[a / b / c / d / e / f / g / gif / h / hr / k / m / o / p / r / s / t / u / v / vg / vr / w / wg] [i / ic] [r9k / s4s / vip / qa] [cm / hm / lgbt / y] [3 / aco / adv / an / asp / bant / biz / cgl / ck / co / diy / fa / fit / gd / hc / his / int / jp / lit / mlp / mu / n / news / out / po / pol / qst / sci / soc / sp / tg / toy / trv / tv / vp / wsg / wsr / x] [Settings] [Search] [Mobile] [Home]
Board
/sci/ - Science & Math

File: Guido_Castelnuovo.jpg (20 KB, 294x394)
20 KB JPG
Guy Newcastle edition
>>11846898
prev
>>
214 KB JPG
>Elliptic curves
>>
Is it possible to describe morality by applying formal logic?
>>
>>11850717
https://en.wikipedia.org/wiki/Is%E2%80%93ought_problem
>>
What are some fields that are essentially dead?
>>
>>11850717
yes with the axiom of cateogrical imperatvie
>>
>>11850726
Planar geometry
>>
File: Kantfem.jpg (798 KB, 1009x1317)
798 KB JPG
>>11850727
Based and Kantpilled.
>>
>>11850728
I'm pretty sure there's an open problem about a square and a circle, can't remember it though.
>>
>>11850737
Are you referring to this?
https://en.wikipedia.org/wiki/Inscribed_square_problem
>>
>>11850740
No
>>
>>11850748
Oh.
>>
>>11850768
Don't worry about it, it's probably not something important. Besides, what you linked is very interesting. Thank you!
>>
Any good texts on representation theory, lads?
>>
>>11850774
Representations of Finite and Compact Groups, by Barry Simon.
>>
>>11850774
Linear Reps of Finite Groups, Serre.
>>
>>11850774
The Fulton & Harris one
>>
Good intro to tropical geometry?
>>
>>11850884
https://www.amazon.ca/Worlds-Beaches-Global-Science-Shoreline/dp/0520268725
>>
>>11850884
tropical geometry is useless, boring, ugly and trivial
fight me.
>>
>>11850884
Does tropical geometry give you brown eyes or turn you non-white in some other way?
>>
>>
>>11850940
>double posting
>being a whiny faggot
>>>/r/eddit
>>
people post here for a couple years and think theyre part of the club
>>
File: C7ntx71VwAACCWD.jpg (112 KB, 1200x586)
112 KB JPG
>>11850911
>Tropical geometry is ugl-
>>
>he thinks he’s part of a special club
>>
>>11850946
Nice try, reddit.
>>
>>11850951
t. has been posting his homework here since middle school.
>>
i am and you arent
in fact, im in several discord groups from here where we laugh at people like you
seethe more and cope more
>>
>he posts in tranny groomer discords
>he has no other means of socializing
Just lol
>>
>>11850973
>t. unironic newfag
>>
>>
File: R14kkDj.jpg (39 KB, 657x527)
39 KB JPG
i don't like set theory
>>
>>11851008
based
>>
>>11850726
elliptic integrals
>>
>>11851008
Find all solutions to $a^2=2b^2+15b$ over the integers. You may use that $\mathbb Z[\sqrt2]$ is a UFD.
>>
>>11849088
pls respond
>>
Ok guys, let's see how tough you really are. Can you solve the following differential equation?
$(y'')^2-\frac{(y')^4}{y^2}=0$
Solutions including real numbers only please!
>>
>>11850774
Etingof is a lovely general purpose intro that doesn't try to go balls-deep into technicalities (representation theory has a bad habit of becoming wildly complicated and totally out of control at the slightest prodding), which is probably what you want if you're looking for a "representation theory" book without any further description. Doesn't do Lie groups though, which may be the only issue if you're a physishit who thinks all groups are matrix groups.
Stay the fuck away from Fulton/Harris. It's trash.
>>
>>11850735
I'd gain some a posteriori knowledge of her thing in itself, if you know what I mean
>>
>>11851060
Just punch it into Wolfram, I'm not doing your homework for you.
>>
>>11851065
My nigger, this is not my homework. Wolfram also shits out imaginary numbers, which I stated I do not want.
>>
>>11851063
>Stay the fuck away from Fulton/Harris. It's trash.
not him, but thank you for saying this, tried reading it and thought it was crap, but saw it recommended everywhere. Doesn't help that they're both trash textbook writers
>>
>>11851063
This looks like exactly what I'm looking for. Thanks, anon.
>>
>>11851047
either $a= \pm \frac{15((3-2\sqrt{2})^{2n}}{4\sqrt{2}}$ and $b=\frac{15}{8} ((3-2\sqrt{2})^{2n} + ((3+2\sqrt{2})^{2n} -2)$ for $n\in\mathbb{N}$
or $a=(something$ $awful)$ and $b=(something$ $worse)$
>>
>>11851063
>Doesn't do Lie groups though, which may be the only issue if you're a physishit who thinks all groups are matrix groups.
based
>>
>>11851060
factor it into $yy''=\pm y'^2$. Then substitute $y(t)=Ae^{at}$
>>
>>11851126
Damnit, there is an easy way, I didn't want this to happen. Anyway great idea, continuing from you
$yy''+(y')^2=0 \implies (yy')'=0 \implies yy'=c_1 \implies (y^2)'=2c_1 \implies y^2=2c_1x+c_2$
and
$yy''-(y')^2=0 \implies \frac{yy''-(y')^2}{y^2}=0 \implies (\frac{y'}{y})'=0 \implies \frac{y'}{y}=c_3 \implies y'=c_3y \implies y=e^{c_3x+c_4}$
Pretty cool right?
>>
>>11851186
Nifty.
>>
>>
File: 9783319784816.png (324 KB, 827x1254)
324 KB PNG
>>11851238
this whole series is a goldmine of spaghetti titles
>>
>>11851250
This can't be real.
>>
File: 9783030355364.png (348 KB, 827x1254)
348 KB PNG
>>11851256
It can.
>>
Pro-tip: name every paper you publish "Proof of a theorem by Euler".
>>
>>11851238
>>11851250
>>11851263

