/sci/ - Science & Math

What's the point of functional programming?

Why would an undergrad be interested in algebraic geometry? Serious question

>>9348319
Depends on your interests. Certain subjects pave natural paths to algebraic geometry, but they are different.

>>9348319
>Why would an undergrad be interested in algebraic geometry?
Presumably for the same reason to be interested in any other field, to research/solve problems using the theory from that field

>>9348319
>Why would an undergrad be interested in algebraic geometry? Serious question
polynomials are very common objects

>>9348319
Either they're patrician or a major pleb

https://www.youtube.com/watch?v=PxMY4NQFrOQ

this isn't algebraic topology...

What's the current state of the art on the category of all axioms?

Why are PDEs harder than ODEs?

>>9348785
Because they have, in some sense, less restrictions.

>>9348319
They fell for the abstraction meme.

Would the homotopy category be concretizable if we relax the restriction that Set must be wellfounded?

>>9349069
the homotopy category of what

>>9348319
it's a very beautiful subject. everyone already knows the most elementary connections between algebra and geometry (analytic geometry), which may inspire them.

>>9348319
it's a very beautiful subject. everyone already knows the most elementary connections between algebra and geometry (analytic geometry), which may inspire them.

>>9349191
>Grothendieck used to draw shit on his notes
just like me!

>>9349203
he drew that because he thought the theorem was satanic

>>9348327
>>9348330
>>9349191
I'm interested in algebra, geometry, and rigour. Which is why I'm not enjoying so much algebraic topology, and I am quite enjoying the small amount of plane algebraic geometry I've done (and algebraic number theory and Riemannian geometry for that matter). Also, how can I explain to a prof that I want to do a PhD in this subject without sounding (a) like a retard, and (b) like I am talking out of my league, given that I don't have that much experience in the subject

>>9349203
>try to write out a theorem in algebraic geometry
>accidentally create a primordial summoning symbol and your stationery becomes infested with demons

How important are anime girls to learning Math?

>>9348319
memes

>>9349272
You will never be able to convince a prof working in the area that you aren't talking out of your league (because you are), but unless that prof is a huge jackass, it shouldn't be a problem.
The question is, how do you really know that you want to do a PhD in it ?

>>9348333
I've never seen a polynomial in my life

how can i get over my hatred for all things set-theoretical or topological
i enjoy algebra but i am at the point where i need a good background in topology to continue and i just don't think i can push forward

>>9349376

>>9349357
not at all, they lead you into falling for meme lists

>>9349272
>interested in rigor

>>9349357
They aren't important but they can increase your enjoyment of doing math. It's always nice to have company when you're engaged with something that pleases you, and anime girls are the most pleasant companions in the world.

>>9349272
>>9349272
Just get an algebraic geometry book and work through it.

Since you have done Riemannian Geometry, start with a book on complex algebraic geometry. That way you can lean back on differential geometric techniques if you aren't comfortable with heavy algebra.

>>9348316
so people can pretend to know category theory

>>9348316
Some people find it easier to problem solve in that mode of thinking. I personally prefer it.

>>9349485
can you teach me the art of mathematical anime grills?

>>9349793
there is something relaxing in the algebraic approach(in contrast to complex analytical one), just take a commutative algebra book such as eisenbud, a theoretical algebraic geometry book such as shafarevich 1 and an enjoy a book such as harris

>>9349917
You should start with classical complex algebraic geometry.

>>9349917
Eisenbud is really long and may get boring if you want to do geometry.

A-M is much shorter, the exercises are nice, and you can probably move through it quickly if you are comfortable with standard algebra.

>>9349917
>>9349922
>>9349952
best tip for doing algebraic geometry is too read a classic or undergraduate level text where the geometry is more obvious. Post Grothendieck Algebraic geometry is awesome and patrician as you can get but without a solid understanding of the actual geometry its is abstract autism.

Shalom /sci/
I was stuck on this problem for an embarassingly long time for some pretty stupid reasons.
The problem is to find the surface area of the cone z^2 = 4(x^2+y^2) the answer is (sqrt5)*4pi
Some guy here http://mathhelpboards.com/calculus-10/surface-integral-2568.html got the right answer. Is this the right way to do it or just a fluke? If it's the right way, why is it R dr dtheta?

>>9350315
this is how you calculate the area of a surface of revolution
just take a differential surfaces book

i want to find square numbers of the form [math] n! + 1 = k^2 [/math] for integers k
there are only three known solutions for n: 4,5, and 7
i would like to know exactly how many there are
i have tried some simple number theory and analysis approaches, but nothing
i found an interesting approach which treats the factorial as the order of a symmetric group, and then used some other basic group theory stuff, and it felt like i was getting close to something, but i am inexperienced and was unable to prove anything significant related to the original problem
ideas?

