/mg/ - /mathematics general/

[Anonymous No.11903921]

Previous: >>11897308

Every counterexample in AG edition

[Anonymous No.11903927]

>>11903921
>Elliptic curves

[Anonymous No.11903942]

Why independent subsamples give non-correlated models (so called bagging technique in machine learning) ?
Can this be proved rigorously or it's just another "empirical" bs ?

[Anonymous No.11903956]

What's a "scheme of integers" of a field? Can't find anything on it on google.

[Anonymous No.11903957]

>>11903927
I was watching for this thread to be made, so I could post a funny edit of your post, but you were too fast... Do you spend all of your time here?

[Anonymous No.11903962]

>>11903957
>Do you spend all of your time here?

[Anonymous No.11903965]

>>11903956
I dont know but perhaps the scheme over the ring of integers?

[Anonymous No.11903970]

>>11903965
>>11903956
like for example, I can think perhaps you have a curve over a field, and there is an associated arithmetic surface over its ring of integers, usually with the curve being its generic fiber

[Anonymous No.11904013]

Threadly reminder to NOT bully physicists.

[Anonymous No.11904030]

>>11904013
I'm really not that interested in science.

[Anonymous No.11904036]

>Me ? I don't believe in the scientific method, only in the axiomatic method.

[Anonymous No.11904042]

>>11903916
>>11903926
Why not ?

[Anonymous No.11904050]

>>11903921
pure mathematics is useless and applied mathematics is just whatever field is applied to so math is useless

[Anonymous No.11904053]

>>11904036
This but unironically.

[Anonymous No.11904055]

>>11904053
wasn't ironic

[Anonymous No.11904075]

>>11903962
Based.

[Anonymous No.11904150]

why the fuck does all this topology seem like heremenutic black magic like wtf are half of these diagrams

[Anonymous No.11904174]

>>11903921
why does bootstrapping use replacement? wouldn't it be better to not?

[Anonymous No.11904183]

>>11903921
Not sure if this belongs here or on /sqt/, but how important is the choice of university for undergrad? I have an offer to read maths at St. Andrews, as an international student, which means fees (study + living costs) of nearly 30k british pounds per year. I also have an offer for a uni in my country (third world latin american country), said uni which has a lot less 'prestige' than st andrews, but fees are ridiculously low (the whole undergrad costs less than one year at st andrews). Anyway, would you recommend to do undergrad home, try to do really good and then aim for post-graduate at somehing more prestigious? Or should I take the offer? Any chance somebody here studied at st andrews?

[Anonymous No.11904184]

>>11904150
>these diagrams
Thanks for sharing a difficult one with us.

[Anonymous No.11904240]

>>11904183
This is a really good question. It really depends on the curriculum and what interests you most.

You never mentioned your financial situation, if you have the money I would go to the nice uni for as long as possible.

[Anonymous No.11904263]

>>11904184
Not him btw

[Anonymous No.11904271]

>>11904150
What could you possibly mean by this?

[Anonymous No.11904277]

>>11904263
What is strange about that?

[Anonymous No.11904281]

>>11904277
my brain is too small to understand it

[Anonymous No.11904283]

>>11904042
Because it's retarded, there are plenty of other new sources that are clearer, cleaner, and more modern. It's been 50 years since EGA was written. It is still a good reference for the more abstract stuff and non-Noetherian schemes, but in practice these aren't as important, and the only reason one should read them is because they actually need them. At the very least read the bulk of Hartshorne.

[Anonymous No.11904289]

>>11904281
All you need to notice is that p corresponds to superscript of sigma and q to the subscript of K.

[Anonymous No.11904296]

>>11904289
holy fuck thanks for the info
it's all clear now
Do you happen to be a topologist?

[Anonymous No.11904298]

>>11904296
No. I just happen to not be afraid of notation.

[Anonymous No.11904302]

>>11904298
notations are scary though

[Anonymous No.11904305]

>>11904302
No, not really. Some may take time, though.

[Anonymous No.11904307]

Does Goertz-Wedhorn have the most based appendix?

[Anonymous No.11904311]

>>11904307
holy fuck this is worse than the "statistics is math" picture

[Anonymous No.11904314]

>>11904311
No, because this is actually very immediately useful

[Anonymous No.11904318]

>>11904263
Isn't it funny that with all that monstrosity and smugness of hardcore homological algebra you still can't compute shit in topology most of the times?

[Anonymous No.11904321]

>>11904311
>Statistics isn't mat-

[Anonymous No.11904323]

>>11904307
>specifying the referrence instead of just writing [math] [EGA] [/math]
big yikes

[Anonymous No.11904324]

>>11904321
what a stupid faggot nigger shit

[Anonymous No.11904326]

>>11904323
This.

[Anonymous No.11904330]

>>11904311
and actually theres one of those too

[Anonymous No.11904341]

>>11904330
What am I even looking at?

[Anonymous No.11904346]

>>11904341
Read the first sentence of the first page

[Anonymous No.11904359]

>>11904321
>>11904330
love diagrams lads

[Anonymous No.11904373]

>>11904359
favorite diagram chase?
mine is splitting lemma for short exact sequences

[Anonymous No.11904374]

>why yes, I invert my ebook reader. How could you tell?

[Anonymous No.11904379]

counterexamples in topology also has a nice series of charts
>>11904374
have fun with your eye strain

[Anonymous No.11904382]

>>11904373
I dont know enough to have one, im just an undergrad with a fetish for arrows

[Anonymous No.11904387]

https://youtu.be/pEJiUnLpxLk

Yeah I'm stupid

[Anonymous No.11904479]

>>11904283
>Hartshorne
ok thanks

[Anonymous No.11904480]

>>11904374
>why yes, I use ebooks rather than buying the hardback off Amazon Student Prime

[Anonymous No.11904484]

Let [math]R_n[/math] denote the Riemann surface for the function [math]f(z) = \sqrt{z}[/math] on [math]\mathbb{C} \setminus \{ 0 \}[/math].
Then all the [math]R_n[/math] are conformally equivalent, right? fuck i'm confused

[Anonymous No.11904495]

>>11904484
reread your post, I'm pretty sure there's a mistake in there.