is this chromogeometry by wildberger?
>>
>>11851267
>>
>>11851267
>Abstract: we prove a theorem of Euler [1]
>[1]: Euler, L: Collected Works
>>
File: 1586959826632.jpg (457 KB, 1080x1175)
457 KB JPG
>>11851276
>[SGA]: Séminaires de Géométrie Algébrique, Alexandre Grothendieck
>>
>>11851058
Bro, like, the best I can do is give you a quick rundown on toric manifolds.
>have hamiltonian Torus action on symplectic manifold
>this means it has a moment mapping
>moment mapping's image is a polyhedra
>Delzant guarantees that the polyhedra is unique
>if you have an irreducible polyhedra, you can do some stuff to construct a symplectic manifold with a Hamiltonian torus action that inverts the previous process
>if the polyhedra isn't irreducible you get a shitty non-smooth toric variety
Read Audin's Torus Actions on Synplectic Manifolds.
>>
Why prove anything when you can just come up with conjectures
>>
File: 9783319125190.png (537 KB, 827x1254)
537 KB PNG
>>11851263
>>
>>11851287
That's how we came up with the whole field of theoretical physics
>>
>>11851287
because if you come up with bad conjectures you look like a retard instead of a prophet when somebody finds a trivial counterexample in 2 weeks
and coming up with good conjectures is hard
>>
>>11851283
Thanks, but is it the same as "toric" in the complex geometry setting? As in complex torus = $\mathbb{C}^*[math]. Probably related, will check Audin's book first. >> >>11851250 What's so bad about detailed and specific titles? Better than most that are just "on X", which is acceptable if and only if you are obliterating that field/problem >> >>11851290 This one actually sounds based. >> File: 9783319066318-1.jpg (21 KB, 265x402) 21 KB JPG >>11851290 >> >>11851305 PDEs are disgusting, I'd rather have the K-theory on algebraic topologic groups one >> >>11851313 PDEs are the answer to the world around us. >> >>11851324 which is precisely why they're so ugly. Same reason statistics is a shit field. >> >>11851324 Yeah and the world around us is gay as fuck I do math as a form of escapism from this doomed material world Reject Yaldabaoth. >> >>11851296 Pretty sure, since Audin uses Toric variety a couple times. Honestly, you'll probably still have to study something about Toric Varieties proper, but you might as well see the symplectic geometric stuff before that. >> >>11851328 >Statistics is a shit fiel- >> >>11851353 Thanks for posting that gigantic tangled web of gross distributions, it makes quite a convincing argument that statistics is shit. >> >>11851357 I think that is what the anon intended with his post. A picture tells more than a thousand words, so there is no reason to finish the actual post. >> >>11851328 In any field there's a point in which you need to say >yes, this is ugly, but that's the reality of what I want to study otherwise you end up doing category theory >> mathematicians use she >> >>11851372 we use "we" which obviously stands for "the female reader and the female writer" >> >>11851377 We need a new pronoun to indicate the female plural how about "shwe" >> >>11851369 >otherwise you end up doing category theory Yes, that's the goal. >> >>11851328 >PDEs >ugly Whut? PDEs are a prime example of simple to pose, hard to solve equations. Of course you can make them look ugly, but that's on you. >> >>11851250 >>11851263 >>11851290 >>11851311 >Springer Briefs in Mathematics not so brief there huh >> >>11851029 nobody does, even the ones who like it >> >>11851498 So, the set of all mathematicians who enjoy set theory is [math]\phi$?
>>
>>11851505
That's not how you write $\emptyset$
>>
>>11851518
>>
>>11851520
>>
>>11851528
True chads use 
>>
>>11851539
Based.
>>
>>11851539
True chads know that the empty set is the initial object of the category of sets, and therefore use 0.
>>
>>11851539
hello based department
here's cringe department
>>11851553
>>
File: after.gif (2.69 MB, 600x600)
2.69 MB GIF
>>11851539
wew
>>
>>11851553
True chads just call it the set of good theorems in category theory.
>>
>>11851567
Stop posting this gif.
>>
2.15 MB WEBM
>>11851595
but it's gud
>>
bros, 1 hour after starting to read tropical geometry and my eyes are burning