>>9350703
https://en.wikipedia.org/wiki/Brocard%27s_problem

>>9350703
Give up

>>9350703
>>9350737
>Overholt (1993) showed that there are only finitely many solutions provided that the abc conjecture is true.
finitely many then

>>9350737
god damnit every time i think i've found something cool ramanujan or terry tao have already published 9 papers and a movie about it

>abc conjecture implies finitely many solutions
so what's the consensus on abc conjecture? has anyone been able to learn IUTT and confirm mochizuki's stuff yet?
i suspected that there were only finitely many solutions after bruteforce searching for n up to about 10,000
i also can't seem to find any bounds on the number of solutions, only that there's finitely many
i must know the number

>>9350947
I'm currently interested in quasi-perfect numbers.
Wanna join an effort?

https://en.wikipedia.org/wiki/Quasiperfect_number

>>9348319
if they like it
if they want to look cool and impress professors/grad students

>>9349069
The axiom of foundation is essentially unnecessary in the definition of Set ... it should remain a well-pointed topos with NNO even without foundation. So it's unlikely to make a difference. The real obstacle in the proof is "size", it's concretizable in proper classes / large sets IIRC.

>>9348316
It's way easier to reason about and prove things about programs that don't have side effects or an environment to worry about. If you can prove things about a program you can optimize it better and make sure it doesn't break stuff - typed functional programming (especially dependent types) allows you to specify the behavior of a program much better than the bolted-on type systems like Java and C++ have.

>>9350947
>so what's the consensus on abc conjecture?
It's now Mochizuki's theorem

>has anyone been able to learn IUTT and confirm mochizuki's stuff yet?
Yes but not peer reviewed

>>9350947
>so what's the consensus on abc conjecture? has anyone been able to learn IUTT and confirm mochizuki's stuff yet?

It's still in limbo basically. Not much news since Conrad's summary. A few people are convinced but they're in the minority.

>>9351085
>Not much news since Conrad's summary.
http://www.kurims.kyoto-u.ac.jp/~gokun/DOCUMENTS/abc2017Nov20.pdf

>>9350970
what kind of background do i need to try to work on stuff like this

i feel like this is one of those things where a proof is going to come from magical arithmetic geometry lala land and it's going to be way too complicated for me to understand

>>9351090
>nationalist jap supports his fellow nationalist jap
Heh

check this out https://www.youtube.com/watch?v=_X1p7HhCzmA and tell me it isn't useless shit

>>9348316
Functional programming is a lot more mathematically natural I think. Also code is usually very short in length.

>>9350947
why don't you see for yourself :)

http://www.kurims.kyoto-u.ac.jp/~gokun/DOCUMENTS/abc2017Oct.pdf

>>9351285
You do realize thats not IUT Mochizuki right?

>>9351319
what made you think I thought it has anything to do with inter-universal Tiechmemer theory?

Please help
>>9351391

why are there four roots to z conjugate = z^2, z is a complex number? I only got two.

>>9351406
i unironically went through the same part of the book 2 months ago and couldnt figure out why either

>>9351196
But that's a good path to learn stuff, I'd argue. I don't know too much about number theory either.

>>9351529
Kek. Pic related is one more I took a while to understand but it wasn't as bad as that one.

>>9351090
I mean news for us non-experts. Consensus last I heard is that this guy is just as incomprehensible as Mochi.

>>9348316
>>9349861
>>9349901
>>9351044
>>9351288
Fuck off to another thread with this garbage.

>>9351626
>Fuck off to another thread with this garbage.
But this is /mg/

>>9351629
Which means programmer garbage is not welcome here.

>>9351631
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence

>>9351631
>Which means programmer garbage is not welcome here.
math is a subset of computer science

>>9351635
subcategory*

>>9351422
>why are there four roots to z conjugate = z^2, z is a complex number? I only got two.
http://www.wolframalpha.com/input/?i=conjugate(z)%3Dz%5E2

>>9351633
Why did you feel the need to post this? Type theory is quite different from "programmer garbage".
>>9351635
>subset
>>>/g/

>>9351633
>https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
https://en.wikipedia.org/wiki/Brouwer%E2%80%93Heyting%E2%80%93Kolmogorov_interpretation

>>9351633
>posting this instead of >>9351645
Pr*grammer spotted.

>>9351645
>>https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
>https://en.wikipedia.org/wiki/Brouwer%E2%80%93Heyting%E2%80%93Kolmogorov_interpretation
https://ncatlab.org/nlab/show/computational+trinitarianism

>>9351635
Exactly backwards.

>>9351650
Thinking in terms of sets is pretty backwards indeed.

>>9351633
So called "functional programming" is in no way related to this. Types in those languages usually fail to even form a category. Discuss "programming" in >>>/g/

>>9351650
can't define logic without computation anon

>>9351684
>logic is all of math
Pr*grammer spotted.

>>9351620
Who did you hear that from? A brainlet?

I love when brainlet westerns don't give the credit Mochizuki deserves because they all see it as incomprehensible alien bullshit when in reality it's just on a way higher level than anything weak brain westerns have come across. The best facepalm moments is westerns who dive into IUT proof without reading the 10+ prerequisite papers required to even begin it and get shook like "woah this is impossible to understand". It's like bunch of highschoolers diving into Perelman proof for Poincaré-Conjecture expecting to understand it because numberphile talked about it. I look down on people with this ignorant-thickheaded behaviour because it contributes nothing to the community and just honestly makes them look retarded. By the way over 30+ European mathematicians and some more from North America have confirmed the proof

>>9351620
>non-experts
Non-experts discussing this should kill themselves.

