/sci/ - Science & Math

>What are you studying right now
Something you probably won't understand, fag.
>Do you have or know of any interesting articles you'd like to share?
To you? Pfft
>Are you alright
Better than you, that's for sure.

>>9647362
Are you the same faggot NEET animeposter who ran away from the other thread? What's it like being useless?

>What are you studying right now?
Applications of non-compact products of compact topological spaces

>>9647384
>Applications of non-compact products of compact topological spaces

>>9647383
>faggot
Why the homophobia?

>>9647388
I'm gay buddy, but still less of a fag than you.

>>9647388
>>9647392
yikes

>>9647392
>faggot calling others faggots
What's it like being a frogposting cuck

>>9647384
I'm very interested in this for my own research. Do you have any preprints for your results yet?

>>9647395
>cuck

>>9647395
>>faggot calling others faggots
Who are you quoting?

>>9647396
>Do you have any preprints for your results yet?
My results are classified.

>ITT: no math

1+1=2, your move brainlet

>>9647402
>My results are classified.

>>9647402
>My results are classified.
Our* results are classified.

>>9647409
>Mathematicians say "we" not "I"
I seriously hope you're not pulling this shit twice. You're an embarassment

>>9647421
>I
Mathematicians use "we", not "I".

>>9647428
Don't you have a cartoon girl you need to jerk off to? Why don't you step aside and let the actual academics speak.

Let's talk about polynomials of this form for a bit (for some [math] \alpha , \beta \in \mathbb{R} [/math]):

[math] P_n^{(\alpha, \beta)}(x) = \dfrac{1}{2^n} \sum\limits_{j=0}^{n}\binom{n+\alpha}{j}\binom{n+\beta}{n-j}(x-1)^{n-j}(x+1)^j [/math]

It turns out they're eigenfunctions of the (Jacobi) differential operator
[math] y \rightarrow - (1 + x^2)y'' + (\alpha - \beta + (\alpha + \beta + 2)x)y' [/math] with eigenvalue [math] n(n + \alpha + \beta + 1) [/math] and all other eigenfunctions of this operator can be expressed in terms of such polynomials.


(Don't let the bullies discourage you friends.)

>>9647433
Trivial, try harder animeposter

>>9647433
Any nice properties if [math] n < 0 [/math]?

>>9647438
Something seem to be pressing heavily down on you. How can I help you?

>>9647442
Anything you'd like, as [math] n \in \mathbb{N} [/math].

>>9647443
Do you have an actual job or professorship related to mathematics? Or do you just post trivial fun facts on an anime forum? That doesn't sound like a wasted life at all

>>9647454
This thread is not an exclusivist club reserved for mathematics professors or people who pursue mathematics professionally. Everyone who likes math is welcome. Please try to understand that. I know you have the capacity to do it.

>>9647467
The thing about 4chan, and you'd know this if you weren't a stinky redditor, is that general threads don't officially exist and as such have no rules. I can derail this thread as much as I want if I don't like you.

>>9647446
I think he's asking if it can be generalized to other n

>walk into math thread
>100% brainlet memes with a side of heavy autism
Thank fuck i'm not a mathematician, imagine basing your entire ego and personality on your """"intelligence""""

>>9647501
Only autists and insecure faggots take 4chan banter and memes as real.

>>9647501
The regular users of these generals are reprehensible avatarfags.
Here's a protip for you guys: General threads are against the spirit of 4chan and are disallowed on multiple boards. If you want to discuss a particular mathematical topic make a thread for that topic. Now delete this thread and kill yourselves please.

>>9647362
Check out pro /'etale topology. https://arxiv.org/abs/1309.1198

>>9647513
no

>>9647497
It can, but then it wouldn't be a polynomial, would it?

>>9647517
It would be some other object, perhaps one with interesting properties. Regardless, you didn't even post the condition that [math]n \in \mathbb{N}[/math] in your original post. If your point was that applying a non-positive n to the formula would result in a contradiction and thus allow any vacuous truth, then you're not clever and that kind of pedantry is a very unlikable trait.

>>9647513
I've been trying to get into algebraic geometry. I'm too stupid to do it though. Thing is, it always gives me the illusion that the subject is attainable for me. I can understand the definitions and the intuition behind the constructions, but whenever I try to play around myself I get stumped, proving that in fact I didn't really understand anything at all.

I wish that guy who posted problems would come back. Many of them were adequate for me.

>>9647526
>I'm too stupid to do it though.
Wow, shocking.

>>9647521
How does one sum a negative number of terms, smarty-pants?

>>9647529
Very carefully

>>9647530
Go on.

>>9647531
Put the negative number in and see what happens.