hold me...
>>
>>11851621
congrats, you have malaria
>>
>>11851621
Should've gotten some sunscreen
>>
>>11851621
>"We need a name for this stuff."
>"Maybe something fun?"
>"Ok how about Tropical Geometry lol?"
>"lol."
I mean I know why it's named like that. But I'm still convinced that the acual reason was as indicated above. Also, is this really that useful? The guys I know who are working on it are pretty powerful, but idk it looked like some weird invariant that is sometimes actually computable and the pictures look nice so publication is easier (not kidding).
>>
>>11851675
>I know why it's named like that.
I don't.
>>
>>11851675
my supervisor told me to learn some because it might be useful in proving a certain result
supposedly its good at turning AG into combinatorial stuff, but so far its only turning my brain to mush and my motivation to zero
>>
>>11851686
What books/articles are you using?
>>
Give me an explicit example of non measurable sets for which the measure of the union is strictly less than the sum of the two measures. I haven't been happy with anything I've found on stack exchange.

self studying and this is the only fucking thing I'm stuck on
>>
>>11851732
suppose I should add that they must be disjoint sets. a sequence of disjoint sets is what the problem asks for but I'm content to let all of the sets after the first two to be the empty set
>>
>>11851732
Don't any bounded non-measurable set and its complement in the bounded set work?
>>
>>11851752
only if they have defined outer measure, no?
>>
>>11851700
Elliott H. Lieb
Robert Seiringer
Jan Philip Solovej
Jakob Yngvason

Tropical
Algebraic
Geometry
>>
>Poincaré groups
>>
>>11851752
Every bounded set has an outer measure, tho.
The definition of the outer measure is the infima along that set A. A is bounded below by 0, and it's non-empty because the set is bounded. So it has an infima.
>>
>>11851765
Should've replied to >>11851758
>>
>>11851765
you're right on that
i think specifically I would need examples with strictly positive outer measure. Sorry for being a dummy
>>
104 KB JPG
>That feeling you get when you go back through all of your undergrad notes and see how far you've come
>>
>>11851841
Very nice
>>
File: 1503228764287.png (262 KB, 591x716)
262 KB PNG
>>11851841
>that feeling you get when you go back through all your undergrad notes and see how much you've forgotton
>>
File: perplexedAnimegirl.png (137 KB, 482x651)
137 KB PNG
Is $\mathbb{Z}/4\mathbb{Z}$ isomorphic to $(\mathbb{Z}/4\mathbb{Z})^\times$?
>>
>tfw dozens of retards in undergrad
>tfw your classes all get curved to high hell so nobody fails
>as a consequence A's mean nothing anymore

a-at least I'll get good letters of recommendation...
>>
>>11852063
What class?
>>
>>11852083
I just finished my undergrad, so all of them. Especially algebra and analysis
>>
>>11852038
No.
>>
>>11852038
Based and noeffortpilled
>>
>>11852063
>bragging
dumass
>>
File: Nord Yes.png (243 KB, 680x709)
243 KB PNG
>>11852134
>bragging
>>
File: 432.jpg (40 KB, 680x366)
40 KB JPG
>>11852142
Jk homie good job
I'm just bitter because my undergrad grades are very poor (starting senior yr next year)
>>
File: Henri_Cartan.jpg (12 KB, 276x400)
12 KB JPG
Why dis nigga be lookin japanese????
>>
>>11852157
Small, ugly and glasses, that's why.
>>
>>11850693
Special functions are such a fun topic to learn. It's shameful how few people are good at using them nowadays.
>>
Competition for last post in previous thread >>11852513
>>
>>11851505
>>11851518
>>11851520
>>11851528

All of these are hideous. The Norwegian glyph is the preferred one (its rendering is left as an exercise).
>>
>>11852458
AGREE...
>>
>>11852157
Honestly everyone in Bourbaki had weird faces, except Dieudonné who was an absolute Chad.
>>
>>11852850
>>
>>11852865
imagine the SMELL
>>
>>11852865
Dieudonné definitely not a chad by the looks of this pic
>>
>>11852458
Best special functions?
>>
>>11852865
>When it's clearly Samuel who's the main man
Look at that jawline, that smile
>>
>>11852850
>>11853009
>forgetting the true gigachad of Bourbaki
>>
File: hqdefault (1).jpg (12 KB, 480x360)
12 KB JPG
>>11852865
>>11853001
>>11853009
200cm tall BVLL
>>
I'm trying to learn high school algebra to calculus fast as possible, should I focus in problem solving than theory? What the best approach? I'm thinking in getting some russian problem books, but I also think the level of these books are too higher
>>
File: 1586328505682.jpg (112 KB, 402x972)
112 KB JPG
>>11850693
Hey /mg/, I'm trying to find 'x' where x%a == 0, x%b == 0, x%c == 0. I have 'a', 'b' and 'c'. What is the name for what I'm trying to find? My numbers are 18, 56 and 72. It's for image scaling. Hope you and yours are well Anons. :^)
>>
>>11853171
find the lowest common multiple
>>
>>11853171
what the fuck notation is this
>>
>>11853184
He's probably a CS nigger. I would bet 10 bucks he has never even heard of LaTeX before.
>>
>>11853005
top tier: theta functions, riemann zeta function, polylogarithms, gamma function
mid tier: bessel functions, hypergeometric functions, elliptic functions
low tier: everything else except
shit tier: Lame functions
>>
>>11853171
you want the least common multiple
>>
>>11853194
Oh so I'm guessing from the answers that "%" somehow means modulo, is that it?
>>
>>11853194
>>11853224
imagine living in the year 2020 and not being able to code
>>
>>11852865
The incel gang
>>
>>11853227
I don't really care.
>>
>>11853176
>>11853216
Thank you