>>9351740
>Non-experts discussing this should kill themselves.
Why?

>>9351727
>t. chink with an inferiority complex

>>9351746
You're fine with buzzfeed journalists who's never taken a course in physics and not beyond highschool math should write articles on black holes and string theory? It's kind of like that.

>>9351771
Not him, but I'm not fine with anyone writing articles on black holes and string theory because black holes don't exist and string theory is a bunch of unphysical bullshit mathematics.

>>9351786
(you)

>>9351787
The fact that you buy that shit is one more reason to distrust Mochizuki actually achieved anything.
(Go back to China.)

>>9351746
So they don't have to embarrass themselves by making retarded posts.

How does one obtain the physical intuitions needed for doing math?

>>9351824
by doing math in the "right" order. real analysis gives you intuition for topology. linear algebra gives you intuition for algebra. complex geometry gives you intuition for algebraic geometry. none of those are actual prerequisites.

>>9351830
>real analysis
Stopped reading right there, what a stupid suggestion.

NEW 3BLUE1BROWN VIDEO

https://www.youtube.com/watch?v=OkmNXy7er84

>>9351830
That's pretty good for wasting your time.

>>9351841
>hurr hurrrrr
if you have anything to say, go ahead

>>9351848
it's faster than the other way around, so where do you waste time?

>>9351849
>hurr hurrrrr
>>>/r/eddit/

I shaved my head today but it's snowing outside and I own no caps. What do?

>>9351853
>it's faster than the other way around
How much does it take?

>>9351877
Die

can someone explain the determinate to me at three different levels?

>fresh out of intro linear algebra level
>graduate level
>wizard level

I still don't really know what "it" is.

>>9351841
>>9351848
This board is a joke.

>>9352033
more evident by the fact that I can not spell it
>determinant *

>>9351841
>Stopped reading right there, what a stupid suggestion.
t. couldn't make it past chapter 2 in Rudin

>>9352033

>intro level
the determinant of a matrix is how much that matrix scales n-volumes

>graduate level
the determinant is a morphism of algebraic groups from the general linear group to the multiplicative group

>wizard level
the determinant is a symmetric monoidal functor from the category whose objects are bounded chain complexes of finite rank vector spaces and whose morphisms are quasi-isomorphisms, to the category whose objects are graded lines and whose morphisms are homogeneous isomorphisms

>>9351924
to get where? for learning basic real analysis, basic topology, linear algebra and basic algebra, that's like a year

>>9352081
>the determinant is a morphism of algebraic groups from the general linear group to the multiplicative group
this does not define it
it's just one property of it

>>9352099
that's not just one property though, it's several properties neatly packed into one, which actually turns out to be sufficient to define the determinant

>>9352033
Let [math] F [/math] be a field.
Consider [math] F^n [/math] as a vector space over [math] F [/math]. (it has dimension [math] n [/math] )
The determinant is a map [math] \underbrace{F^n \times \ldots \times F^n}_{n \text{ times}} \to F [/math] such that:
1) It is multilinear. (linear in each slot, if the other slots are fixed)
2) It is alternating. (swapping two slots multiplies it by -1)
3) It maps [math] (e_1, \ldots , e_n) [/math] to 1. Here [math] e_1=(1,0, \ldots ,0) , e_1=(0,1, \ldots ,0) [/math] etc.

Such a map Exists and is Unique. The usual formulae follow: first the product one with the permutations, the the other one with the minors.
See how you get them here:
https://www.youtube.com/watch?v=23LLB9mNJvc

From these properties if your field is [math] \mathbb{R} [/math] , you can see that the determinant is the (signed) volume of the input vectors.

Also, if your field is [math] \mathbb{R} or \mathbb{C} [/math] then the deteminant of a matrix is equal to the product of the matrix's eigenvalues. (I guess it holds for other fields as well, if you extend to the closure, but not sure.)

Definitely watch this as well for geometric intuition:
https://www.youtube.com/watch?v=Ip3X9LOh2dk

>>9352198
it's always the product of the eigenvalues. the eigenvalues always live in the algebraic closure.

even in R, they can be strictly in C, consider
(0 -1)
(1 0)

>>9352206
Yes, I know that eigenvalues exist in "the" algebraic closure of the F.
But what if the algebraic closure of F is not of finite dimension over F?

>>9352217
Wait nvm I guess this doesn't make it problematic.
But, when you have R as the field, you can prove that the determinant is the product of the eigenvalues by complexifying the operator.
How do you go on about doing a similar process for an arbitrary field?

>>9352067
Yeah, you would have to at least start the book to make it past chapter 2.

>>9352217
well, what then? an nxn matrix over the field K has n eigenvalues on an algebraic closure F

if the eigenvalues are x1,x2, ..., xn, then there is a finite (since the xi are algebraic) extension K(x1, x2, ..., xn) that contains them as well, the splitting field of the characteristic polynomial

>>9352081
The third one doesn't uniquely define it.

>>9352239
the determinant is the characteristic polynomial evaluated at 0. the eigenvalues are the roots of the characteristic polynomial.

>>9352082
> basic topology, linear algebra and basic algebra
>that's like a year
What exactly is basic topology and basic algebra?

