/sci/ - Science & Math

>>11834614
maths is a useless subject

>>11834614
Help with my PDE homework? I'm not sure what is meant by infinite series here, I don't think its taylor, idk how to do fourier. I believe lambda_n are the eignvalues for the DE.

>>11834625
https://www.youtube.com/watch?v=JDGPnLfH1Io

>>11834625
>maths is a useless subject
The entire world is based around mathematics.

>>11834625
>Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.

>>11834614
are there any good, technical books on the poincare conjecture proof?

>>11834708
https://arxiv.org/pdf/math/0610903.pdf
and its references

>>11834626
Fourier series is very commonly used in PDE. Try assume that your function can be written as [math] \sum_k=0^\infty a_k cos(kx)[/math] for some coefficients [math]a_k[/math]. Look up Fourier series for a rigorous version.

When you were doing your undergrad, how much time did you have for your social life and other hobbies?
Going into pure Math in the Fall.

>>11834902
6-7 hours of sleep leaves pretty much 10-12 hours of free time.

>>11834906
So those ~8 hours are for lecture and studying then? How much do you factor commutes to class?

>>11834914
That includes traveling.

>>11834920
To be more precise: one way trip was 1 hour when walking, half an hour if I took the tram.

>>11834920
>>11834924
Looks like I'll be enjoying uni then.
Thanks.

>>11834929
You're welcome.

>>11834902
Only weekends

>>11834950
>>11835048
what type of math did you major in?

>>11835085
What I had as my courses was
>linear algebra
>analysis
>algebra
>topology
>introductory model theory
>measure theory
At the same time some master level courses like topo & algebra II, and minor (I guess that's the right term) stuff like baby level theoretical physics and astronomy.
t. >>11834906

>>11835099
Do you regret pure maths? I'm a math major looking a little bit everyday at the salary and job security of an applied mathematics degree. I don't think I'm cut out for a research career if I'm going to have to deal with bureaucracy.

>>11835128
Couldn't care the less. It gave me something to do for a few years and it was occasionally fun. I regret starting a PhD, though. I can either struggle for a few years with an ever shrinking glimmer of hope that I will find my passion again, or I can quit and make my supervisor sad (he's super nice and likes me), neither of which seems like a good idea.

>>11835143
What jobs could you have been eligible for with a BSc in Math?

>>11835151
No idea, to be honest. Maybe some code monkey stuff. I could try googling, but so could you.

Thoughts on this definition?

>>11835171
>an affine scheme is just an array of numbers
wow incredible great job mr. alexandre "greatest mathematician of xxi century" grothendieck

Can you write a proof as a poem /mg/?

>>11835201
Yes but it won't rhyme.

>>11835201
Perhaps, and for sure you can write sad haiku poetry

The attaching map/
I cannot seem to detect/
by homology

>>11835201
unless you're retarded it's not really news,
but modulo prime p, there are p-1 nonzero residues.
assume the condition "a is coprime with p" is met,
then [math]x \mapsto ax[/math] is a bijection on the nonzero residues set.
now multiply everything by sides and you will see
that [math]a^{p-1}[/math] equals 1 mod p.
all of this is a distant memory
of times when i didn't know basic group theory

redpill me on tropical geometry

>>11835201
Let f be arbitrarily
some real function on R to d,
such that for any point below
and error there exists just so,
a margin which when satisfied
by other points ensures that quite
the difference in the function there
shall errors magnitude still bear.

Now let us have, for any n,
a point x_n, which satisfies,
whenever n is greater than
some other N, that choose we can,
a bound, to N it has no ties,
exists in which the difference lies,
to some fixed point, that we name x.
which limit we shall call up next.

If then, for some small epsilon,
the x_n move ahead as one,
towards where our limit sits,
then surely there must then exist,
a number N, so afterwards
the difference to our x just thwarts
which margin our function coined
for error eps around this point.

a

Hello incels! Have a nice day studying your numbers shit, i'm about to fuck the gf for the third time today.

>>11835280
Your orgasm will last 30 seconds my Theorem will last an eternity.

>>11835284
ok gotta admit that was fucking based
you're still picrel tho

>>11835280
joke's on you my girlfriend has a penis

>>11834614
Is collatz conjecture really that difficult? It's clear that some numbers are more even than other numbers, for example 20 is has an odd factor if factored using 2. 16, 32, or powers of 2 don't. So the purpose of 3N+1 just means to reach a whole log_2_ N number. What's the fuzz about it?

>>11835317
>Is collatz conjecture really that difficult?
Yes.

>for example 20 is has an odd factor if factored using 2
What the fuck does that even mean?
20 is 2*2*5, obviously it has an odd factor, just like 20/2.

>So the purpose of 3N+1 just means to reach a whole log_2_ N number.
This is not a sentence.

>What's the fuzz about it?
Nobody has proven it.

>>11835201
gotta feeling that something's not right
the primes they arent finite
in the naturals if you assume
they are bounded you will be doomed
so ill provide you with some insight

enumerate your primes from 1 to n
take the product and add one again
you will see they are coprime
please note now this is the time
this number has new prime factor(s) thus condradicting n

>>11834614
What the heck is wrong with me /mg/? I was always a top math student in high school. But as soon as I got introduced to "higher level" mathematics, I just can't wrap my head around it. Makes me think this subject requires a great deal of natural talent.

>>11835317
>So the purpose of 3N+1 just means to reach a whole log_2_ N number.
Exactly. Now prove that always happens.

>>11835178
>xxi century

>>11835280
Imagine posting in /mg/ and not having a boyfriend.

>>11835411
What have you tried?

Bros... how do I get a math gf, so we can read Serre together?

>>11835550
Become the gf

>>11835550

Guys, I haven't taken a math course in 4 years. Since I graduated with my BSc. I'm taking a course in Topology this September for fun and to maybe prepare for grad school. I'm self studying Rudin right now to practice but can barely do any problems. How fucked am I? I want to get an A.