[Anonymous No.11904513]

>>11904495
i just learned what's a "riemann surface" today, you'll need to spell it out for me

[Anonymous No.11904523]

>>11904495
>>11904513
its obvious that what he's missing is nth root

[Anonymous No.11904531]

>>11904523
yes that's what i meant

[Anonymous No.11904555]

>>11904484
We consider three separate copies of the complex plane [math]\mathbb{C}_1[/math], [math]\mathbb{C}_2[/math] and [math]\mathbb{C}_3[/math] (Scholze btfo).
We have [math]f_n (z) : \mathbb{C}_2 \rightarrow \mathbb{C}_3[/math], which you've already defined. We also have [math]g_n (z) : \mathbb{C}_1 \rightarrow \mathbb{C}_2[/math] given by [math]g_n (z)[/math].
Notice how the multivalued function [math]f_n[/math] lifts through [math]g_n[/math], a covering map, to a single valued function [math]h: \mathbb{C}_1 \rightarrow \mathbb{C}_3[/math] given by [math]h(z) = z[/math].
Does this imply that [math]( \mathbb{C}_1, g_n , \mathbb {C}_2 )[/math] is [math]f_n[/math]'s Riemann surface?
I dunno, I don't remember how you defined the Riemann Surface of a function and I can't find it on wikipedia, but I do think so.

[Anonymous No.11904560]

>>11904555
* [math]g_n (z) = z^n[/math]

[Anonymous No.11904674]

>>11903921

DESK REJECTED
E
S
K

R
E
J
E
C
T
E
D

[Anonymous No.11904735]

i can only stomach math classes, the rest are infected with too much politically infused opinion
what are my job options outside of academia
i am willing to take on ee/cs but math is my main squeeze

[Anonymous No.11904755]

>>11904735
Based schizo.

[Anonymous No.11904774]

>>11904735
>i can only stomach math classes, the rest are infected with too much politically infused opinion
um, don't think you've taken a category theory class yet, sweaty.

[Anonymous No.11904783]

>>11904774
>Category theory was a mistak-

[Anonymous No.11904854]

Who here has actually read Bourbaki?
Tell me, was it worth it?

[Anonymous No.11904866]

>>11904854
I read Théorie des ensembles. It's good if you already know the subject, otherwise you won't understand anything.

[Anonymous No.11904882]

>>11904854
What do you mean "read Bourbaki"? Elements of Mathematics is like 20 volumes long.

[Anonymous No.11904894]

[Anonymous No.11904898]

>>11904735
if you cannot adopt the philosophies of those around you to your own benefit, then you are not smart and you will never make it in academia

[Anonymous No.11904976]

>>11904882
You've almost got it. Keep at it, champ.

[Anonymous No.11904982]

>>11904674
You fooled me because I have no idea what you're saying

[Anonymous No.11904991]

Anyone used the Putnam and Beyond book? Looks nice

[Anonymous No.11905019]

>>11904991
department head here uses it to teach the putnam practice class
i couldnt tell you anything much about it because even though im in the class, i fucking hate competition math
but if he uses it, it should be good enough, besides its available online

[Anonymous No.11905023]

>>11903957
>he doesn't spend all his time here
LMAO.

[Anonymous No.11905029]

>>11905019
>putnam practice class
This is a real thing?

[Anonymous No.11905039]

>>11905029
yup, even my mediocre community college has one

[Anonymous No.11905043]

>>11905039
I hate competitive math so much, bros.

[Anonymous No.11905071]

>I hate competitive math


stop seething and just say it isn't for you, very cringy sour grapes

[Anonymous No.11905073]

>>11904263
Why is every introduction to spectral sequences so botched and mishandled?

[Anonymous No.11905075]

>>11905043
not a fan of them either but the Putnam gets a special exemption from me, since it actually requires nontrivial knowledge and results from my undergrad education and knowing how to use them

[Anonymous No.11905148]

I dislike the following
>Algebra
>Complex analysis
>Discrete math in its entirety
Am I a brainlet? Should I become a physicist instead? I like differential geometry a lot.

[Anonymous No.11905162]

>>11905071
>stop seething and just say it isn't for you, very cringy sour grapes
Bro you're one to talk about seething, he said he hates it which is equivalent up to homotopy to saying it isn't for him

[Anonymous No.11905173]

>>11905148
>likes differential geometry
>dislikes complex analysis
How?

[Anonymous No.11905204]

Is there any way that you can explain why there's no general formula to calculate the roots of [math]p(x)=x^k+x^{k-1}+...+x^0, \forall k \geq 5[/math] to a layman, without getting into high level algebra or is that pretty much impossible?

[Anonymous No.11905387]

>>11905173
I don't understand it either, I just can't bring myself to care about zeros and residues and holomorphic wankery.

[Anonymous No.11905414]

>>11905204
A formula to calculate the roots of a quintic polynomial or higher using only radicals depends intimately on the algebraic behaviour of the ambient space that the roots reside in, under permutation of the roots. For general polynomials of degree 5 or higher, the behaviour is too rigid to say anything about ALL polynomials of that degree.

[Anonymous No.11905427]

>>11905387

[Anonymous No.11905431]

>>11905427
I understand the subject itself, as much as a one semester course allows to at least. It's just painfully boring to me and I don't know why.

[Anonymous No.11905674]

>>11905148
not even physics, go be an engineer instead
trust me, it's better for you, you'll actually make money and have a life

[Anonymous No.11905864]

>>11904894
kek

[Anonymous No.11905872]

>>11905148
Physicist use a lot Lie algebra, group theory and complex analysis.

[Anonymous No.11905874]

>>11904894
Underrated.

[Anonymous No.11905915]

>>11904898
imagine being this dumb

[Anonymous No.11905922]

>>11905915
i assumed he was just really bad with words, but i will second this

[Anonymous No.11906280]

Is there a field which you know you are bad at, and you wish you were better?

[Anonymous No.11906288]

redpill me on cardioids

[Anonymous No.11906289]

>>11906280
Differential geometry and calculus in general.

[Anonymous No.11906290]

>>11906288
What is there to be redpilled about

[Anonymous No.11906296]

>>11906290
why did it take me 30 minutes today to remember what they are called

[Anonymous No.11906302]

Hello, retard here.
Is any topological space the classifying space of its fundamental group? If not, what are some counter-examples?