>>9352250
at the level of Weil's Basic Number Theory

>>9352250
basic topology means a book like munkres, enough theory to prove things like tietze's extension theorem and the baire category theorem. basic algebra means part of a book like rotman's "introduction to abstract algebra", maybe groups and rings.

>>9352258
>enough theory to prove things like tietze's extension theorem and the baire category theorem
>basic algebra means part of a book like rotman's "introduction to abstract algebra", maybe groups and rings.
>that's like a year
Maybe for someone severely handicapped.

>>9352250
basic should be normal undergraduate = basic graduate

>>9352262
read the whole post. the year also includes linear algebra (up the say the JNF) and real analysis (up to say implicit / inverse function theorems)

linear algebra is some crazy shit man
it blew my mind when they figured out the moon's orbit with matrices

>>9352266
>real analysis
Might as well ignore it.

>>9352242
>>9352247
Oh right I am retarded.
[math] p(x) = |A-xI| = \sum a_i x^i \implies a_0=p(0)= |A| \\
p(x)= \prod (x-\lambda_i) \implies a_0 = \prod \lambda_i [/math]

>>9352269
learn it in a week to understand why basing a theory on inequalities is shit for your future

>>9352266
Even that taking someone a whole year pretty much means mental retardation.

>>9352269
hahahahah you're so funny anon, this joke cracks me up every time you make it hahahahaha

>>9352275
>a week
What a waste of time.
>>9352277
That's not a joke though.

>>9352273
nah mate sounds like you learned your material pretty well. keep it up. hmu if you need anything

>>9352246
prove it

Alright bud, I'll take your shit bait. Explain to all of us why real analysis isn't worth the time of day.

>>9352279
>>a week
>What a waste of time.
I don't expect a highschool student to take less time if he wants to go through any verification
and it's not really a waste of time for them

>>9352292
It looks like you're new. Just ignore him. It's just one finitist crank. He doesn't believe infinite sets exist.

>>9352350
Oh, I see.

>>9352291
It doesn't define it and therefore doesn't uniquely define it.

>>9352350
>finitist
Not even close, I literally believe in large cardinal axioms.

>>9352350
it's not the finitist crank. it's the "i only do useless non-mathematics" categorytard. he actually believes he's doing algebra or something.

>>9351877
Another problem occurred guys. I went to do my groceries this evening and I ended up staring at the cashier's boobs because they were pretty plump, and she noticed and started to laugh at me.
I fear I may never be able to do my shopping there again.

>>9352389
I would laugh at someone who likes chest tumors too.

>>9352382
>useless
Engineer spotted.

>>9352382
I think it's the same guy. He only changed his tack.

>>9352402
Foundational mathematics ARE useless.

>>9352402
not the first time you call this algebraic geometry student an engineer, mr useless

>>9352406
Yes, but set theory is pretty much the only thing which is described by this and it has been obsolete for quite some time now.

>>9352410
>algebraic geometry student
Doesn't really matter. They can be engineer-like too, as you have just shown.

>>9352415
>my work in foundations is not foundations because that's an ugly word
kek
set theory is enough, your shit is literally useless

>>9352398
Boobs are great. Are you perchance a homosexual?
(I really liked that hypermarket too. Great prices and wide variety of produce. And it is very close to my apartment.)

>>9352420
>your shit is literally useless
It's used pretty often in mathematics, someone who enjoys "real analysis" obviously wouldn't know.

>>9352420
>kek
I hope being retarded works out for you, anon.

>>9351824
>>9351830
I somewhat agree. For group theory you can get intuition from either geometric (linear/affine) symmetries as in linear algebra, or finite set permutations. I'm not sure why you put complex geometry before alg geometry, it seems no more concrete to me.

>>9352422
>hypermarket

>>9352542
I take it you don't have hypermarkets in America?

>>9352425
>w-weal anawisisssss!!!
>REEEEEEEEEEEEL ANAAAAAAAAAL ISISS!!!!!
WHEEEEELLL
UHHHHHHH
NAAHHHHHHH
LISSSSSSSS
ISSSSSSS!!!!!!!!!

>>9352499
with complex geometry I kinda also mean classical algebraic geometry in CP2 and so on, gives you good intuition for the general theory of schemes

>brainlets still falling for the troll's lame as fuck bait even after all these months
It's the Wildberber shitposter ffs. He's constantly bringing up the same talking points, except he's now changed his backstory a little.

> I literally believe in large cardinal axioms.

>>9352081
>category whose objects are bounded chain complexes of finite rank vector spaces and whose morphisms are quasi-isomorphisms

This would be the category of perfect complexes on a point, right?

>>9351824
Do physics and math in parallel during your first years of uni, desu. Also, look for examples for each notion and try to see each new theorem in action on your examples

>>9352564
Put a bullet through your head.
>>>/r/eddit/

>>9352634
>Do physics
Nope. Not interested in engaging in subhuman activities.

>>9352499
>get intuition for group theory
>""concrete""
Haven't heard of a more retarded waste of time in a while. Is this truly what the less fortunate ones do to learn mathematics?

>>9352404
>I think it's the same guy.
I'm not a "guy".