>>11835564
Are you over 24? You sound like you're over 24. If that's the case, don't even bother, you can't do math after 24.

>>11835564
https://www.amazon.com/Introduction-Topology-Third-Dover-Mathematics/dp/0486663523/ref=sr_1_2?crid=1CQZA72OM0ZCL&dchild=1&keywords=introduction+to+topology+mendelson&qid=1593094864&sprefix=Introduction+to+To%2Caps%2C179&sr=8-2

>>11835564
>I'm taking a course in Topology this September for fun
topology and fun are mutually exclusive

>>11835605
[math]\textbf{Fun}( \textbf{Top}, \textbf{Ab})[/math]

>>11835605
If it's not fun, what's the point?

>>11835605
You're retarded. Topology is the funniest area of math after algebra

>>11835630
I agree that what topologists call a "proof" is quite funny, but that doesn't change the fact that it's not fun.

>>11835564
>>11835609
>>11835616
>>11835630
>>11835633
These really read like posts written by people who don't really enjoy topology much.
Here's the secret: no topologist gives a single shit about rigor and you fucking morons belong in algebra.

Topologists don't actually think in terms of proofs, that's a common misconception. Handwavy techniques are all that it it takes. For example, in topology to prove S^n and S^m are not homeomorphic it's enough to say that an embedding of it into R^k separates it into two components only for the appropriate k. You don't actually need to prove it because it's intuitively obvious. We've localized the topological nastiness from of the problem into an extremely particular and uninteresting situation. Such is the goal of topology

>>11835640
>>11835650
fuck off

>>11835652
This really reads like a post written by someone who doesn't really enjoy topology much.

Damn topologists sure do get a lot of hate.
Feels good to be part of the number theory master race.

>Elliptic curves

>>11835668
100% without a shadow of a doubt, unequivocally based

[eqn]\color{red}{\text{redpill}} \color{blue}{\text{ me on }}\color{green}{\text{tropical}}\color{yellow}{\text{ geometry}}[/eqn]

>Feels good to be part of the number theory master race.

>>11835668
Nice. I was just reading about them, and I'm a bit confused. This is Course in Arithmetic, p. 82
What does Serre mean by isomorphic elliptic curves? And how does this relate to actual curves on the plane?

>>11835668
>abelian varieties

[math]u(x)[/math] is finite and [math]L^1[/math] locally (the integral of its modulus on any compact set of the real numbers is finite).
[math]f(x)[/math] is [math]C^\infty(R)[/math] and [math]sup_{x\in R} \mid{x^h \frac{d^kf(x)}{dx^k}}\mid<+\infty \space\forall h,k[/math].
How can I prove that [math]\int_{-\infty}^{+\infty}u(x)f(x)dx[/math] exists? Or do you know any books where I can find the proof?

>>11835683
I'm pretty sure he means isomorphic as groups.

>>11835682
Reply to me when you talk shit you little bitch
You ain't shit, I fucked your mom while shooting heroin and listening to acid bath and now I'm on my way to fuck your sister with my limp dopedick.
And you're not going to do a single thing about it because you can't even reply to people when you talk shit online like a beta fuck.

>>11835693
Surely that can't be true because then all quotients C/Gamma are isomorphic: just take the linear map which sends the basis of one lattice to that of the other.

>Reply to me when you talk shit you little bitch

>>11835732
Kek
Based

>>11835683
biholomorphic

>>11835770
Is the linear map I mentioned not a biholomorphism. If <v1, v2>, <w1,w2> are the two lattices you can take a linear map f(v1)=w1, f(v2)=w2. It composes and factors through to give a bijection C/<v1,v2> <-> C/<w1,w2>. Is this not a biholomorphic map?

>>11835732
Nice selfie. I always like to see what the people who talk sideways shit at me look like.
I'd send you a selfie, but I'm currently on top of and balls deep in your sister and she doesn't want her weird virgin brother to be jacking off to her titties.
>>11835755
Ah. I see you can reply, just to yourself.

>>11835640
Based. Sounds like my kind of course.

>Nice selfie. I always like to see what the people who talk sideways shit at me look like.

>>11835802
>>11835755
>>11835732
>>11835707
>>11835682
>>11835814
This is /mg/. You're ruining the thread with your low IQ shitposts. If you want to fight here, at least have a math duel or something.

>>11835711
>>11835683
That's isomorphism as modules - is it a group isomorphism though? ie - does it take the identity to the identity?

>>11835830
>does it take the identity to the identity
Yes. It sends one lattice to the other.

>>11835830
How is the group structure defined on it?

>>11835844
quotient group structure induced from the complex numbers, ie [math](a+\Gamma) + (b+\Gamma) = a+b+\Gamma[/math] for complex numbers [math]a,b[/math]. I was mistaken in saying that the problem is the identity - what really is the problem is that there is no well-defined homomorphism if the lattices are not homothetic, since addition of numbers in one lattice usually lands somewhere different than those same numbers in a different lattice.

>>11835550
w2f 10 foot gf

>>11835865
>addition of numbers in one lattice usually lands somewhere different than those same numbers in a different lattice.
I'm really having trouble understanding why would this be true and why my construction doesn't work.
Could you give an example of two lattices that are not homothetic but where my construction fails to preserve the group structure?
What's wrong with
[eqn]
\Gamma_1 = \mathbb{Z}v_1 + \mathbb{Z}v_2 \\
\Gamma_2 = \mathbb{Z}w_1 + \mathbb{Z}w_2 \\
f: \mathbb{C} \to \mathbb{C}/\Gamma_2 \\
f(v_i) = w_i \\
f(\Gamma_1) = \Gamma_2 \\
\Gamma_1 \leq \mathbb{C} \\
\ker (f) = \Gamma_1 [/eqn]

Someone told me once that it is possible to count how many polynomial rings have a given hilbert series

can't find any source

Thoughts on Gregorious Maths's K-Theory lectures? (he's 13 btw)
https://www.youtube.com/watch?v=88H_AO4OfhY

>>11835886
For starters, you can't define a map by defining where the generators of the lattice are going to go, because inside the group [math]\mathbb C/\Gamma[/math], both generators are the same number, 0. So your map is only telling me where 0 is going to go, which I already know should to go 0 in the other lattice anyway, I don't know anything about the rest of the numbers.