[Anonymous No.11906305]

I know how to use trigonometric functions... but why do they work. why does it happen that when I give them angle and a side I can calculate another side. I kind of understand but not really.

[Anonymous No.11906311]

>>11906305
black magic

[Anonymous No.11906313]

>>11906302
An easy example would be the space [math]\mathbb{R}P^2[/math]. Its fundamental group is integers mod 2, and if we would then take [math]B(\mathbb{Z}/ 2\mathbb{Z})[/math], its homotopy groups would be trivial for degrees higher than 1, which is not the case here, as the following link tells us: https://en.wikipedia.org/wiki/Real_projective_space#Homotopy_groups (note that [math]S^2[/math] has integers as its second homotopy group). Now that I wrote this, I am wondering why I did not just use a sphere.

[Anonymous No.11906322]

>>11906313
Thanks. But for which [math]G[/math] do we have [math]G = \pi_1(BG)[/math]? Is it known?

[Anonymous No.11906338]

>>11906322
The Eilenberg-MacLane spaces of type [math](G, 1)[/math] for any group (at least discrete). If go non-discrete, you can get funny stuff like [math]BS^1 \simeq \mathbb{C}P^\infty[/math]. It's an easy exercise to prove that if you haven't done/seen it yet.

[Anonymous No.11906349]

>>11906302
>>11906322
To actually construct an example from what anime anon mentioned, [math]\mathbb{Z}[/math] has a free action on [math]\mathbb{R}[/math], which is contractible, and then [math]\mathbb{R} / \mathbb{Z} = S^1[/math].

[Anonymous No.11906405]

>>11906305
If you proportionally enlarge every side of a triangle, the resulting triangle is called similar. That is, if you take any side of the original triangle and the same side of the old triangle, and divide one by the other, you will get the same result if you take any other side - the enlargement factor. Any two similar triangles have the exact same angles of the corners, because enlarging the sides does not affect the angles.

Trigonometry makes two observations. First, that to describe any right angled triangle, it is enough to specify only a side length and an angle of the triangle, or alternatively, it is enough to specifiy just two side lengths. Second, every right angled triangle where a certain angle is given is similar to any other right angled triangle with that certain angle.

The observations leads to the following conclusion: given a right angled triangle with some angle [math]\theta[/math], then the ratio of any two sides is equal to the ratio of the same two sides of any other right angled triangle with the same angle. So if you fix a side and the angle, any ratio between the sides is a constant for the right angled triangled of that angle, which we call [math]\sin\theta,\cos\theta,[/math] etc. Alternatively, if you are given two side lengths, you can calculate the third using Pythagoras' theorem, and use that to calculate all the trigonometric functions of the angle of the triangle. It turns out that in the cases of triangles, there is a 1:1 correspondence with possible angles [math]\theta[/math] and values of [math]\sin\theta[/math] or other trig functions - so once you know the sine of an angle, you can find out what the actual angle is.

[Anonymous No.11906426]

Is it possible to express a real number in Pi base?

[Anonymous No.11906493]

>>11905204
There is and its actually very simple.

[Anonymous No.11906518]

How the fuck do I cite /mg/ for my article?

[Anonymous No.11906520]

>>11906518
why would you cite it?

[Anonymous No.11906522]

>>11906520
It would be dishonest to claim a proof idea as my own when I saw it on here.

[Anonymous No.11906524]

>>11906522
>dishonest
NEVER gonna make it

[Anonymous No.11906526]

>>11906522
>dishonest
so like everyone?

[Anonymous No.11906530]

>>11906524
>>11906526
Ok then you faggots, I'll steal your ideas and cite nothing

[Anonymous No.11906531]

>>11906518
>>11906522
Bro no one gives a shit, just say you came up with it.

[Anonymous No.11906532]

>>11906530
based

[Anonymous No.11906533]

>>11906530
>implying I have any idea, ever
if I had ideas, I wouldn't be posting here. The anon who wrote the proof probably read it in a paper

[Anonymous No.11906534]

>>11906530
Based.

[Anonymous No.11906547]

>>11903956
If you are talking about a global field, then probably the spectrum of the ring of integers

[Anonymous No.11906555]

>>11904854
No. I have read portions of it that I needed, but reading all of it is a waste of time.
It should be used as a reference book, that's it. Like an encyclopedia or a dictionary.

[Anonymous No.11906619]

>>11905148
>>11905387
>>11905431
we're in exactly the same boat. know that complex analysis is beautiful and wonderful but it only gets good after a few courses in it. or at least, complex dynamics and complex manifolds are beautiful. obviously doing dumb integrals is boring as fuck, it's much more fun when you have nasty objects which are made so much nicer by a complex structure. reveals tons of inner beauty and directions for study.

[Anonymous No.11906707]

>>11906530
Thanks

[Anonymous No.11906754]

What is /mg/'s opinion on calculus of variations?

[Anonymous No.11906759]

>>11906754
Based.

[Anonymous No.11906771]

>>11906754
It varies.

[Anonymous No.11906783]

>>11903921
Let [math]F:Set\to Ab [/math] be the functor that maps a set S to the free abelian group generated by the elements of S.
What can I say about [math]F(A \times B)[/math]?

[Anonymous No.11906787]

>>11906771
Kek

[Anonymous No.11906792]

>>11906783
[math] F(A \times B) = F(A) \times F(B) [/math] because [math]F(A) [/math] is abelian for all [math]A[/math].

[Anonymous No.11906798]

>>11906783
What even interesting can be said about the free abelian groups in the first place. Do the arrow images F(f) of plain functions have any interesting properties.

[Anonymous No.11906813]

>>11906754
ups and downs, innit?

[Anonymous No.11906837]

>>11906792
that's wrong

[Anonymous No.11906838]

>>11906837
prove it nigger faggot

[Anonymous No.11906856]

>>11906838
[math]F(\{1\} \times \{1\}) \simeq F(\{1\}) \simeq \mathbb{Z} [/math]
but [math]F(\{1\}) \times F(\{1\}) \simeq \mathbb{Z}^2 [/math]

[Anonymous No.11906863]

>>11906783
[math]F(A \times B) \cong F(A) \otimes_{\mathbb{Z}} F(B)[/math], innit?