>>9352675
>pretending to be another guy
>>>/b/

>>9352650
>subhuman activities.
Way to be a freshman. I don't even like physics but I do regret not having applied myself when I had physics classes. I'm just saying that the intuition you gain there can be very beneficial when working in geometric/analytic areas (ie. differential geometry, ODE, PDE, dynamics etc.) and provide both intuition and a large stock of examples (and for good reason, since many problems in these areas arise from physical problems)

Threadly reminder to work with physicists.

>>9352675
>>9352720
>>>/r/taiwan/

>>9352717
>working in geometric/analytic areas
I genuinely feel sorry for you.

>>9352766
Go on

>>9352663
Is it the same retard posting this same reply to everything in this thread?

>>9352720
dude, so many details in this image i really love it, i hope i'll someday be good enough in physics/math to understand that book

>>9348310
how long are string-theoretic strings?

>>9352919
[eqn]\mathbb{B}[/eqn] [eqn]\mathbb{A}[/eqn] [eqn]\mathbb{B}[/eqn]

>>9352919
String length is not a fixed parameter.

>>9352930
>String length is not a fixed parameter.
alright what kind of ranges of lengths are we talking about then (theoretically)

>>9352919
>>9352922
>>9352930
>>9352934
Please keep it contained to >>>/x/

>>9352942
Witten is the absolute Chad of /sci/, sorry you can't handle the PHENOTYPE

>>9352934
String length is has an inverse square proportionality with string tension. String tension of course measuring the energy per unit in the string.

>>9352919
We need an image exactly like this but with Mochizuki holding Hartshorne's AG

[eqn]\int \text{erf}(\csc(x))\ \text{d}x[/eqn]

>>9352675
What are you?

>>9348310
Why are (co)ends denoted by integral signs? I don't see the relation.

>>9353328
>What are you?
Not a "guy".

>>9353331
I think end/product coend/coproduct(sum)

been years since I looked at that, and I never needed it, but maybe the category of elements construction helps
https://ncatlab.org/nlab/show/category+of+elements

where you get a disjoint union of things out.

Also has a short Wikipedia page. And btw. the so called Grothendieck construction is related.

----

What are relevant stochastic processes, where the variance does NOT take the form proportional to t^a, for some a? (E.g. a=1/2)

>>9353331
>I don't see the relation.
The relation to what? Does something else in math use an integral sign?

>>9353375
>integral

>>9353378
Yes, the integral sign. Usually it is written as [math]\displaystyle \int[/math]

>>9349369
You've never worked with rings then

>>9350970
>>9353371
There are special websites for avatar users.

>>9353383
Ok that doesn't help me make sense of [math]\operatorname{hocolim} \left( F \right) = \int_{}^{c \in \mathcal{C}} {N\left( {{}^{c/}\mathcal{C}} \right)} \odot F\left( c \right)[/math]

>>9353375

>>9348310
>Lurie won't win a fields ever
Why are we here? Just to suffer?

taking projective geometry next semester, can anyone drop me some red pills on it?

>>9353449
coordinates are for plebs, axioms are for patricians

>>9353449
projective geometry <---> graded commutative algebra

affine geometry <---> commutative algebra

>>9353454
>>9353455
will it make women wet?

>>9353475
I don't see why not. And if it doesn't, are those really the kind of women you need in your life?

>>9353480
very valid point

do i need a [math]\mathbb{BAB}[/math] to understand gauge theory?

how many cliques are there on a complete graph K_n?

What's a quick redpill book of Galois theory?

>>9354084
>redpill
>>>/pol/

>>9353455
explain a bit pls

>>9353475
Whispering how Proj construction is done in a girls ear is the only time I've made a girl multiple orgasm

>>9354091
Projective space is the space of lines, and lines are invariant under scaling. The algebraic manifestation of invariant under scaling is homogenous polynomials and graded algebras.

>>9353840
[math] \binom{n}{1} + \binom{n}{2} + \cdots + \binom{n}{n} = 2^n-1 [/math]

>>9354086
What does /pol/ have to do with movies?

>>9354084
johnstone for polynomials

>>9351529
>unironically
are you retarded?

godel proved logicians were fag
at least model theory is somehow useful

>>9354388
>godel proved
stopped reading your pop-sci garbage right there.

>>9353574
What the hell is a bab?

>>9354407
Big Ashkenazi Brain

>>9354416
He talks like a girl.

>>9354419
That's because his vocal chords are 11 dimensional d branes

>>9354115
Thanks this is what I was suspecting with K_5 but it was a slog looking at every case like a peasant because my brain hasn't been math for years

>>9354278
i am unironically retarded

>>9354115
>>9354594
Oh one more thing, Choose(n,k) for the clique on k vertices, right? So if I want only cliques of 3 vertices and higher, it's
sum_k=3^n choose(n,k)
or
what you've said, minus n, minus the count of pairwise edges

>>9354607
>Oh one more thing, Choose(n,k) for the clique on k vertices, right?
Yes
> So if I want only cliques of 3 vertices and higher, it's
sum_k=3^n choose(n,k)
Yes
> or what you've said, minus n, minus the count of pairwise edges
Yes to that as well, it is the same thing as the previous one.
No

>>9354607
>Oh one more thing, Choose(n,k) for the clique on k vertices, right?
Yes
> So if I want only cliques of 3 vertices and higher, it's sum_k=3^n choose(n,k)
Yes
> or what you've said, minus n, minus the count of pairwise edges
Yes to that as well, it is the same thing as the previous one.