>>11835912
You misunderstand. f is a linear map. A linear map is uniquely defined by where it sends the elements of a basis.

>>11835920
I misunderstand? Youre the one equating a linear map to a group homomorphism

>>11835920
I mean f is a composition of a linear map given by g(v_i)=w_i with a projection C -> C/Gamma_2.

>>11835686
what do you mean "u(x) is finite"
>>11835903
soulless as fuck i feel sorry for him
let the boy study IMO problems, not fucking cathegory gay bullshit

>>11835903
Why is a 13 year old making YouTube videos on K-theory?

>>11835903
Won't watch further than 5 seconds because he can't pronounce Grothendieck
I'd fuck him though.

>>11835903
>category theoretic math is so easy an autistic 13 year old can teach it
trannies btfo

>>11835930
>soulless as fuck i feel sorry for him
I'm pretty sure that by the time he is 18 and has had time to digest this, he is going to be a beast

>>11835920
>>11835923
>>11835924
Let me explain it properly, this time without latex. Let G_1, G_2 be two lattices, G_1 = Z*v_1 + Z*v_2. G_2 = Z*w_1 + Z*w_2.
Define an R-linear map f: C->C by defining it on the basis
f(v_1)=w_1
f(v_2)=w_2.
Then f is a linear isomorphism. The image of G_1 under f is G_2.
It's also a group homomorphism. We compose f with the projection pi: C -> C/G_2, to get a group homomorphism.
f': C-> C/G_2.
The kernel of f' is the inverse image under f of G_2, which is precisely G_1. Thus f' induces a group isomorphism
f'': C/G_1 -> C/G_2.

>>11835945
Yeah just like every "young genius". What has Barnett done again?

>>11835951
Jacob Barnett is 22. Give him some time. What have you done?

>>11835903
Honestly, I wish the worst for this kid. I am very bitter that I didn't have the talent or inclination at his age to do what he's doing.

>>11835959
He's almost 24, NGMI.

>>11835947
Let's see - an element of [math]\mathbb C[/math] can be written in terms of the first lattice as [math]z=av_1+bv_2[/math] since this is a linear basis. Your linear map sends [math]v_i\mapsto w_i[/math]. The quotient map for the lattice [math]\mathbb C\mapsto \mathbb C/\Gamma_2[/math] sends [math]w_i\mapsto w_i+\Gamma_2=0+\Gamma_2=0[/math]. So [math]z=av_1+bv_2\mapsto aw_1+bw_2\mapsto 0[/math]. So you've defined the zero map.

Stop thinking in terms of linear maps, because the basis corresponds to the zero element of the quotient

>>11835959
In two years he will be 24 (i. e. his math career will be over) and he still hasn't published anything lmao.

>>11835971
I'm not, he just had more educated parents me.

>>11835976
>z=av1+bv2aw1+bw20
That's wrong, because a, and b are not necessarily integers. It's true if and only if a,b, are integers.

>>11835976
>[math]z=av_1+bv_2\mapsto aw_1+bw_2\mapsto 0[/math]
That's wrong, because a, and b are not necessarily integers. It's true if and only if a,b, are integers.

>>11835976
The thing you misunderstood here is that it's only linear when we construct it. After we've constructed f, we regard it as a group homomorphism instead of a linear map. That way quotienting out by G_2 doesn't destroy the whole group. It makes perfect sense and induces an isomorphism between the two quotient spaces.

>>11835983
Cope

>>11835930
[math]-\infty<u(x)<+\infty \space \forall x\in R[/math]
Sorry I'm not a native speaker, maybe the right word was "bounded"

>>11835227
Noice.
>>11835903
Am I gonna have to be the one to tell him he's young and should concern himself with studying and researching rather than teaching?

>>11836008
That's true though. My parents are highschool educated, I learned about math as being an active area of research two years ago. Obviously this kid received intensive training all his life.

>>11836036
both my parents are phds (neither in math but still) yet i was nowhere near this level at his age. i did well in my math classes but i definitely had no idea what k-theory was, let alone knowing k-theory well enough to lecture to people online

>>11836032
he is studying
telling people what you learned is part of reinforcing it and since he's 13 and the kids at school probably think he's a spaz, he makes youtube videos about it

>>11836049
Having educated parents is a necessary but not sufficient condition to be a child prodigy.

>>11836003
actually the mistake I made is saying [math]v_i\mapsto w_i[/math] implies [math]av_1+bv_2\mapsto aw_1+bw_2[/math], this is not true in general for group homomorphisms. In fact, abelian groups are [math]\mathbb Z[/math]-modules, and group homomorphisms are [math]\mathbb Z[/math]-module homomorphisms, so the [math]\mathbb R[/math]-module homomorphism, or [math]\mathbb R[/math]-linear homomorphism you described is not actually a group homomorphism.

Ever wondered what the hell you're supposed to write on a diversity statement?


https://ofew.berkeley.edu/sites/default/files/rubric_to_assess_candidate_contributions_to_diversity_equity_and_inclusion.pdf

>>11836076
You're just wrong dude.

>>11836091
Alright bud, better send an email to Serre explaining how he's wrong then

>>11836087
>Ever wondered what the hell you're supposed to write on a diversity statement?
Now that you ask... Nope.