[Anonymous No.11906866]

>>11906754
It's based. CoV is a wonderful toolkit for PDE and all the good things in geometry. Absolutely beautiful stuff.

[Anonymous No.11906870]

>>11906792
Remember that the product of groups is really more of a sum. I think what you mean is that the disjoint union in Set leads to cartesian product of groups on the right. Just look at the ranks.
>>11906863
This is definitely more like it. Think finite sets. On the left the set has |A||B| elements, on the right the group has |A||B| generators.

[Anonymous No.11906879]

>>11906870
>Remember that the product of groups is really more of a sum. I think what you mean is that the disjoint union in Set leads to cartesian product of groups on the right. Just look at the ranks.
And later just remember that left adjoints preserve colimits, the free whatever functor is a left adjoint and coproducts are colimits.

[Anonymous No.11906888]

>tfw "free functor" is but an informal concept
yikes

[Anonymous No.11906891]

>>11906888
What disease does she have? I wanna make super sure I avoid it.

[Anonymous No.11906901]

>>11906891
being a fatass

[Anonymous No.11906904]

>>11906783
>>11906792
>>11906798
>>11906837
>>11906838
>>11906856
>>11906863
>>11906870
>>11906879
I've solved it. Remember that for any abelian group A the functor [math]A \otimes - [/math] is the left adjoint to the hom functor and therefore preserves colimits.
Now,
[math]F(A)\otimes F(B) \simeq (\oplus_{a \in A} \mathbb{Z} )\otimes (\oplus_{b \in B} \mathbb{Z} ) [/math]
[math]\simeq \oplus_{b}((\oplus_{a} \mathbb{Z})\otimes \mathbb{Z} ) [/math]
[math]\simeq \oplus_{b} \oplus_{a} \mathbb{Z} [/math]
[math]\simeq \oplus_{a,b} \mathbb{Z} \simeq F(A\times B)[/math]

[Anonymous No.11906905]

>>11906904
Basado.

[Anonymous No.11906907]

>>11906891
>What disease does she have?
I am quite sure that this is exactly what happens if you become really fat and then come to your senses and manage to get back to healthy weight.
The skin around the areas where a lot of fat used to be was once stretched out and keeps that way, even if the fat is removed.

In short, don't get fat.

[Anonymous No.11906917]

>>11906904
or, you know, the free abelian group (FAG) depends only on the cardinality of the set over which it is taken, and [math]A\times B[/math] has cardinality [math]|A||B|[/math]

[Anonymous No.11906923]

>>11906917
then you still need to show that the tensor produkt of the FAG with |A| generators and the FAG with |B| generators is the FAG with |A||B| generators

[Anonymous No.11906931]

>>11906917
Non-canonical isomorphisms aren't as cute as canonical ones.

[Anonymous No.11907002]

>>11906917
this is not a proof, moron, it's just the intuition i gave

[Anonymous No.11907015]

look, the animes stopped posting for a while, and what do we get? set theoretic category theory

[Anonymous No.11907033]

>>11907015
Good or bad thing?

[Anonymous No.11907047]

nullstellencatz

[Anonymous No.11907066]

>>11907015
I'm still here.

[Anonymous No.11907074]

>>11907066
you're not cute and you don't look like that.

[Anonymous No.11907137]

>>11907015
Exactly. Anime is the only thing that keeps this thread healthy.

>>11907047
What did he mean by this?

[Anonymous No.11907144]

>>11907137
nullstellencatz - a slang for "CATegory theoretic NULLSTELLENsatz"

[Anonymous No.11907147]

>>11907144
sounds cute.

[Anonymous No.11907155]

>>11907147
sorry i just made it up sir...

[Anonymous No.11907158]

>>11907155
still cute though

[Anonymous No.11907176]

Bomballenclaat

[Anonymous No.11907181]

>>11906891
https://youtu.be/CpKDteQ3FIQ?t=125

[Anonymous No.11907183]

Kumquat

[Anonymous No.11907190]

>>11907176
>>11907183
not math or science... or am i not educated enough to understand those posts?

[Anonymous No.11907194]

>>11907047
Every time an American says
>Nallsdellensads
a baby frog dies

[Anonymous No.11907207]

>>11907194
I pronounce it nullshtellensatz.
I also don't speak german.

[Anonymous No.11907230]

Let X be an array of numbers.

[Anonymous No.11907237]

>>11907147
>>11907158
Post 'kaguya_47'.

[Anonymous No.11907239]

>>11907237
bit lewd

[Anonymous No.11907241]

>>11907230

[Anonymous No.11907242]

>>11907237
No do 'kaguya_1'

[Anonymous No.11907247]

>>11907242

[Anonymous No.11907249]

>>11907247
Now post your own face.

[Anonymous No.11907251]

>>11907249

[Anonymous No.11907255]

>>11907251

[Anonymous No.11907262]

maybe dumb question, but is [math]k[x]\otimes_k k[x]=k[x][/math]?

[Anonymous No.11907263]

>>11903942
I only opened this thread to see the retarded csfaggot post in the first 5 replies and here it is.
>>11904030
>>11904036
Homo mindset, desu.

[Anonymous No.11907267]

>>11907262
no sir i don't think so

[Anonymous No.11907275]

>>11907262
k[x, y]

[Anonymous No.11907281]

>>11907262
Assuming this problem follows the earlier pattern, [math]k[x] \otimes _k k[x] \cong k[x, y][/math].

[Anonymous No.11907297]

HOW THE FUCK AM I SUPPOSED TO MEMORIZE THE HARDY INEQUALITIES
SERIOUSLY WHAT IS THIS UNINSPIRED BULLSHIT WHO THE FUCK CARES

[Anonymous No.11907303]

>>11907144
>nullstellencatz - a slang for "CATegory theoretic NULLSTELLENsatz"
Autism

[Anonymous No.11907311]

>>11904036
So much this.
Empiricism is extremely cringe.