>>9354607
>Choose
What if I don't accept the axiom of choice?

>>9354106
What about the affine part?

I've been stuck on the second half of this problem. I'm completely lost on how to do it.
I did the first part just fine and got 96 pi, but I can't figure out how to do the double integral.

>>9354901
And as soon as I posted I think I came up with a solution.

>>9354901
S is a sphere centered at O of radius 2, you can integrate it in spherical coordinates (no shit), the normal vector to S at (x,y,z) is [math]\vec n = \frac{(x,y,z)}/2[/math] and the surface element is [math]dS = 2\sin(\theta)d\theta d\phi[/math]

>>9354918
Thanks.
How did you find the normal vector and dS? I kept fucking up when I tried to do it in spherical coordinates.

need advice about gre, posting here instead of /adv/ because I figure I might get more grad students to read this

applying to (applied) math programs. first time I took general test, got 170 math, 161 verb, and 3.5 writing. I retook it to fix my writing score, and got 163/163/5.0 the second time. so in the quant section, I dropped from 97 percentile to 84. however, my math subject test score is decent—790 (77 percentile). with this in mind, would you send the first or second general scores, or both?

>>9353449
You can think of the projective line in two different ways: as the space of lines through a point, or as the real line plus a point at infinity.

You can see these as homeomorphic by taking the lines through the point (0, 1), so each line corresponds with the point on the x axis it intersects, except the horizontal line which "is" the point at infinity.

>>9353422
He'll win the Abel prize though, so that's pretty good.

>>9354992
Send the second, your math gre score will count for a hell of a lot more than just the quant section alone, plus your verbal is higher than before and your writing score went from shit to pretty good. The second all around is stronger even if the quant is slightly lower.

>>9354920
well for the dS I don't know what to tell you (also, my bad, it was 4*sin... instead of 2*sin...), I can give you a handwavy explanation for it: If you're at a point with spherical coordinates [math](2, \theta, \phi)[/math] and move to [math](2, \theta+d\theta, \phi+d\phi[/math], then you move along [math]e_{\theta}[/math] by [math]2\sin(\theta)d\theta[/math], since you're moving on a circle of radius [math]2\sin(\theta)[/math] by an angle of [math]d\theta[/math] (draw it), and you move along [math]e_{\phi}[/math] by [math]2d\phi[/math] because you're moving on a circle of radius 2 by [math]d\phi[/math], spanning a surface of [math]4\sin(\theta)d\theta d\phi[/math].

For the normal vector, again, draw it and you'll understand why it works, but by definition the normal vector to a surface defined by an equation f(x,y,z) = 0 at a point p is the normalized gradient [math]\dfrac{\nabla f(p)}{||\nabla f(p)||}[/math], which here turns out to be exactly what I said. But I think it would be much more enlightening to just doodle it and see that it works.

>>9355011
Thanks for explaining, I really appreciate it.
I went back over my notes and it turns out that I was confusing the del operator with gradient which is why I kept fucking up the normal vector.
I bet you can never guess what I'm majoring in.

>>9355010
thanks chief

>>9354388
Löwenheim-Skolem theorems are cooler

>>9355191
>Löwenheim-Skolem theorems
not science or math

>>9355197
how ?

>>9355202
>how ?
What do you mean?

>>9355262
>What do you mean?
why do you ask ?

>>9355265
>why do you ask ?
Because I don't know what you mean.

>>9355267
huh ?

>>9355271
>huh ?
What are you confused by?

>>9355272
Hello?

>>9355262
how is lowenheim-skolem not math ?

>>9355296
>how is lowenheim-skolem not math ?
That's a bit of a bizzare question. It's the same reason Occam's razor isn't math, simply because there's nothing mathematical about it.

>>9355191
yes, with compactness, quantifier elimination and the theory derived from considering arrows that 'preserve truth' is the only thing I can appreciate from logic

>>9355197
>>9355318
that's because you are thinking about Skolem paradox and not lowenheim-skolem theorem (up/downward)? Skolem paradox is just a historical misunderstanding, not that interesting yes

What's the intuition behind conferences for female mathematicians?

http://www3.mathematik.tu-darmstadt.de/index.php?id=3312

>>9354847
You can understand a space by understanding functions on it. So polynomial rings.

>>9353343
not a guy.
So a boy? you must be at least 18 to post on /sci/

>>9354403
>pop-sci
keked at you internally right there

>>9354992
a lesson for all you kids don't take the quant high/drunk

>>9349861
Why not use Hoare triples instead?

>>9348310
Hi. Quick question.


P(n,k) is the number of permutations of k-sized subsets of an n-sized
set. C(n,r) is the same but when order doesn't matter.

This can be calculated as:

P(|A|, k) = |{x | x ⊂ A ∧ |x| = k}|

And is the permutation or combination depending on whether you are
working with ordered sets or unordered sets.

But this need not use the counting measure.