>>11835205
sleep tight steeler

>>11836094
>>11836076
Let me explain to you again.
Let G_1, G_2 be two lattices, G_1 = Z*v_1 + Z*v_2. G_2 = Z*w_1 + Z*w_2.
Define an R-linear map f: C->C by defining it on the basis
f(v_1)=w_1
f(v_2)=w_2.
Then f is a linear isomorphism.
Important step!: now we ignore the linear structure and view f as solely a homomorphism from C->C, where (C, +, 0) is the abelian group under addition.
The image of G_1 under f is G_2.
Since f comes from a linear map, we see that f(0)=0 and f(a+b)=f(a)+f(b), so f is also a group homomorphism. We compose f with the group projection pi: C -> C/G_2, to get a group homomorphism
f': C-> C/G_2.
The kernel of f' is the inverse image under f of G_2, which is precisely G_1. Thus f' induces a group isomorphism
f'': C/G_1 -> C/G_2.
Point the step with which you disagree.

>>11835903
>>11835930
>>11835935
>>11835938
>>11835940
>>11835971
>>11836032
>from integrals to category theory in 5 months
So this is the power of "pure" mathematics.

>>11836087
I'm assuming this is for faculty jobs, so no. I never had to write one of these for anything. A few of the graduate applications I filled out suggested I mention diversity-related stuff on my SoP but I didn't say anything and some of them still accepted me (although Berkeley did not, take that as you will). Most math departments I've seen have 0-2 diehard SJW profs and the rest of them can't be fucked and only do the minimum diversity nonsense the administration requires them to do.

I'm trying to solve the left sum but I got the right sum instead which is even more complicated. How do I do this more easily?

>>11835821
ok mom sorry

>>11836011
in that case, don't think the statement you are trying to prove is true
find any f which satisfies the conditions, but has noncompact support
then if you define u appriopriately, the integral doesn't exist
>>11835947
>>11836110
mate you are technically correct but your isomorphism
1) is dependent on the choice of v1, v2, w1, w2
2) fucks up the complex structure because it's only R-linear
this is why mr. serre doesn't care about this isomorphism

>>11836159
im assuming x < 1
why did you introduce primes and what i think is a totient function

>>11836159
What do you mean "solve the sum"? You want the closed form of the series on the left? It's [math]\frac{-x(x+1)/(x-1)^3[/math] . You just do the standard trick of "differentiate then multiply by x" twice.

>>11836180
[eqn]\frac{-x(x+1)}{(x-1)^3}[/eqn]

tfw latex stroke

>>11835930
absolutely based. Competition math is unironically the pinnacle of math

>>11836180
>>11836189
I was trying to do it on my own to a degree but thanks

[math]\int_0 ^1 x^xdx=\int_0 ^1 e^{log(x^x)}dx=\int_0 ^1 \sum_{\varrho=0}^\infty \frac{x^\varrho log^\varrho(x)}{\varrho!}dx \approx .7834[/math]

>>11836213
But can you swap the integral and the sum though?

>>11836213
I've seen this posted here before, but I fail to see why it's interesting.
The last equality is not evident to me either. Seems all random.

>>11836189
mfw someone latex stroked me

>>11836190
Competition math is the Pokemon of mathematics
everybody plays it when they're young and you should too but if you're still obsessed with it when you're 35 it's kind of sad

>>11836190
What is ironically the pinnacle of math?

>>11836213
If you're going to keep spamming this can you at least post more than just
>trivial substitution
>skip the entire interesting part of the calculation with [math]\approx[/math]

Is there any logic to what mathematicians "find interesting."
Seems to me that young mathematicians just babble what they hear from their older colleagues and tutors and then end up mastering those thing and the cycle repeats.

Most math papers don't prove shit but just introduced new concepts. And the standard to when something is "finally proven true" is also icky:
It requires some famous mathematician to make a claim.
Then, in case the claim is actually true, what happens is that legions of unnamed mathematicians work out the actual prove of the thing over some details, and then the result might get named after one or more famous people.

Is there any logic to what mathematicians "find interesting."
Seems to me that young mathematicians just babble what they hear from their older colleagues and tutors. Whatever is fashionable at the time. And then end up mastering those thing and the cycle repeats.

Most math papers don't prove shit but just introduced new concepts. And the standard to when something is "finally proven true" is also icky: It requires some famous mathematician to make a claim.
Then, in case the claim is actually true, what happens is that legions of unnamed mathematicians work out the actual proof of the thing over some decades. And then the result might get named after one or more famous people.

what does /mg/ think of logic
is it real math or just philosophers jacking off in the wrong department

>>11836245
>Seems to me that young mathematicians just babble what they hear from their older colleagues and tutors and then end up mastering those thing and the cycle repeats.
Well, yeah. How else are you supposed to learn things? Mathematics is complicated, you have to shut up and listen for a long time before you can form your own opinions without sounding like a retard.


None of what you posted in your second paragraph is remotely true.

>>11836257
>is it real math or just philosophers jacking off in the wrong department
Yes.

>>11836257
Math is inherently philosophical.

>>11836257
I am fairly sure we all agree with this post.

>>11836269
very funny
>>11836271
yes but I use the terms in their institutional meanings here

>>11836257
Mathematical logic is essentially empty of actual philosophy, it's just a big pile of supreme autists who love nitpicking trivialities so much they decided to do it for a living.

>>11836230
I'm gonna have to go with supergeometry.

>>11836275
>>11836285
how do you respond to logicians who insist their work has massive implications wrt all other mathematicians' work

>>11836305
>that's nice
>ok
>who's a good boy

>>11835143
What's so bad about doing a Phd?
How hard can it possibly be? You have a professional who is there to assist you apparently.

Can I be a good mathematician if I get a degree in physics and study math on the side? Math is my passion but physics seems more conducive to my life goals. I also have the thought that since math is more artistic it might be better to not be indoctrinated by University methods. But maybe that's wrong because it's a very technical art needing lots of rote training?