>>11853184
>>11853194
I know of Tex but havn't learned how to use it.
>>
>>11853262
ayy
>>
>>11853290
Me btw
>>11853276

So now that that's over, what should I do?
>>
>>11853295
Stop posting anime. Start doing maths.
>>
>>11853300
Start doing meths? On it
>>
>>11853302
>>
does curving the opposite faces of a cube to meet give a klein bottle?
in the same way associating opposite sides of a square make a torus
like the first two sides gives a 4-ridged ring, then streching the next two gives a hollow torus then the last two sides are the inside and outside, what happens when stretching through the 4th dimension to make them touch
>>
>>11853314
You're just upset that I stole last post, aren't you?
>>
File: image.jpg (1.12 MB, 1812x1501)
1.12 MB JPG
https://en.wikipedia.org/wiki/Tits_metric
How do I convert this to cup size?
>>
>>11853399
Nope. I wasn't involved in that contest. Your joke was just so low effort.

>>11853384
Yes. Glue the opposite sides together normally to get a torus, one normally and one twisted to get the Möbius band, and both twisted to get the Klein bottle.
>>
>>11853405
By letting me cup a feel
>>
What are the prerequisites for learning measure theory?
>>
>>11853422
Topology and analysis.
>>
>>11853422
almost no prerequisities
if you know what does it mean for an infinite series to converge or diverge, you're good to go
also some basic topology, but again all you need to know is: open set, closed set, compact set
that said, most people learn differentiation and riemann integration (1-variable) before learning measure theory and lebesgue integration
>>
>>11853409
i mean adjoining the faces of a cube without twisting, i.e. the curved inside surface and curved outside surface of a semi-hollow torus
i think it might be the homology 2 sphere now but im not 100% sure
>>
File: 1593017155913.jpg (1.72 MB, 2160x3840)
1.72 MB JPG
>>11853430
What about probability theory? I am learning from this list.
>>
>>11853444
>you're now smarter than 99% of quants
what kind of dumbass pseud wrote this

you're not gonna turn into a professional after one book. The finance professionals have all read that book too, and an entire library of other financial literature.
>>
>>11853470
>pseud
hello r*ddit
>>
File: 1592672705522.jpg (63 KB, 796x767)
63 KB JPG
anyone wants to help me wioith revisiong for my differential eq course?
>>
>>11853473
>thinking pseud is reddit slang
go back
>>
>>11853477
ODEs or PDEs?
>>
bros... i just want to be good... at maths...
>>
>>11853473
pseud has always been 4chan slang, newfag
>>
>>11853444
I would start with "Probability with Martingales" by David Williams, but otherwise, sure.
>>
>algebraic geometer
>geometric algebraist
well /mg/, which one it is?
>>
>>11852038
imagine being such a retard
>>
Guys what the FUCK is an automorphism and how do you show that f(1) = 1 is an automorphism on a finite field?
>>
>>11853579
geometer, period
>>
Is there more math than any other field of study out there?
>>
>>11853613
No.
>>
>>11853607
>Guys what the FUCK is an automorphism
what part of the definition do you find confusing? you did read the definition, right?
>>
>>11853496
ODEs
I was stuck, I'm doing alright noww.
But help is always appreciated.
>>
>>11853638
It's an isomorphism on itself. And isomorphism is a bijective mapping between two objects.

But how do I show that f(1) = 1 is an automorphism on a finite field?
>>
>>11853661
>But how do I show that f(1) = 1 is an automorphism on a finite field?
What have you tried?
>>
>>11853661
assuming we're talking about ring automorphism, then necessarily f(1)=1 by definition of ring homomorphism. are you sure youre not missing any other information? because it is known that automorphisms of finite fields are given by frobenius-type maps
>>
>>11853677
It says "K be a finite field. Show that the mapping f is an automorphism on K" or something like that (translated from German)
And then it says: f(1) = 1
>>
>>11853699
can you show the full picture of the statement?
>>
>>11853699
This question doesn't make any sense. You're either mistranslating or whoever wrote it fucked it up.
>>
>>11853706
>>11853708
I fucked up, I started working out and misremembered what it said.
Sorry for the confusion.