[Anonymous No.11907338]

Well I'm trying to prove that if [math]\Gamma[/math] is a finite group of automorphisms of a separated finite type scheme [math]X[/math] over a field [math]k[/math], then that the quotient scheme [math]X/\Gamma[/math] exists if any two points are contained in an affine open of [math]X[/math].

If the scheme [math]X=\text{Spec}A[/math] is affine, we can just take the ring of fixed elements [math]X/\Gamma=\text{Spec}A^{\Gamma}[/math] (and we don't need the other conditions). Using this as inspiration, then if [math]X=\bigcup_{i=1}^n\text{Spec}A_i[/math], then define as a set [math]X/ \Gamma := \bigcup_{i=1}^n \text{Spec}A_i^{\Gamma}[/math], and give it the topology where a subset [math]U\subset X/\Gamma[/math] is open if and only if [math]p^{-1}(U)\subset X[/math] is open, where [math]p:X\to X/\Gamma[/math] is the quotient map. To show it is a scheme, we have to show some glueability conditions, namely that there are some subsets of the [math] \text{Spec}A_i^{\Gamma}[/math] that glue consistently. So to that aim, since [math]X[/math] is separated we have affine intersections of affines [math] \text{Spec}B_{ij}:=\text{Spec}A_i^{\Gamma}\cap \text{Spec}A_j^{\Gamma}[/math] which I want to glue together - however, the problem that arises is that [math]B_{ii}\neq A_i^{\Gamma}[/math], so I can't glue.

[Anonymous No.11907352]

>>11907262
Yes.
>>11907267
Retarded anime tranny.
>>11907275
>>11907281
Also correct.

[Anonymous No.11907374]

What's up with premeds? What is it that they have in common that makes them so insufferable...

[Anonymous No.11907377]

>>11907352
>[math]k[x] \cong k[x,y][/math]
what was meant by this post

[Anonymous No.11907379]

>>11907374
You're posting in the wrong thread buddy. While you're here, may we interest you in some puzzles?

[Anonymous No.11907392]

>>11907379
Use names with different first and last letters. You're just making this needlessly painful to read. This is /mg/ not /eng/

[Anonymous No.11907424]

>>11903921
Think I'm finally going to pull the plug on my PhD lads, I really can't fucking stand academia any more.
Going to just go back to being an unemployed retard posting about conspiracy theories I suppose

[Anonymous No.11907427]

>>11907424
Is academia really that bad?

[Anonymous No.11907430]

>>11907392
I'm getting smooth brain vibes from this post

[Anonymous No.11907448]

>>11907377
They are, as vector spaces (maybe even as rings).

[Anonymous No.11907460]

>>11907427
For me, yes. Got stuck with a real asshole of an advisor who won't even read papers he cites so doesn't even understand the research anymore. Kind of just bullies his way into coauthorship.
Spent the last few months alternating between saying my research was great and would look excellent on the thesis and then saying it was completely useless, saying he'd have to fail me and I'd have no career, blah blah blah, until I finally had enough. I don't even care if they won't give me a masters, this whole experience has been pure cancer.

[Anonymous No.11907464]

>>11907460
Protip: Go drinking with your advisor. Only discuss your research next to drinks.

[Anonymous No.11907468]

>>11907448
they aren't

[Anonymous No.11907471]

>>11907464
Yeah this is good advice, get him drunk, drug him and then blackmail him

[Anonymous No.11907473]

>>11907464
Unfortunately doesn't work with all types, especially not the micromanagers

[Anonymous No.11907474]

>>11907448
>maybe even as rings
They aren't.
You can prove this by conjuring up basic results in dimension theory/algebraic geometry OR by remembering that one of those is a PID and the other isn't.

[Anonymous No.11907475]

>>11907379
so whats the answer then

[Anonymous No.11907478]

>>11907374
Okay so I went in for a physical since I've been having some aches in my lower testicle area. My mom was worried so she insisted on me going even though I hate physicals. I’ve never had sex or anything like that so I know its not like any kind of std.

So I went in not knowing it was a female doctor performing the physical check up. I was stunned cuz up until that moment I found out women perform physicals on males (I thought it was same sex physicals all my life). She must have been in her early 30s, average in looks but pretty cuz of the blonde hair and eyes. I was so embarrassed when I had to pull my trousers off. I had a rock solid boner! I was apologizing to her every second.

She then asked me to leave the pants on the floor and socks off to direct me to the paper bed. She started feeling me and it was weird cuz she was touching the head of my penis asking if I felt anything. She started massaging n rubbing the tip while asking me a couple questions and I came!!! She had a cup in her other hand to collect the sperm.

I didn’t tell my mom. Was she supposed to do that? Everything checked okay in the end but idk. I was profoundly embarrassed cuz she did that.

[Anonymous No.11907485]

bros... i love all of you...
stay safe...

[Anonymous No.11907489]

>>11907485
Only if you also stay safe... bro... <3

[Anonymous No.11907491]

>>11907485
I love you too except if you think dynamical systems are fun

[Anonymous No.11907504]

>>11907379
I'm literally a brainlet i can't work it out

[Anonymous No.11907551]

>>11907485
>stay safe...
Don’t. Existence with the only goal of prolonging it as long as possible is no different from suicide.

If you want to truly live you need to take risks!

[Anonymous No.11907567]

>>11907475
>>11907504
call [math]Pa[/math] and [math]Ph[/math], Paul and Phils current ages respectively
call [math]Pa_p[/math] and [math]Ph_p[/math] their ages when Paul was the same age as Phil is today, so [math]Pa_p = Ph[/math]
call the time between the past and now [math]T[/math]
then [math]Pa_p + T = Pa = 33[/math], and [math]Ph_p + T = Ph[/math]
Since Paul is 3 times older than Phil was then, [math]Pa = 3 * Ph_p \implies Ph_p = 11[/math]
So [math] Pa_p + T = 33 \implies Ph + T = 33 \implies Ph + (Ph - Ph_p) = 33[/math]
and then we get [math] 2*Ph - 11 = 33[/math], so Phils age is 22

[Anonymous No.11907571]

>>11907567
>2 letter variables instead of single letter with multi symbol subscript
Ngmi

[Anonymous No.11907582]

>>11907567
I swear to god

I'm capable of solving much harder math problems... Any ideas on how to improve problem solving?