>>11836319
>How hard can it possibly be?
It's not the difficulty per se. It is more just the fact that I can't see the point in any of it and find no joy in doing the stuff anymore. I remember my letter of recommendation that said I am one of the most passionate students the writer has had in a decade, but I just don't recognize myself from those words. I mean, it is hard, no kidding. He reminds me of that pretty often.
>You have a professional who is there to assist you apparently.
Yes and he feels like he got 25 years younger (yet still older than 24 sadly) when he realised I can be his excuse to dig up all the stuff he never finished. We've been working on his old stuff and I really like it when I see his grumpy face in the beginning of our meeting and a happy face in the end. It just feels like my inner fire is gone and now I am here just to be a reason for him to have money to once more work on what he used to do. I just don't want to make an old man sad.

>>11836345
>Math is my passion
>physics seems more conducive to my life goals
Pick one.

>>11836356
>find no joy in doing the stuff anymore
this is literally me
fuck

>>11836356
>I just don't want to make an old man sad.
Don't be a slave to the feelings of others.

>>11836357
Physics will in the long run enable me to be a better mathematician by giving me the know-how to engineer a robot body with distributed computer processer cores added to my brain.

>>11836356
>muh passion
You're an idiot.
It's just work. You're not supposed to have a "passion" for everything. There are lots of things in life we just have to do. You probably won't have a "passion" for your next job either.

>>11836257
Mathematical logic is real math, but the kind of math that only logicians like to think about

>>11836368
Unlike you, I have a soul

>>11836363
alway rember happy day

>>11836364
Yeah, I shouldn't. I think I'll give it a month or two and see if that helps at all.

>>11836368
Opinion read and discarded.

>>11836356
You'll problt feel better qhen you're done with it, just power through
Unless you just started the PhD then maybe you could just quit if you decide to

>>11836378
>Unless you just started the PhD then maybe you could just quit if you decide to
Almost a year ago.

Is doing a PhD really that bad, bros?

>>11836305
There are some famous examples of logicians whose work has had direct impact on "normal" mathematics
https://en.wikipedia.org/wiki/James_Ax
https://en.wikipedia.org/wiki/Jan_Denef
https://en.wikipedia.org/wiki/Ehud_Hrushovski
https://en.wikipedia.org/wiki/Saharon_Shelah

>>11836384
No. It gives you a lot of freedom to do the stuff you like without having to worry about funding or anything like that. If you are interested in doing maths research, I really recommend applying for a position somewhere.

>>11836384
If at any point you get tired of your subject (and you will), then yes.
The thing is, you are completely free to do as you please, which is great when you are passionate about what you do because you can just push everything aside and do nothing but work.
However, when you are feeling down, there is no one around that you can talk to (because no one, not even your fellow grad students) understand what you do, and that freedom of being able to work anytime anywhere becomes the burden of knowing that, at any time you could be working, but you aren't. And that feels like shit

>>11836227
That's true but I personally hold it in high esteem because it was my first exposure to "real" math and what got me really into it. I'll never get mind-blown like that again desu
>>11836230
idk solving anime math problems on 4chan?

>>11836384
If at any point you get tired of your subject (and you will), then yes.
The thing is, you are completely free to do as you please, which is great when you are passionate about what you do because you can just push everything aside and do nothing but work.
However, when you are feeling down and stuck, there is no one around that you can talk to (because no one, not even your fellow grad students understands what you do), and that freedom of being able to work anytime anywhere becomes the burden of knowing that, at any time you could be working, but you aren't. And that feels like shit

>>11834614
can i get a rec for proofs books for someone thats done with calc and learning real analysis?

>>11836402
pma

>>11836402
Proof books are a meme. Pick up techniques as you go along.

>>11836319
Try to have a toxic advisor.
I now have anxiety whenever I hear my phone ringing because my old advisor. He used to shit on me (and everyone else) through the phone whenever something goes wrong.
He procrastinatesthen blame his students, etc.
I literally couldn't do anything because he's the one who will write me a letter of recommendation. Without him I'm not able to go anywhere.
This did not happen in the US btw. I don't think the US has it that bad.

>>11836416
This.

>>11836402

I'll never stop shilling this book.

>>11836423
Eastern Europe?

Anyone else feel like they are larping as if they actually like math when they don't?

>>11835821
shut the fuck up and enjoy your free bumps mouthbreather

>>11836462
No.

>>11836460
No. East Asia.

>>11836462
I used to want to like math because it seems cool to do it. Not sure why.
Now I genuinely enjoy math and just want to spend all my time solving silly recreational problems (if I have the time).

>>11836462
only to my phd supervisor

>>11836305
I work in computability theory, and wouldn't say it has massive implications, but there are implications. Mathematical logic is a huge field, here I am talking about the big four, set, proof, computability, and model theory. It really depends on what questions interest the actual researcher. Computability has been instrumental in a lot of proofs of undecidibility, like the MRDP theorem, and the group iso problem, tiling problems among others. Set theory has shown quite a few problems independent in algebra and analysis. For example the Whitehead problem, and Suslin's problem, and a lot of other little results. Necessarily most of these problems deal with uncountable sets, which is why set theory has the right tools to deal with them. I know model theory has been used to prove some results in algebraic geometry, but I don't understand that stuff. I can't really say anything intelligent about proof theory, though I did go to one talk where they used proof interpretations to extract some content out a proof in functional analysis, it kind of went over my head. There are subfields of all of these that are bringing tools of logic into standard mathematics, you can look at computable structure theory, which looks at logical complexity of mathematical structures. You could also look at invariant descriptive set theory that looks to classify natural equivalence relations on Polish spaces of countable mathematical structures. Another example is there is a computability theorist right now who is working on generalizing Hilbert's 10th problem to arbitrary rings. It uses some pretty hardcore number theory, so much so that he has been working with a number theorist. But, most people working in their field though just work on problems that are specific to that field. Mathematical logic doesn't need to be justified for its applications to regular math, in the same way that pure math doesn't need to be justified for its application to applied math.

>>11836462
Anyway, regardless how you feel about math, don't let "I love math" be your only defining trait. It's cringe.