It's actually "f be an automorphism on a field K, show that f(1) = 1"
>>
>>11853728
Suppose f(1)=x. Then f(1)=x^2. Use the fact that you have a field and x^2 = x.
>>
>>11853728
x=f(1)=f(1^2)=f(x)f(x)=x^2 (by property of homomorphism)
then x=x^2
now tell me why x =/= 0
>>
>>11853736
I'm not sure what are the necessary conditions that a mapping is an automorphism. I mean it sure is bijective, suppose there is a field A which contains number 1 and field B containing also 1 and the 1 gets mapped to the 1. There is nothing else. So by this its already an isomorphism. But what makes it an automorphism? Is it because the fields A and B are actually identically?
>>
[eqn]\lim_{a\to0^+}\frac{1}{ia+\omega}=PV(\frac{1}{\omega})-i\pi\delta(\omega)[/eqn] Please explain to a retard how to go from the left expression to the right one. PV is the cauchy principal value
>>
>>11853780
It is an isomorphism and A=B.
>>
>>11853775
I understand the equation using the property of homomorphism but how does x=x^2 help me?
>>
>>11853780
>I'm not sure what are the necessary conditions that a mapping is an automorphism.
This is why the very first thing suggested to you over an hour ago was to go read the definition of an automorphism.

Why is it such a common trend here and in /sqt/ that people insist on trying to solve problems when they don't know what the words in the problem mean?
>>
>>11853788
>>11853775
Is the point of the equation that it fulfills the necessary conditions of a homomorphism?
>>
>>11853788
Is x=0? If not, you can divide it away.
>>
>>11853797
No, you defined x as f(1), so x = 1 because f(1) = 1. Dividing x = x^2 by x is x = 1 again. That's what you defined it as.
>>
>>11853803
>>
>german
>is autistic
Like pottery.
>>
>>11853816
This.
>>
>>11853816
>>11853823
If I would be autistic i would have understood this shit immediately you fucking fags why the fuck do you think im asking for help on an website full of real autists like you.
>>
>>11853803
>No, you defined x as f(1), so x = 1 because f(1) = 1
This doesn't make any sense. f(1) = 1 is the result you're trying to prove, not an assumption
>>
>>11853827
You are not asking for help. You are simply wasting our time by not even trying.
>>
>>11853830
Yeah you're right.
I'm doing this in between sets of lifting. Now this makes more sense, gonna look at this again later.
>>
>>11853836
>I'm doing this in between sets of lifting.
Kek
>>
>>11853844
I thought I could save some time because I want to Netflix and chill later but It turns out you can not concentrate on math between deadlifts while listening to metal.

Let's just say this was a scientific experiment and the result was I'm retarded. Sorry for wasting your time.
>>
>>11853836
Ok cunt. f(1) = å, so it follows that å = f(1) = f(1^2) = f(1)^2 = å^2. Now if å=0, then 1=0, since f is bijective and f(0)=0, so we may conclude that å is not 0. Then we just use the fact that every non-zero element has a multiplicative inverse, let ä be the inverse of å, so we have 1 = äå = äå^2 = å. Now die and never come back.
>>
Alright no more Germans ever again
>>
>>11853227
>>
>>11853888
Trips of truth.
>>
>>11850726
general topology
>>
>>11853888
Holy based.
>>
>>11853858
That makes sense to me.
I usually understand this kind of reasoning but I have trouble doing it myself.

How did you come up with that. Like did you look up properties of homomorphisms or do you know them by heart? Where did you get the idea to use the multiplicative inverse to show it has to be 1?
>>
>>11853910
I used to be an algebraist, so I used to grind these things a lot.
>>
>>11853910
He has iq.
>>
What exactly does it mean by combinatorial type?
For example, 3 points in the plane can only have two combinatorial types: triangle, colinear.
I have a feeling I know what it means but I can't exactly define it. One thing that bugs me is that, by using combinatorial type, are we treating all triangles the same way? It feels wrong.
>>
File: 1592038260061.jpg (30 KB, 631x480)
30 KB JPG
>>11853728
$\text{Let }x\in K,\text{ then: } f(x*1)=f(x) \text{ and } f(x*1)=f(x)*f(1),\ f(x*1)=f(1*x)=f(x)*f(1)\\ \Rightarrow f(x)=f(x)*f(1)=f(1)*f(x) \\ \Rightarrow f(1)=1$
>>
>>11853920
When you say you used to be on it sounds like it was your job. What does an algebraist do practically?
>>
>>11853949
last implication isn't true in general
>>
File: 1592090312225.jpg (64 KB, 860x1137)
64 KB JPG
>>11853953
Is it not the multiplicative identity for all elements of $K$?
>>
>>11853951
It was a hobby. The good thing for us euros is that we can just do that. An algebraist does algebra.
>>
>>11853962
no
>>
>>11853962
I mean it is, but your proof is wrong. go find your mistake, chop chop.
>>
>>11853962
It is.
>>
>>11853962
Unless it is already given in the definition that homomorphisms mean those group homomorphisms that also respect the product and take 1 to 1, then no. Without the last condition f(1)=0 gives you a well defined ring homomorphism: f(x+y)=0=f(x)+f(y) & f(xy)=0=f(x)f(y). Check the details if you don't trust me.
>>
>>11853982
To be added: here it can be shown that the only possibility is f(1)=1, but not in general.
>>
>>11853982
>NOOO YOU HAVE TO EXPLICITLY SAY THAT THE ZERO MAP ISN'T BIJECTIVE YOUR PROOF IS WROOOONG
are you German, by any chance
>>
File: 1592054637088.jpg (87 KB, 960x943)
87 KB JPG
>>11853982
>>11853988
I do believe we were talking about automorphisms, aka isomorphisms, not homomorphisms
>>
>>11853995
Never said that.