[Anonymous No.11907587]

>>11907582
>Any ideas on how to improve problem solving?
solve more problems

[Anonymous No.11907591]

>>11907582
nah it took me longer than id like to admit, and i was convinced it was a trick question for a while anyway
Im total shit at problem solving myself actually, guess the moral of the story is stick with it and give the right names to things
>>11907571
>Ngmi
fuck
should i do Multilinear algebra to get used to all the scripts

[Anonymous No.11907599]

>>11907591
[math]^m_ay^b_e[/math]

[Anonymous No.11907602]

>>11907591
>should i do Multilinear algebra to get used to all the scripts
Is multilinear algebra that bad for subscripts? Usually it's differential geometry that has the reputation of being where indextards run wild, I thought.
Although I will remark that I've seen exactly one triple-subscripted variable in my life and it was in a combinatorics paper.

[Anonymous No.11907605]

>>11907591
>should i do Multilinear algebra to get used to all the scripts
What does multilinear algebra have to do with it?
If you want disgusting algebra problems, you should look for them in physics, economics and engineering.

[Anonymous No.11907615]

>>11907587
which ones?

[Anonymous No.11907622]

>>11907605
>disgusting
>economics

I know econ is a but of a meme, but is it really that bad for math? I was considering working through MWG and LS to get a general idea of the field.

[Anonymous No.11907624]

>>11907599
[math] S_{t_{o_{p_{ _{t_{h_{a_{t}}}}}}}} [/math]

[Anonymous No.11907631]

The Millenium Institute offers a money prize as an encouragement for mathematicians to work on the Millenium problems.
However, this has proven to be an extremely ineffective incentive with only one Millenium problem having been solved (and the prize money rejected).
I believe that a date with a cute, shy girl interested in maths would be a very attractive offer to the mathematician target public and I project all Millenium problems thus being solved within the decade.
Do any of you know any potential candidates?

[Anonymous No.11907636]

>>11907622
>but is it really that bad for math?
It's not bad. In fact, microeconomics has some cute theorems and structures.
Stuff just pathologically accumulates variables, tho, and sometimes that produces ugly things.

[Anonymous No.11907637]

>>11907485
thank you, love you too...

>>11907491
do you have any particular kind of dynamical systems that you hate
not that i really like this subject either

[Anonymous No.11907645]

>>11907602
>>11907605
Damn, I could just have been mistaken

[Anonymous No.11907711]

>>11907379
Are Professor Layton games unironcially good for problem solving skills?

[Anonymous No.11907763]

[Anonymous No.11907770]

>>11907763
Holy kek

[Anonymous No.11907780]

>>11907763
>welcome to /mg/
>trannies with anime avatars and dumbasses who can't do 7th grade algebra
seems about right

[Anonymous No.11907807]

included more responses

[Anonymous No.11907813]

>>11907807
Based.

[Anonymous No.11907827]

>>11907807
lol /mg/'s seriously all just IYIs who've read EGA but can't into subtraction.

[Anonymous No.11907840]

>>11907827
the fuck is an iyi

[Anonymous No.11907841]

>>11907763
>>11907807
>includes random unrelated images and posts
Fucking kek.

[Anonymous No.11907847]

reminder that this is the kind of person you share a thread with

[Anonymous No.11907849]

>>11907841
Everything in the image is very, very related.

[Anonymous No.11907853]

>>11907847
Unironically based.

[Anonymous No.11907869]

>>11907807
>includes me saying i thought it was a trick at first
>doesnt include me solving it
im ngmi

[Anonymous No.11907874]

>>11907807
Oh yeah! Twice in the same image with the touhou poster!

[Anonymous No.11907880]

>>11907847
https://www.youtube.com/watch?v=XYQmSvKnJ9A

[Anonymous No.11907936]

es ist moglich zu erhalten einen Grant zum miete als auslandischer Student? In Bonn

[Anonymous No.11907937]

>>11907936
Fuck off Scholze.

[Anonymous No.11907944]

>>11907937
ich bin nur trainieren mein deutsche, ich bin Amerikaner

[Anonymous No.11907950]

could someone briefly translate this please?

[Anonymous No.11907955]

>>11907950
Google translate is a lot better than you think it is.
Why are you reading the EGA btw.

[Anonymous No.11907958]

>>11907955
It's SGA but because it has a solution to the thing I'm trying to prove

[Anonymous No.11907997]

>>11907936
>>11907944
speaking a language that isn't english outside of /int/ is forbidden.

[Anonymous No.11908011]

>>11907997
hon hee hon

[Anonymous No.11908018]

>>11908011
oui oui baguette

[Anonymous No.11908023]

>>11907950
Say x is a preschema(?) where the finite group G operates to the right. For G to operate in an admissible way, it must and it suffices that X is open affine invariant for G, or still the whole trajectory of G in X is continuing in an open affine

the prior condition is evidently implied by the first, and in turn implies; because T has a trajectory of G, U which is an open affine it contains, the intersection of transformations of U with the g in G is still an open U' stable by G, containing T and continuing in the open affine U. Like in U, all finite parts in a fundamental system of affine neighborhoods, there exists a neighborhood open+affine V of T contained in U'. These transformmations by the g in G are also affine and contained in U' which is separate, also their intersection U'' is an open affine which is invariant by G and contained in This being so, the condition from 1.8 is necessary, because one takes the inverse images of X, open affines of Y, then recoveres Y. It is sufficient because one could, by 1.1, construct the quotients Yi = Xi/G - in each Y, the image of Xi intersecting Xj is an open Yij identified with Xij/G by 1.4, in particular, one deduced the isomorphisms Yij --> Yji permit the presence of the Yi, for constructing Y. Serre preferred constructing directly the topological space quotient Y of X by G put on the beams p*(0x)^G and verified that Y becomes a preschema and one is in accordance with the conditions of 1.3

[Anonymous No.11908025]

>>11908011
>>11908018
Seethe more retards. French is the language of mathematics, the best mathematicians were all french.

[Anonymous No.11908031]

>>11908023
>preschema(?)
Ancient notation for scheme.