For the counting measure one counts all the possible subsets B that solve:

Σ [x ∈ B] = k; B ⊂ A

This seems "obviously" generalizable to me as:

∫^{∞}_{-∞} B(x) dx = k; ∀x. 0 ≤ B(x) ≤ A(x)

or maybe even for quantum mechanics something like (where B gives a complex result):

∫^{∞}_{-∞} B(x)2 dx = k

But how do I "count" the amount of possible solutions for B?

>>9355619
really all it was is I made a silly mistake and spent too much time on one question, so I had to rush throught the last few questions.

>>9355640
if A is big enough, with integral (or square integral in the second case) bigger than k, then too many Bs will satisfy the condition to be useful

the point about combinatorics is that you can count finite things.

>>9355691
But couldn't you count degrees of freedom for example?

>>9355640
>>9355702

Interesting question. It's only a linear space when k = 0, otherwise it's an affine space so you can measure it via affine dimension. But it will probably be infinite dimensional in general.

>>9355777
*convex, not affine (because of the 0 ≤ B(x) ≤ A(x) condition)

>>9355377
Women suck at mathematics, so they have to build a safe space for themselves so that they won't feel too bad about it.

I'm not going to post this in /sci/ general because that place is a shit hole, but do you guys think that IQ corresponds to math performance because one can do math at a very superficial level just via symbolic manipulation without actually learning the material? This advanced symbolic manipulation ability would be good in passing exams and perhaps even solving some research problems; however, it seems like that "age" of math is coming to an end. This is why I think Grothendieck is a greater genius than Von Neumann, because Von Neumann was gifted with very high processing speed and was thus able to state space search the solution to various problems, but he was never able to come up with a discovery like Grothendeick was . We all know by this point that Grothendeick was not known for his processing speed nor his technical mastery( Grothendieck prime). People who can do state space searches will be replaced by advanced neural networks who will out class them in every way possible, but can we make a machine that will encompass Grothendieck's level of insight and inner wisdom? Perhaps that's why he went insane later in his life.

>>9348310
I am trying to grasp existence and uniqueness theorem
https://en.wikipedia.org/wiki/Picard%E2%80%93Lindel%C3%B6f_theorem

I do not understand why do they say without any justification that
[math]f(s, y(s))ds[/math] is integrable?

>>9355377
They want to motivate you to improve your life and immigrate somewhere without this shit.

>>9356110
That is why there are still people doing category theory and such feminine things. When proper mathematics like real and complex analysis are too hard for them, they tend to avoid such matters and do the more "artistic" stuff.

>>9356357
e.g. infinite groups instead of finite ones

>>9356116
You could make an argument out of that line of thought, but stating Neumann wasn't innovative is just silly. He worked in set theory and invented game theory and classes of automata, etc.

>>9356176
I can't find where they say that.

If you're stating it's equal to y' at that point, then it is.

>>9356176
>I do not understand why do they say without any justification that
>f(s,y(s))dsf(s,y(s))ds is integrable?
It says that f(t,y(t)) is Lipschitz continuous, which implies uniform continuity, which implies continuity, which implies integrability.

>>9356475
Only in the second variable, not in both, but in the integral both are changing.

>>9356412
Is any derivative integrable?

>>9356597
Which derivative? Doubeault? Frechet? Fractional?
Which integral? Riemann? Stieltjes? Lebesgue?

>>9356600
Lebesgue obviously

>>9356600
Riemann
>>9356601
Fuck off shill

>>9356601
I don't think so

>>9356613
>>9356616

>>9356623
you think every derivative is integrable ?

>>9356613
This isn't the engineering general anon

>>9356412
> If you're stating it's equal to y' at that point, then it is.
It is true for the solution y.
But to prove its existence we consider convergent sequence of continuous functions [math]\varphi_n[/math], and we need [math]f(t, \varphi_n(t))[/math] to be integrable as a funnction of t for all functions [math]\varphi_n[/math].

Ok, which one of you wrote this and what is the point of it

>>9354751

>>9357130
There are no points in topology.

>>9357141
But the opening topological space is pointed!

>>9357145
The category of topological spaces is equivalent to the category of non-pointed topological spaces.

>>9357149
See
>>9354751

>>9357145
That was an indirect way to say I dindu nuffin. Regardless, there are no points in topology.

>>9357155
Fucking hell I had a feeling it's the Finnish anime poster.
Fuck you.

>>9357162
>Fucking hell I had a feeling it's the Finnish anime poster.
>Fuck you.
cringe

>>9357162
R*ddit scum is not welcome here.
>>>/r/eddit/

>>9357141
>>9357155
>algebraist thinks he knows jack shit about topology

>>9357162
Oh but that's not very polite, but quite unimaginative at the same time. Not even mentioning how my parents are disappointed at me, not threatening to kill me, no clever "I don't believe in God but I've been praying you'd get cancer and died", not a little variation in your use of swearwords. Low energy rage.

>>9357173
Point-set topology is physics. I can admit I'm bad at physics.

>>9357141
So categories which topologists work with have no terminal object?

>>9357178
>point-set topology is physics
>differential topology is based on pointed spaces
>equivariant cohomology is based on differential topology
>the development of equivariant cohomology led to the discovery of new diffeomorphism invariants of exotic manifolds
>hence physics led to the discovery of these invariants which solved open problems in math
Math truly is too difficult for mathematicians.