>>11853998
In this case that is ok then.
>>
>>11853607
Isomorphisms are just structure preserving maps.
>>
>>11853998
>>
>>11853964
I see. It sounded like you were employed for your algebra skills but changed your job. I assumed that if it's your hobby then you don't just quit being one.

Anyways thanks for the help.
>>
>>11854009
No problem and it just got boring.
>>
>>11853888
This. Fuck g*rmans and fuck scholze.
>>
>>11853910
All you really need is that f() is surjective from K to K, and preserves products,, and that K has a multiplicative identity "1".
Then by surjectivity, there exists x such that f(x) = 1.
So 1 = f(x) = f(1 * x) = f(1) * f(x) = f(1) * 1 = f(1).
>>
>>11854004
Is it, though?
>>
File: 1491269710063.jpg (472 KB, 1280x1005)
472 KB JPG
>>11854037
nice one! very slick
>>
>>11854049
yes. the last line doesn't follow from the previous line.
>>
What are the prerequisites for K-theory and what is a good introductory book?
>>
>>11854081
what k theory? algebraic or topological
>>
>>11854082
Don't know, are they that different?
>>
>>11853953
>>11853967
>>11853970
What's wrong with the proof?
>>
>>11854103
yes, completely
>>
>>11854104
f(x) needs to be guaranteed non-zero
>>
>>11854107
Well, what are the prerequisites for each of them? And what are some good introductory books for each of them?
>>
>>11854123
Do you know what vector bundles are? Do you know how cohomology works? Topological K-theory is a generalized cohomology theory.
>>
>>11854103
They're technically the same because of Serre-Swan, but they're still very, very different.
>>
>>11854131
>Do you know what vector bundles are? Do you know how cohomology works?
Yes. Is it just a branch of algebraic topology?
>>
>>11854123
Both require some maturity and maybe acquaintance with hard subjects. I'd recommend having seen some algebraic topology before looking at top k theory. Atiyah's book is good but a bit dated, and Hatcher's is alright too, but im not a big fan. Those are the only two Ive read so cant say about others. As for prereqs for top k theory, I'd say basic point set topology as a given and abstract algebra, at least to the point of being acquainted with exact sequences and tensor products. vector bundles are defined in both books so they are not technical prereqs.

Alg k theory i dont have that much experience with, but there you're gonna need a lot more commutative algebra and homological algebra to get anything out of it. maybe some algebraic geometry too, depending on the flavour of k theory, and motivation.I remember perusing some cute book on alg k theory that had very little reqs, only basic linear algebra and abstract algebra, but cant remember the name.
>>
File: serre swan.png (2.48 MB, 1194x900)
2.48 MB PNG
>>11854136
4 u <3