Hey guys. I just finished my bachelor's in CS. I'm thinking about trying to do a PhD in math. I took several proof-based upper division math courses along the way, so I'm not too much of a math noob. I really want to do research (I also enjoy teaching, but that's not my main goal by any means). The area which I want to study is abstract algebra, number theory, and mathematical cryptography.
Should I go for it?
What's the GRE like? Is there anything in particular I should prepare for it?
In addition to the usual calculus/linear algebra/DEs for engineers courses, I've taken an intro to real analysis course, the intro to mathematical proofs course, and the number theory, abstract algebra, and cryptography course (which was unfortunately wrapped up into one course -- I'm currently working through individual textbooks to brush up and broaden my knowledge). Is there anything else which you guys think is absolutely necessary to start a math grad degree? I also plan on working through textbooks in combinatorics, graph theory, ODEs, and maybe topology, but those are on the back burner while I finish my current textbook loadout.

>>11836466
Asia seems like a horrendous place to work/study. Power heirarchies are so absolute over there that the system is basically "take it up the ass and say thank you from everybody who outranks you for a couple decades until you're old and it's your turn"

>>11836496
not gonna make it.
number theory is brutal

Is there a chef's edition of job shop scheduling problems?
In this case, there are multiple machines that can operate in parallel (e.g., stove, oven, cutting station, etc) but only one operator that has deadlines for when he must stop a machine (e.g., to prevent food from burning)

>>11836492
What about "I love math and heroin"?

>>11836517
wrong thread, youre looking for /sqt/ or /ck/

>>11836528
Is combinatorial optimization not /mg/?

>>11836536
neither combinatorics, nor optimization is /mg/

>>11836492
Math, philosophy, and music are the only worthwhile endeavors in life.

>>11836539
I see, you're a bunch of theoretical nerds

>>11836505
I guess my main goal would be to apply NT and AA to build cryptographic primatives and attack current primatives.
But yeah, I wonder a lot if maybe I'm not smart enough.
I still want to try, you know? I'm not going to say "I fucking love math XDDD", but some of my fondest memories from undergrad were when I would take ridiculous hits off my dab pen and work on analysis homework. Maybe I'm gay, but I fucking loved handling all those balls.

>>11836545
I almost posted advice, but your dude weed posting is too cringe. I hope you don’t get into any programs.

>>11836543
>you're a bunch of theoretical nerds

>>11836550
>tfw I had half a post typed up and just closed it
get out of my head jon

>>11836550
This but unironically.

>>11836550
Thanks, I'm going to try that much harder now that I know you don't want me to succeed.

>>11836560
>he's gonna try for reals now because anon insulted him
Yah, I don't think you're gonna make it.

>>11836560
It's honestly becoming funny to me how EVERY single one of these posts follows the exact same pattern
>long-ass rambly blog
>bros can I have permission to do what I want with my life?
>"no"
>well FUCK YOU now I'm gonna train harder and prove you wrong anime style!!!!

>>11836573
We are living in a hyper real world in which fact replicates fiction and fiction replicates fact. Soon somebody will start doing maths in a gravity chamber.

Bros, I don't even like maths anymore. I wanna quit and just spend the whole day picking mushrooms and herding goats, do I go for it?

>>11836517
can you give a more concrete description of the problem?

>mfw the strong goldbach conjecture has been rigorously proven in north korea

>>11836594
no

Is knot theory for recreational purpose only?

>>11836613
Guess I'll stay in maths, then. Thanks bro.

>>11836634
say that shit to my face not online nigga see what happens

>>11836305
I agree with them

>>11836356
>>11836363
what were you researching and do you know why you lost the passion?

maybe you stopped doing it for the thing of it, and maybe that's because you had to get into a field not of your choosing?

>>11836489
nice

>>11836710
Groups and the homotopy theory of finite CW complexes which is pretty much exactly what I chose. It's just the academic world and me being non-compatible. I don't know. He talks about writing a paper together, but I don't want to have my name on it, I just don't feel like it deserves to be next to his.

>>11836650
I know that is a statue, but the .gif made me hope it would move.

>>11836743
>He talks about writing a paper together, but I don't want to have my name on it, I just don't feel like it deserves to be next to his.
seems like your issue is that you're a bitch
have you tried not being a bitch?

>>11836750
>you're a bitch

>>11836750
I've tried.

>>11836764
not hard enough, evidently

>>11836710
i will be doing dynamical systems stuff, sorry but i don't want to post more details here
getting into wrong field is probably part of it, but mostly just generally getting bored with maths

>>11836743
>I just don't feel like it deserves to be next to his
That sounds like a personal issue you have there.
It's how it works, bre.

>>11836776
Math overall, including the applications?

I did my PhD in theoretical/computational chemistry and only learned math in my free time. Maybe that's path for you to connect with it.
I think everybody should just do the math they like.

Jesus, you're such a bunch of crybabies
Do you know how many people would like to be where you are? And all you do is complain. Fuck you, this is why you'll never amount to anything.

>>11836872
I know.

>>11836884
Yes.

I'm looking at Bert Mendelsons intro to topology book (dover). Seems pretty good. Any opinions?

>>11837152
Why don't you read it and find out?

>>11837152
It's a good intro.

Anyone here studied Cesaro summation deeper? Know of any resources for understanding the meaning of it?

>>11836269
kek

>>11836489
Based and logicpilled

>>11836543
That guy's just a dickhead, some of us here are into computational stuff.

>>11836634
It has applications in theoretical physics (lmao).

>>11837184
Just search for book with the keyword "divergent series" in the title

I have no recommendations but I saw books in the library

>>11837152
It's good.

>>11837184
>in-depth study of cesaro summation
it's called ergodic theory mate

>>11834902
> social life
> hobbies
I can't tell if your serious or not.

>>11837566
>your

>>11836458
What's so good about it

has /mg/ become more popular recently? threads are flying by in no time

>>11837646
It's always been ~40 posters.

>>11837646
What are you talking about? It's been like this since a bit after the start of the quarantine.