>>9357178
>>9357191
>physics
Dog-eaters are not welcome here. >>>/x/

>>9357194
What's wrong with eating dogs?

>>9357187
Sure, they can work with categories with terminal objects if they want to.

>>9357191
>exotic
Pls no more niggers.

>>9357194
But I don't even like physics.

>>9357202
>But I don't even like physics.
Then don't mention it here. It's in bad taste.

>>9357202
>Pls no more niggers.
What did you mean by this?

>>9357173
>>9357206
>>>/r/taiwan/

>>9357205
I'll behave from now on. Back to the shadows ->

>>9357206
Niggers are exotic. Considering exotic things may lead into considering niggers, and BOOM you have a tribe on your backyard playing bongos and eating human flesh.

Cya boyos and the "I'm not a 'guy'" guy who's totally a guy.

>>9357202
>they can work with categories with terminal objects
Then the terminal object is pointed.

>>9357211
>Cya boyos and the "I'm not a 'guy'" guy who's totally a guy.
Why do you think I'm a guy?

>>9357216
see >>9357210

>>9357211
>Niggers are exotic. Considering exotic things may lead into considering niggers, and BOOM you have a tribe on your backyard playing bongos and eating human flesh.
Holy FUCK you're right we should just WLOG consider smooth k-forms and discrete topologies and acyclic exact sequences and soft sheaves fuck all that "special case" noise lmfao all categories only have one object and one morphism on it.

I really like this place when it's lively and chatty.

>>9357178
>Low energy rage.
It wasn't rage. It was disappointment. For once I thought a non-anime poster had made a half-decent thread on /sci/ and you had to ruin it.

>>9357272
>r*ddit image
R*ddit scum is not welcome here.
>>>/r/eddit/

>>9357216
"guy" has become gender neutral in amerimuttese

Here is a great example of how NOT to teach math: https://www.youtube.com/watch?v=vgZhrEs4tuk

The guy gives zero motivation, it's just playing around with some apparently random rules for making funny diagrams. He presents a formula without any reasoning or even saying how to calculate it fully, and only explains how when prodded.

early new >>9357573

>>9357912
Well representations of finite groups are pure cancer so what did you expect...

>>9358597
>Well representations of finite groups are pure cancer
What did he/she mean by this?

>>9358598
https://en.wikipedia.org/wiki/Representation_theory_of_the_symmetric_group

Could be a start

I'm retarded, what's the best way to take math related notes? Makes sense to me to go for a mix of theorems/proofs/examples, but I always seem to get too verbose.

Why is this wikipedia page so good?

https://en.wikipedia.org/wiki/Adele_ring

>>9358607
>https://en.wikipedia.org/wiki/Representation_theory_of_the_symmetric_group
What is cancerous here?

>>9358626
The whole thing. (thinking something is cancerous is subjective u kno, ppl here hate integration theory, i like it).

>>9358624
in your head

but seriously, im assuming theyre for yourself? then what I do is simply write down all definitions and theorems without proof, very important examples (the ones that are key for the theory) and nothing else, other than maybe a couple remarks on why an object is important or how to go about the proof.

In essence, on a second read, i should be able to recreate every proof, so the notes are just there so i can quickly read the precise definitions or lemmas that can aid me in such an endeavour

>>9358597
Not the point. It's the presentation not the content.

I'm in calc II right now and want to self study calc III (multivariable calc, parametric equations, polar coordinates, vectors and vector calculus, partial differentiation, multiple integration, Green’s theorem, divergence theorem of Gauss, Stokes’ theorem etc.) which textbook covers these topics? I know Stewart does but I don't like it. Anything better? Does Spivak? All advice is appreciated.

How much math can I learn in two years? I'm about to start a two-year master's program in philosophy and I would like to study math throughout (philosophy programs allow you a shitload of free time). I last studied math (pre-calc) six years ago and I remember it being easy. My plan is to completely finish Calc 1-4 + Analysis and Linear Algebra. I'm studying this math mainly because I need it to be able to write about advanced theoretical physics. Is this doable? Keep in mind I'll also be studying any physics that my math skills permit at the time.

Thanks.

>>9361507
it

>>9361609
depends

>>9360735
>I'm in calc II right now and want to self study calc III (multivariable calc, parametric equations, polar coordinates, vectors and vector calculus, partial differentiation, multiple integration, Green’s theorem, divergence theorem of Gauss, Stokes’ theorem etc.) which textbook covers these topics? I know Stewart does but I don't like it. Anything better? Does Spivak? All advice is appreciated.

http://matrixeditions.com/5thUnifiedApproach.html

>>9361507
>A Primer of Abstract Mathematics by Ash
>Introduction to Calculus and Analysis, Volume I&II by Richard Courant and Fritz John
>Differential Equations with Applications and Historical Notes by Simmons
>Linear Algebra by Shilov
>Differential Geometry of Curves and Surfaces by do Carmo

That's probably the max you will do in 2 years.

>>9361611
On what? Also, checked.

>>9361638
Thanks.

>>9360735
Lang has a book titled calculus of several variables, if you enjoy his style. It seems to have most of the things you are interested in. Spivak doesn't cover such material. I believe the later apostol volumes do, however.