>>11854145
Do you know how projective modules work? Algebraic K-theory starts by taking a ring, then taking its finitely generated projective modules and then you play with their isomorphism classes and construct a Grothendieck group out of that etc. Then you start getting all sorts of K's and they are somehow related to the properties of your ring. I don't remember how.
>>
>>11854159
OK thanks.
I've had courses in topological algebra, basic commutative algebra (up to Hilbert's nullstelensatz) and an intro course on AG. If by any chance somebody here has read Cartan-Eilenberg, would you recommend it to me?
>>
>>11854176
you shouldnt read a book on homological algebra unless you need something specific about it. by knowing homological algebra, i mean it being used in a certain context, that being some specific use like cohomology in AG or in AT, or perhaps in some algebraic context. otherwise ure not going to get anything out of it, and are going to forget the facts as soon as you stop reading the book
>>
>>11854212
Thanks.
>>
>>11850726
finite group theory
>>
>>11850693
What are the prerequisites for algebraic and arithmetic geometry?
>>
If there is formal logic, then what is informal logic?
>>
>>11854337
>then what is informal logic?
that's called mathematics.
>>
>>11854293
algebra
>>
>>11854358
That's all?
>>
>>11854362
and some point set topology I guess
>>
>>11854285
Pretty sure that's false.
>>
Mochizuki's "proof" of ABC is a failure.
>>
>>11854410
germans aren't allowed in this thread anymore peter
>>
>>11854421
Post some anime Chang.
>>
File: 1592805105691.jpg (229 KB, 1354x1800)
229 KB JPG
>>11854455
>>
>>11853910
This kind of thing becomes very easy with practice. Once you know the properties of a homomorphism and have seen enough problems that proof is basically the only thing that makes sense to try.
You start with wanting to show something has a particular value. You write that thing out and think about how you can use the assumptions you have. You're talking specifically about fields so multiplicative inverse will most likely have to come into things at some point (or some other property of fields, but we try the obvious one first).
>>
>>11854293
open up liu's AG and arithmetic curves and see what you need
basically, commutative algebra (think atiyah macdonald), and to start, basic field and galois theory (think morandi)
>>
What are some other good boards or generals for the mathematically minded person? Despite being on /sci/ for the past 9 years, I don't think ive really browsed many threads outside of sqt and mg for the past 3, the board's a bit of a shithole
>>
>>11854608
/jp/ and /s4s/
>>
>>11854618
>/jp/
Kek
>>
>>11854625
/jean-pierre/
>>
>>11854636
Based.
>>
>>11854608
Unironically /lit/
>>
>>11854642
Not anymore. The entire board has been overrun by unironic polddit boomers and the mods do nothing about it. It did used to be pretty good, though.
>>
>>11854656
/pol/ is a fucking plague that kills anything it touches.
Same as leddit.
>>
>>11854608
Other than 4chan, is math stackexchange good enough?
To be honest I don't even know any good forum about /math/ or /sci/ in general.
>>
>>11854718
It's alright for checking stuff, I wouldn't spend much time on it though. There are good forums I know, but none of them are in English.
>>
>>11854718
stackexchange is a good resource if you have a specific, moderately technical question that you can't answer and can't be easily looked up. or if you have a highly technical question and you're lucky enough to work in a field where the experts actually use the Internet.
for everything else it's trash
>>
>>11854726
>Good forums
>Not in English
Pick one.
>>
>>11854743
Whole English-speaking internet is trash.
>>
Is Verbal (GRE) related to any math skill?
>>
>>11854782
word problems
>>
https://en.m.wikipedia.org/wiki/Irreducible_polynomial
I'm reading this and it says that all polynomials of one variable with degree n>1 can be reduced to n polynomials of degree 1 in $\mathbb{C}$. This is a pretty basic consequence of the fundamental theorem of algebra (or just a rewording), but is there any kind of concept of how difficult a reduction is to reach?
What I'm asking is are there algebraic polynomials with algebraic complex roots where the roots exist and are easy to calculate but where factoring the full polynomial analytically is extremely difficult? Not in the sense of computational difficulty but just difficulty.
>>
>>11854799
Isn't finding root of anything, from quintic equation and above, is generally difficult?
>>
>>11854799
If you know all the roots factoring the polynomial is literally just a matter of looking at the leading coefficient.
>>
>>11854825
More like impossible in most cases.
>>
>>11854835
This is looking at the difficulty of factoring independently of the difficulty of root finding.
>>
>>11854851
Bro you aren't getting it.
If you know all the roots and multiplicities you immediately have the factoring. There isn't any effort involved.
>>
Any combinatorics problem that is easy to state and can probably be solved with the aid of strong computers?
I just want to do something else this weekend instead of agonizing over the problem I'm stuck right now.
>>
>>11854858
Not him but you are not the one getting it.
What you said is exactly what he said, read it again.
>>
>>11854858
Supposing you restrict yourself to avoiding "easy" root-finding methods.
>>
>>11854859
Find the number of latin squares for n=12? I think this is unsolved but idk.
>>
>>11854799
It depends on what you consider a "valid" solution is. You probably think saying $\sqrt2$ is a valid solution to $x^2-2=0$, until you realise $\sqrt 2$ is defined to be a solution to this equation. Galois theory can show that solutions with terms of the form $\sqrt[n]a$ can only be attained in general for polynomials up to degree 4. But if you allow to also use, for example, solutions to $x^5+x+a$ aka Bring radicals $\text{BR}(a)$, then you can express the solution to any quintic in terms of radicals and Bring radicals. I'd assume the trend continues upwards in degree, but what I'm trying to say is that there is inherently nothing special about nth roots, other than they coincidentally happen to be aesthetically pleasing solutions. Numerical solutions can be very easily computed for any polynomial. You can't "analytically" factor a rational polynomial until you define what the allowed terms for the roots are.
>>
>>11854799
Depends what you mean by "find a root".
It's not too tricky to get an arbitrary close decimal expansion of a root (via homotopy continuation). If you want an "exact form" then this isn't possible in general. In some sense it's not a reasonable thing to ask, as we can't even describe most (all but countably many) complex numbers beyond an approximation.
>>
>>11854870
Not him but I tried and it becomes impossible to do with a computer for n>7 without certain highly non-trivial mathematical results.
>>
>>11854870
>>11854897
Anons, if you have a computer that can generate all of them with n=12, the computer is probably more expensive than every asset on earth.
>>
>>11854859
>Any combinatorics problem that is easy to state and can probably be solved with the aid of strong computers?
Not that anybody knows about. If a problem is likely solvable by letting a program run for a weekend or even a week or two, the author would've just done that before he published. Virtually all open problems, even the most minor, have been checked up to huge numbers (huge being relative, 23 can be huge due to how combinatorial problems tend to explode in number of cases).

There definitely exist "open" conjectures that could be easily resolved with a computer, but they're all going to be buried in some pre-computer or crappy-computer era paper that everybody alive has forgotten about. Nobody's going to just feed you easy solvable problems, you have to dig those up yourself.