Is Serre's algebra book any good?
https://www.amazon.com/gp/product/038795385X?pf_rd_r=2MQ9BP36H6HBCENASQGV&pf_rd_p=edaba0ee-c2fe-4124-9f5d-b31d6b1bfbee

>>11837747
Yeah, but his book on hyperbolic pdes is even better.
https://www.springer.com/gp/book/9780387878225

>>11837849
Thank you, animeposter.

>>11836462
Sorta, but I do like it. I'm just a bit ashamed of not being great at it

>>11837868
Unironically this.

>>11837747
serre lang

>>11837929
L.O.L.

future bleak fellows

>>11838097
The future has never looked more promising.

>>11838102
why

>>11838124
Because my book on Lie groups of PDEs just came in.

the fuck?

>>11838211
The one by Olver?

>>11838224
Xu
https://www.springer.com/gp/book/9789811063909

Good morning /mg/!

>>11838705
fuck off

>>11838233
Looks nice.
I see an earlier version of it is online
https://arxiv.org/pdf/1601.07646.pdf

How do PDE's come into the theory?

What do you do when you hit a plateau?

I am going to attempt make the most competent I can collection of problems and solutions regarding chaos theory and butterfly effect in relation to vulnerability in every day life

I am also going to recieve my cosplay which I will use in front of a mirror with a dildo

>>11838848
suicide

>>11838848
do something else?
ask a friend?
set and reach a fitness goal?

>>11838848
Get a sword and learn sword dancing.

>>11838872
https://www.youtube.com/watch?v=AN3uhImuy6E

>>11838848
>hit a plateau
I don't

ok i've watched a 3blue1brownpill video
how do I prove that i cannot embed a mobius strip in R^3, in such a way that the boundary is contained in [math]\mathbb{R}^2 \times \{0\} [/math]?

>>11838942
intermediate value theorem

>>11838936
kek

>>11838942
what have you tried?
(I don't know)

>>11838952
>you mean the intermediate value fairy tail?

tale, I guess

I once had a screenshot of that youtube Wildberger comment, but sadly I can't find it anymore

without saying too much, who Rising Sea here?

>>11838957

>>11838957
>>11838985

>>11838985
based, thx

>>11838985
While we're on the topic, I remember a Wildberger image somebody made a long while ago that said something like "the circle and the line don't intersect, because that would be counterintuitive" with a smug Wildberger on it.
Does anyone have/remember what I'm talking about?

>>11838211
>Lie Groups
nice
>of PDEs
ew

>>11838862
When can we expect to see either of those things?

>>11835686
>>11836178
I thought I had proven it but maybe I'm wrong. Can you make an example where it doesn't hold?
For the proof I have used the fact that u is bounded so the integral is equal or less than |sup(u)| times the integral of |f(x)|. But as I later found out that definition of f(x) is a Schwartz space (S) and it's known (tho I would like a proof) that [math]S \subset L^p(R)[/math], so the integral of |f(x)| exists and the starting integral is less than some real number. In a similar way the starting integral can be shown to be greater than some real number.

Homotopy equivalence is like bimbofication for shapes

Very slow thread today...

>>11839541
it's friday nigga

Good graduate level linear algebra books?

>>11839643
Lang

>>11839541
Nothing to post about.

>>11839643
>graduate level
>linear algebra
what kind of linear algebra exactly do you have in mind?

>>11839838
N-dimensional spectral theory

>>11839177
If [math] u [/math] is bounded then [math] \int u f d\mu < \infty [/math], but this is false in general for [math] u [/math] satisfying only [math]\infty < u(x) < \infty [/math] for all [math] x \in R [/math]. Take for instance, [math] u(x) = exp(x^4) [/math] and [math] f(x) = exp(-x^2) [/math].

To see the bounded case, we just that [math] f \in S[/math] is integrable, which is true because every Schwartz function is bounded by [math] Cmin(1, x^{-2}) [/math] for some constant [math] C [/math]. To see that [math] f \in L^p [/math], we just use that [math] f^{p} [/math] is also in [math] S [/math] (use the Leibniz rule), and apply the above. More generally, we could take [math] u [/math] to have polynomial growth and apply a similar argument.

Hope this helps!

>>11840080
Based and Leibnizpilled.

If you're ever feeling depressed or like a failure, always remember that Terence Tao's wife is fat, ugly and an engineer.

>>11840236
Lmao yeah he could definitely have done better. He looks autistic but if he paid to have someone chose clothes for him and cut his hair in a normie style he could have probably bagged a fairly hot woman. If I had to guess, I would say that he is not interested at all in having sex or being in love and got a wife to please his aging parents.

>>11840236
My boyfriend is an engineer, but he is not ugly or fat.

>>11840275
Are you a fag, woman, or okama?

>>11835979
https://mathoverflow.net/questions/191929/are-there-any-serious-investigations-of-whether-mathematicians-do-their-best-wo/191980#:~:text=For%20instance%2C%20mathematicians%20peak%20on,38.5%20(Simonton%2C%201997).

Wrong

>>11840258
Sex is overrated.
Math is much better. The satisfaction you get when your resolve somethig or when you prove something is really out of this world

>>11840278
I am not a free abelian group.

>>11840288
I agree. In fact, as I started doing math more frequently / seriously my libido has decreased to near nothing.

>>11839643
Book titled Advanced Linear Algebra by Roman is nice.

Let's post problem books we've tried and liked. I got a lot out of Halmos's Linear Algebra Problem book freshman yr

>>11840288
Unironically this.
Newton considered one of his hreatest achievements to be voluntary celibacy.

>>11840292
Based.

>>11840370

>>11839541
>>11839625

>>11840372
If it's so easy (since math destroys libido, according to definition) then why would it be an achievement, never mind his greatest. This is a contradiction, and thus it must not be this

What exactly is induction?

>>11840370
halmos is gigabased, i went through his "hilbert space problem book" and it was a valuable read
>>11840374
planar geometry is fun
sadly it's a dead field, no point in learning this stuff unless you enjoy it or you are preparing for high school competitions

>Noetherian modules

What's the best introduction to cohomology of sheaves?

i've been doing math for 20 years now and i don't have a job. Did i get mem'ed?

