance/brainletism
Refer to >>>/r/incels

>>10768748
>intuition
>>>/x/

>>10768748
>Undergrad with zero intuition detected.
What did he/she mean by this? There's plenty of intuition available for rings, it's just not visual intuition since rings are non-visual objects.

>>10768792
Who are you quoting?

>>10768817
>What did he/she mean by this?
We're not a he/she.

>>10768467
>admits zero divisors
Not if your ring is commutative, and most rings are, statistically speaking.

>havent passed analysis
just fucking kill me already I've fucking had with it epsilons and deltas

>>10768792
>not wanting statisticians and accountants discussing their off-topic subjects on a math general is """elitist"""
Hang yourself.

intuition is the mathematical form of schizophrenia, literally a meme

>>10768845
>math
This is not well defined.

"Ring" is not supposed to be a brilliant new concept, it's a definition made to facilitate studying stuff which can be multiplied and added in some generality. There also isn't much too visualise.
You simply want to define an object X which fits as most structures you already know (integers, reals, matrices, polynomials etc) but also not too general, so that you can have nontrivial theorems about X's, this is how people came up with rings/fields/algebras
The exact definition is somewhat arbitrary, that's why some authors mean commutative ring, or a ring with identity, when they speak of rings.
so stop your retarded de

>>10768898
>There also isn't much too visualise.
There's nothing to visualize, rings are non-visual objects.

>>10768865
>meme
Refer to >>>/b/.

>>10768792
Don't respond to the "refer to" spammer

>>10768905
>rings are non-visual objects
Why not?

Are contemporary PureMaths literally neo-Pythagoreans, still blindly following wimpy footsteps of Hilbert long since overthrown by chad Godel, engaging in useless pointless inscriptions shuffling that isn't ever going to be applied anywhere simply by force of the current notion of mathematical rigor used, itself, being flawed to the point of principal unusability of 99.9% of results derived using it?

>>10769159
>Hilbert
>Pythagoreans
>Godel
Refer to >>>/lit/.

>>10767664
that is fucking annoying