>>11854870
There are a few BOINC projects doing Latin squares, although I think they're trying to build a database of more tractable families. The number of Latin squares isn't really interesting beyond a curiousity since there is an explicit formula for counting them, it just has a stupidly bad complexity.
>>
>>11854897
>>11854897
Interesting. Can you share some more about what those results were? I remember when I took my combinatorics class we had to do it for n=3 and it was pretty nontrivial. However, I thought with a computer it couldn't be too bad?
>>
>>11854924
I was actually interested in the prime power conjecture which is a somewhat equivalent problem. I gave up trying to find an efficient algorithm and now my approach is to use groups of transformations as invariants.
>>
these threads are barely lasting a day now
>>
>>11854939
Is that supposed to be a bad thing?
>>
>>11854939
good.
>>
>>11854939
What's with the sudden influx of people? Summer has been going on for a while but the threads weren't this fast.
>>
>>11854939
Everyday gets hotter than the one before
Feels like summer
>>
>>11854939
Good, I don't like asking a question and have it answered 3 days after I found the solution myself.
>>
>>11854950
They were a month and a half ago. I'm sure the high school students/teachers are back or something now that it's almost july
>>
>>11854946
given the amount of polshit on them, yes, it's a bad thing
>>
>>11854960
/mg/ is the last channel of 4chan that /pol/ hasn't invaded, though.
>>
File: whatshesoys.jpg (125 KB, 718x519)
125 KB JPG
>given the amount of polshit on them, yes, it's a bad thing
>>
File: file.png (18 KB, 654x509)
18 KB PNG
haha based and funnypilled
>>
>>11854985
I'm the 69 and I don't even browse /pol/. Ask me anything.
>>
>>11855039
what anime should i watch next?
>>
>>11855039
What's the general form for the solutions of a quartic?
>>
>>11855039
are the french white
>>
>>11855042
Have you watched Kimagure Orange Road? It's a nice summer time anime. Otherwise maybe Haibane Renmei.
>>
>>11855045
No.
>>
>>11855044

>>11855045
No.
>>
>>11855046
watched haibane renmei so ill trust your taste for the other one, but actually the correct answer was aria
>>
>>11855052
>>
>>11854890
have heard of bring radicals before, I only have a weak understanding of galois theory
are there equivalents for higher than degree 5 polynomials or do bring radicals do the job, or do some polynomial roots need numerical methods
>>
>>11855065
Apparently jacobi theta functions, but they are very complicated, bring radicals only work in degree 5. Ultimately saying sqrt2 is a solution is pointless unless you have a numerical method to finding sqrt2, that is, there is no difference to saying "the number that is defined to be the solution to this polynomial equation is the solution to the polynomial equation", than when saying sqrt2 is the solution to x^2=2
>>
>>11855074
You called?
>>
im trying to get ahead before my Precalculus class starts is this a good book? http://precalculus.axler.net/
>>
>>11855129
Axler has never written a bad book, desu.
>>
>>11855074
sqrt2 at least gives an immediate hint of its size, we know (3/2)^2=9/4 > (sqrt2)^2 > 16/9=(4/3)^2, unless you count that as a numerical method
>>
>>11854971
Wait a second, you lads don't browse /pol/? Luv the humor threads, they get me cachinnating.
>>
>>11855168
Would you say they make you guffaw?
>>
>>11855133
That's different from saying all his books are good tho isn't it
>>
>>11855190
Well, I've never read his one on pre-calc, so I can only attest to it insofar that I've enjoyed his other texts.
>>
>>11855185
They get some chortles out of me, yeah.
>>
File: Houppelande.jpg (24 KB, 320x600)
24 KB JPG
>>11853645
the only help i can offer is a suggestion to do as many problems as you can. also paul's notes (https://tutorial.math.lamar.edu/classes/de/de.aspx) helped me when the textbook was too unclear
>>11854293
i reco having some complex analysis and diff geometry as well as commutative algebra
>>11854782
important for IUTT
>>
>>11855264
What is the absolute best text on commutative algebra?
>>
>>11855272
The best text is obviously Eisenbud.
But you should probably read Atiyah.
>>
>>11855272
>>11855324
also consider this http://web.mit.edu/18.705/www/13Ed-2up.pdf
>>
>>11855350
Does MIT have one of these for elliptic curves?
>>
>>11855552
What, a class? yeah probably
>>
>>11855557
I'm talking about the PDF of all the notes. Are these just readily available on their site?
>>
>>11850884
Are you in the tropical geometry summer school? If you want, I can link you the lectures. They also have some references as well.
http://www.cs.technion.ac.il/~janos/COURSES/238900-13/Tropical/MaclaganSturmfels.pdf
>>
>>11855564
yes if the professors chose to upload them on their class web pages. just google "mit elliptic curves" and go from there
>>
>>11855565
not that anon but can you post the lectures? also is anyone here in the utaustin minicourses slack (https://web.ma.utexas.edu/SMC/) just wondering
>>
>>11855570
Holy based.
https://ocw.mit.edu/courses/mathematics/18-783-elliptic-curves-spring-2019/lecture-notes/index.htm
>>
>>11831961
>>
>>11855589
Anon, I....
>>
>>11855589
What did he mean by this?
>>
File: you got trolled.png (9 KB, 252x200)
9 KB PNG
>>11855603
>>11855607
>>
>>11855577
Here you are