>>11840585
No, you're just a dingaling

>>11840585
No, you're just a r*ddit NEET.

>>11834614
Is it too late to ask my grad school to defer my enrollment for the fall by a year? If not, how much can I delay? Virus is pretty bad in the school's state and I sure as hell don't want to risk it by going there. On the other hand, online sucks balls, especially for first year of grad school (Imagine the nightmare of explaining calculus to freshmen in zoom TA sections) I also want a break from math

Btw my school's policy is that we can defer up to a year but we have to contact the department first to get permission

>>11840615
contact them and ask retard
I don't work for your school

>>11840615
Covid isn't real faggot, litteraly only 60+ yo boomers dying

>>11840623
how likely is it that they let me defer you think
>>11840624
Still want a breather, I'm tired from 4 years of nonstop math

bros...

>>11840631
>how likely is it that they let me defer you think
I don't know you fucking drooling moron
nobody knows
ask the department

>>11840582
A book about Several Complex Variables.

>>11840599
>>11840604
Tell me where you work in the industry as well as what you studied then.
Looking online, i'm not the only one: https://www.indeed.com/community/skills-training/depressed-math-major-can-t-find-job/td-p/1786897

>>11840582
What sheaves and how deep?

>>11840634
OK what do you think I should say while requesting a deferment

I want to maximize my chances of getting approved (without being told to reapply, that'd be horrible)

>>11840637
>Indeed.com

>>11840648
>sheaves
I don't know, sheaves ? Maybe in relation to AG
>how deep
Balls deep

bros... i dont feel it...

>>11840670
are you feeling it now?

Just want to die, lads.

>>11840659
still waiting

>>11840631
>tired of math
You won’t make it just take wagecucking in industry as your consolation prize.

>>11840624
This.

>>11840701
you have no idea how much I've been slaving recently and it's probably not a good idea to make uneducated guesses
let's just say I'm deadset on taking a break and want to know how to get it without being told to leave by my grad school

>>11840675
Same.

>>11840713
>gurl you don't KNOW ME you don't KNOW how hard I been slaving I DESERVE a break
NGMI

>>11840713
Seize the means of production.

>>11840719
Unironically based.

>>11840719
just answer my question or don't bother replying, I'm not going to bite your shitty bait or bother trying to explain my decision

>just answer my question or don't bother replying, I'm not going to bite your shitty bait or bother trying to explain my decision

I've got this concept of a website that would allow users to make their own 4chan style board. Problem is I don't think there's enough potential outcomes for the labels system 4chan uses(/x/, /b/, /pol/,/r9k/,/sci/ for example)

The numbers I was using was 36(letters + numbers) and 4 for the number of potential board names.

36*4= 144
144*36=5184

5184 is not nearly enough long term. I also know I'm fucking up the math here, so any help would be great.

>>11840730
>I've got this concept of a website that would allow users to make their own 4chan style board
That's called 8ch*n faggot

So I'm fucking around on saltybet and I'm wondering if there's an equation I can use to figure out who to bet on based on their win-rate and matches fought.
Like, a 100% winrate on a character with only 1 match would be a less reliable bet than a character with 60% winrate and 500 matches played, right?
I want to know how to properly express that.
I've been looking up binomial distribution methods, but I don't think it's quite what I'm looking for.

>>11840731
yeah, but better and with different features. I hate 8ch*n's usability.

>>11840734
How about 9ch*n?

why should I care about modes of convergence unironically
how do they help outside of pedantic measure theory

>>11840736
eh, I'm autistic as a mother fucker and like things just so. Nothing is as clean as 4chan imo. I wanna copy that cleanness with a different aesthetic.

>>11840730
>5184 is not nearly enough long term
You're right in a sense, it's not "near enough", it's like an order of magnitude too much already

I have no idea what you did with your math. If you have 36 letters and are allowing up to 4-character names (is that what "number of potential board names" is supposed to mean?) Then you have either 36^4 or 37^4 (depending on whether you treat 0 as blank or 0 as separate from blank) names. Either way 36^4 is about 1.7 million.

>>11840744
Thanks, famalam. That's what I was looking for.

>>11840667
Bosch in AGCA gives a quick rundown of cohomology of sheaves of schemes, with both Cech and Grothendieck cohomology, but of course, assumes acquaintance with schemes already, at least at the level already given by the book - he's probably the fastest getting from nowhere to basic cohomology, but he doesn't prove the deep results, just gives an overview.

The GOAT is probably Serre's FAC, which is in French, although if you don't mind reading a fansub, it has already been done here: http://achinger.impan.pl/fac/fac.pdf

I don't like Vakil's style, but could be useful supplement. Probably the one that goes ballsdeepest still is Hartshorne, but if you do go through it, I really recommend having Bosch at hand.

I don't know about non-AG sheaves

>>11840753
when is gortz/wedhorn vol. II gonna come out
fuckers have had a decade now, it's time to stop jacking off

>>11840730
>26 letters
Pls.

>complex numbers are equivalence classes of polynomials with coefficients in equivalence classes of Cauchy sequences of fractions of equivalence classes of couples of natural numbers
Why is this allowed?

>>11840719
based

>>11840799
what's the matter froggy
2 deep 4 u?

>>11840799
What do you suggest as an alternative?

>>11840982
I propose that we take the definition of the complex numbers as the algebraic closure of the reals and we phrase it categorically.

>>11840799
good post

>>11840732
you're looking for a rating system, like elo or glicko, although that would require historical data to be useful. funnily enough, I wanted to do that exact thing back in high school but never did

>>11841244

For historical data, there's plenty of it

https://raw.githubusercontent.com/synkarius/saltbot/master/data/2018-03-25/saltyRecordsM--2018-3-25-17.4.txt

Though you'd have to program something to parse that information into something useful

>>11841290
Nice, now just use elo or glicko to assign a rating to every fighter