[Anonymous No.11908032]

>>11907936
https://youtu.be/2flpdqGfAsw

Gibt doch aber bestimmt genug drecks Vereine an der Uni die bei solchen Sachen helfen. Frag die doch einfach mal ...

[Anonymous No.11908033]

>>11908023
Damn thanks anon

[Anonymous No.11908036]

>>11907997
being a rule addict is forbidden by the lord

[Anonymous No.11908037]

>>11908025
Wiles and Perelman are spinning in their chairs

[Anonymous No.11908039]

>>11908037
Literal whos.

[Anonymous No.11908040]

>>11908025
All good mathematicians wrote in Latin.

[Anonymous No.11908041]

>>11908025
Only good reason to learn French is for mathematics at this point.
To be fair, German, Russian, and I guess even Chinese would be next on the list.

[Anonymous No.11908042]

>>11908023
>he translated sheaf as beam

[Anonymous No.11908047]

>>11908042
>he translated sheaf as beam

[Anonymous No.11908053]

>>11908040
In the XVIIIth century, maybe.
>>11908041
french will be one of the most spoken language in the world very soon
>chinese
lul

[Anonymous No.11908058]

>>11908053
>In the XVIIIth century
And ever since/before.

[Anonymous No.11908065]

>>11908058
so before real math was invented ?

[Anonymous No.11908069]

>>11908053
>french will be one of the most spoken language in the world very soon
Because it is spoken in parts of the worlds where the french used to have colonies and now are experiencing an explosion in population.

Hardly something to feel good about, for anybody involved...

[Anonymous No.11908072]

>>11908069
Quality and quantity never overlap.

[Anonymous No.11908073]

>>11908065
>so before real math was invented ?
Real math was invented when Euclid’s elements were first published.

[Anonymous No.11908076]

>>11908073
This but unironically.

[Anonymous No.11908081]

>>11908072
Euler's entire body of work disagrees.

[Anonymous No.11908083]

>>11908073
No retard. Real math was invented when Bourbaki started publishing.

[Anonymous No.11908088]

>>11908073
>geoshit
>doesnt even have sets
>only axiom anyone cares about is parallel
>>11908083
Bourbaki is shit, but youre closer

[Anonymous No.11908092]

>>11908088
>Bourbaki is shit
Bourbaki is the only rigorous math book ever written.
>inb4 Russell
I said math, not logic.

[Anonymous No.11908097]

>>11908088
The elements are literally the defining work for all of mathematics after it.

> axiom
Math isn’t about axioms.

>>11908092
> rigorous
Cringe

[Anonymous No.11908102]

>>11908023
If Paul has an age(?) where the age of Phil is to the right (along the number line). For the age of Phil to be equal to what Paul's age was July 20 1969 (moone landings), or to be a third less than one sixth and a 4, to the inferred age of Pope Sylvester V, then I have (x^n(Pa/Pu-Po) many eggs in my quilted breast-pocket.

[Anonymous No.11908105]

>>11908092
>Bourbaki is rigorous, lol
just study the MetaMath database if you want actual proper rigor

[Anonymous No.11908106]

>>11908097
>dude let's work with dubious mathematical concepts without ever understanding their structure

[Anonymous No.11908108]

>>11908092
>Bourbaki is the only rigorous math book ever written.
Bourbaki isn't a book

[Anonymous No.11908109]

>>11908092
Logic is math.

[Anonymous No.11908110]

>Logic is math.

[Anonymous No.11908111]

>Doing an exercise
>stuck somewhere
>frantically google
>find an MSE post with the same question
>it's my post
I have somehow managed this >10 times across the years. Why am I so retarded?

[Anonymous No.11908113]

>>11908106
>the concept of two is dubious
this is your brain on logic

[Anonymous No.11908115]

>>11908111
>asking textbook exercises on stackexchange
[math]\mathscr{CRINGE}[/math]

[Anonymous No.11908117]

>>11908106
The goal of math isn’t rigour, but understanding.

[Anonymous No.11908120]

>>11908113
It is unless properly defined. For the concept of two it hasn't much importance, but for more complicated concepts, it is necessary to have a coherent theory.
>>11908117
can't have one without the other.

[Anonymous No.11908122]

>>11908120
>It is unless properly defined.
logic
not even once

[Anonymous No.11908127]

>>11908122
what's two then?

[Anonymous No.11908130]

>>11908127
even once

[Anonymous No.11908131]

>>11908120
>can't have one without the other.
You are delusional. Mathematics is derived from our intuition about the world, not the other way around.

The naturals are not the result of set theoretic thoughts, but of intuition about quantitative reasoning, which are then cast into set theory.
You can two thousand years of mathematics the wrong way around...

[Anonymous No.11908137]

>>11908131
so the laws of physics are the result of our intuition, and not of a more fundamental truth about our world?

[Anonymous No.11908153]

>>11908127
>logicians are so retarded they don't even know what two is

[Anonymous No.11908159]

>>11908137
I have absolutely no clue what you are on about.

The laws of physics are the result of people trying to justify experimental results through the language of mathematics.
Of course they are based on our intuition WHAT ELSE could they be about?
Seriously, what alternative is there to our intuition (sharpened by observation) when it comes to deriving laws of physics??

> and not of a more fundamental truth about our world?
There is no evidence that any law of physics is true.
Most strikingly historically basically any law has been disproven, see e.g. Newtonian mechanics.

[Anonymous No.11908409]

Remember to keep on trying even though it feels useless sometimes. Good night, /mg/.

[Anonymous No.11908412]

>>11908409
night anon

[Anonymous No.11908432]

>>11908409
danke du

[Anonymous No.11908439]

>>11908409
Nighty night.

[Anonymous No.11908449]

>>11908409
Night, lad.

[Anonymous No.11908471]

>>11903927
he strikes again!

[Anonymous No.11908480]

>>11908409
>good night
are you just a yuro or are you going to sleep before 9 pm

[Anonymous No.11908525]

>>11906619
>complex manifolds are beautiful.
Anytime I see a Riemann surface I think to myself I'd rather be studying curvature and tensors and other shit.

[Anonymous No.11908545]

>>11907807
Happy to finally be included in one of these!

[Anonymous No.11908548]

>>11908525

[Anonymous No.11908744]

I have been awake since around two days ago, maybe this is why am so slow at solving problems

[Anonymous No.11908747]

>>11908744
Why are you still awake anon?

[Anonymous No.11908802]

How much do you interact with staff? How much do you want to? What country are you in?

Personally, I only ever go to lectures and hate going to support classes, so ideally I never talk to staff.
In the UK btw

[Anonymous No.11908850]

I have a number. Is there a way to prove that this number can't be gotten by dividing two numbers in a certain base?

[Anonymous No.11908874]

>>11908802
A lot.
A lot.
US.

[Anonymous No.11908898]

>>11908850
Every number is a quotient. If you have a number p, pick literally any (nonzero) q and then (p*q)/q = p.
I'm not sure what you're trying to do here.

[Anonymous No.11908899]

>>11908850
Brute force the problem with a sieve?

[Anonymous No.11908908]

>>11908898
I think he means integers in different bases, but the answer's the same; being a rational number is a property independent of natural number base systems.

[Anonymous No.11908909]

>>11908802
Middling amount. Not as much as the Stacies who show up to every office hour and stay until they get shooed out, but most of my department recognizes me.
Not at all, but talking to people is good for you in multiple ways so I do it anyway.
Canada

[Anonymous No.11908921]

>>11908525
you can do both at the same time if you're not studying the simplest shit possible though

[Anonymous No.11908933]

is math a science or is science math?

[Anonymous No.11908939]

>>11908933
Neither.

[Anonymous No.11908943]

This seems like a really important inequality and it should not be that hard to prove but I can't seem to find any trick to prove it
[math]\frac{1+||y||^2}{1+||x||^2}\leq \left(1+||x+y||\right)^2\quad x,y\in\mathbb{R}^N[/math]
Any ideas?

[Anonymous No.11908988]

>>11904307

the hierarchy of scheme properties at the end of Gortz-Wedhorn is also incredible.
although the book is super fucking technical. I haven't done math for a while and just picked up the book and starting anywhere except the beginning is unreadable

[Anonymous No.11909060]

>>11908909
This (all of it)

[Anonymous No.11909082]

I keep seeing a remark that the Riemann-Stieltjes integral [math]\int_a^b f \, \mathrm{d}\alpha[/math] doesn't exist if [math]f[/math] and [math]g[/math] share a point of discontinuity. How and why?

[Anonymous No.11909085]

>>11909082
meant to say [math]f[/math] and [math]\alpha[/math]

[Anonymous No.11909131]

>>11909082
The limit would probably depend on the partition taken and thus it doesn't exist. Too lazy to write it out though, measure theory exists for a reason.

[Anonymous No.11909179]

If we let F be a field and K = F(x) be the field of rational functions with coefficients in F, it necessarily follows that (x) is a prime element of K, right?

[Anonymous No.11909185]

>>11909131
>>11909131
No worries, I was able to cook up a nice example that shows what can go wrong.
[eqn]
f(x) = \alpha(x) =
\begin{cases}
0 , & \quad 0 \leq x < 1, \\
1 , & \quad x = 1.
\end{cases}
[/eqn]
Upper and lower sums will never be equal for any partition of [math][0,1][/math] so [math]\int_0^1 f(x) \, \mathrm{d}\alpha[/math] does not exist.

[Anonymous No.11909191]

>>11908933
Unlike those filthy science math is not empirical, which means that it can actually describe truth.

[Anonymous No.11909193]

>>11909082
I don't know where you would be seeing this remark, since it's false. You can still have RS-integrability if they share a discontinuity, they just can't both be discontinuous _from the same side_. If f is left/right continuous at c and alpha is the other one, then you're still fine.

[Anonymous No.11909196]

>>11909191
Based.
https://en.wikipedia.org/wiki/Problem_of_induction

[Anonymous No.11909260]

>must proof statement through recursion
>verify if statement is true with the first 3 cases
>try to prove it
>can't
>still try hard for 3 hours
>open the ti-nspire
>insert recursif forumla
>compare first 10 case
>first 4 cases work, everything doersn't after that
>mfw

[Anonymous No.11909351]

/gmmg/

>>11908412
>>11908432
>>11908439
>>11908449
Thanks.

>>11908480
Yes.

>>11908802
I am the staff, UK. You definitely should interact with them if you want to be recommended by anyone.

[Anonymous No.11909370]

>>11907936
iirc you can get BAföG as a foreign student but they're some requirements

[Anonymous No.11909378]

>>11909351
Good morning, "the staff, UK".

[Anonymous No.11909390]

>>11909179
yes, x is a prime element if the ideal generated by x is a prime ideal
since F(x) is a field every ideal is either 0 or F(x), and F(x) is prime
unless you mean something else by a prime element

[Anonymous No.11909411]

>>11909390
wrong. prime ideals have to be proper ideals, units are never prime elements

[Anonymous No.11909694]

Are there ordinary and partial 'integral' equations as well? What's so special about differentiation?

[Anonymous No.11909695]

>>11907474
How do you show that k[x,y] is not a PID?

[Anonymous No.11909696]

>>11908943
It is enough to deal with [math]||y|| \geq ||x||[/math], since otherwise leftside <= 1 <= rightside.
[math]||x+y|| \geq ||y|| - ||x|| [/math] so it is enough to prove
[eqn]\frac{1+||y||^2}{1 + ||x||^2} \leq (1 + ||y|| - ||x||)^2. [/eqn]
Multiply sides by [math]1+||x||^2[/math], move everything on one side, and for simpler notation put [math]a=||x||[/math], [math]b = ||y||[/math].
You will arrive at some ugly polynomial expression involving a, b. The original inequality is an equality when [math]||x||=||y||[/math] and this tells you that you can factor out (a-b) from this ugly expression. Ultimately you arrive at
[eqn](b - a) (-a^3 + a^2 b + 2 a^2 - 2 a + 2) \geq 0[/eqn]
which is clearly true when b>=a.

>>11909351
good morning!

[Anonymous No.11909762]

>>11909695
Consider the ideal generated by [math]x[/math] and [math]y[/math].

[Anonymous No.11909844]

>>11909838
fresh