>>9647511
>General threads are against the spirit of 4chan
What's the spirit of 4chan?

>>9647537
Certainly not general threads.

>>9647538
That's a very unsatisfactory answer.
>>9647432
>Why don't you step aside and let the actual academics speak.
Are you one?
>>9647454
>Do you have an actual job or professorship related to mathematics? Or do you just post trivial fun facts on an anime forum? That doesn't sound like a wasted life at all
Do you?

>>9647540
To elaborate further, the purpose of 4chan is anonymous discussion. General threads promote e-celebs, avatarfagging, drama, and carryover from previous threads. In general, having a continuity between multiple threads is discouraged for obvious reasons.

>>9647540
>Are you one?
Yes
>Do you?
Yes

>>9647544
How is the life of a proffessional mathematician?

>>9647546
Boring. It beats a lot of other things though.

>>9647544
>Yes
Doubt.
>Yes
Doubt.

>>9647550
Good thing I don't care if you doubt it.

>>9647536
You do it and teach me later.

>>9647553
Exercise for the animeposter.

Can someone help me find what P(O) is?

>>9647556
I broke my neck trying to view that image, now I have to go to the doctor, thanks a lot.

>>9647559
I'm sorry I'm a filthy pleb

>>9647548
>Boring
How so?
Jesus fucking Christ, is that Captcha shit really going to drive cars?

>>9647554
Why?

>>9647556
I assume that's the complement of O. You have [math]P( A\cap O)= 0.1P(O)[/math] and [math]P( A\cap \bar{O})= 0.8P(\bar{O})[/math]. Now, notice that [math]P(\bar{O}) = 1 - P(O)[/math], so [math]P( A\cap \bar{O})= 0.8P(\bar{O})=0.8 - 0.8P(O)[/math]. Since [math]O\cap\bar{O} = \emptyset[/math], you have [math]P(A) = P(A\cap O) + P(A\cap\bar{O}) = 0.1P(O) + 0.8 - 0.8P(O) = 0.8 - 0.7P(O) = 0.6[/math] from which it follows that [math]P(O) = \frac{0.2}{0.7} = \frac{2}{7}[/math].

>>9647400
The situation

>>9647562
It's math, it isn't always interesting. I love it but even I can admit that.
Just pray that someone gets killed by the google car, this shit has to stop.

>>9647552
Why are you even here? Seemingly constantly I might add.

>>9647575
I first started posting in these threads this morning. I'm mostly sick of it so I might leave soon. Just know that you're ruining the board. The subject that is most popular on the board and literally comprises half its name doesn't need a general, the board is its general. If you want to discuss a math topic, post a thread about it and you'll get more relevant replies. If you want to post anime girls and larp as a mathematician go to /a/. I know you're going to reply to this post with a smug anime girl and a mocking tone so save us both time and don't.

>>9647568
Thank you kind mathbro

>>9647586
You're welcome but don't call me a mathbro. Bro is better.

>>9647575
I think you should kill yourself. Your autistic anime is beyond gay. Do you ever want to become a man?

>>9647575
I've been on 4chan since 2006 (yes, I know I'm a newfag), I avoid these threads because I'm not afflicted with autism.

>>9647583
>I first started posting in these threads this morning.
No one is going to buy this lame fake-out pal.

>>9647589
ok bro

>>9647598
I got sucked into the /biz/ trap for a long time, I only recently came back to /sci/.

>>9647600
>he's a mathematician (who works in academia) that posts frogs and makes fun of other people for being "stupid"
>he got sucked into the "/biz/ trap", a board full of NEETS fishing for info on how to invest their welfare checks
I think you can dig your hole deeper.

>>9647362
Is it normal to find writing existence proofs much more difficult than anything else?

Is this good?

Stirling's Approximation: For positive integers, [math]n[/math], the value of the factorial function, [math]n![/math] is given asymptotically by [eqn]n!\approx \sqrt{2\pi n} n^n e^{-n}[/eqn]

Lately, I've been working on a cryptosystem based on the nonexistence of a complete ordered field.

>>9647654
jesus fucking christ, when will people learn how to rotate images.

>>9647719
It may seem alien to you as it is not written in Latin alphabet. Maybe you will learn other languages than English one day.

>>9647736
You still have to rotate your head 90 degrees to read that Cyrillic.

>>9647743
I didn't and I read it just fine.

>>9647743
No. Cyrillic is read from left to right. If you want to have to tilt your head while reading, try a reading language read vertically but do it by holding the text so that it must be read horizontally. I'm not sure if you are smart. Also, that is not hard to read, see. >>9647746

>>9647622
well of course, because when somethign "exists", you need to construct it

>>9647752
Did you quote the wrong guy or are you just taking the piss? That's a Russian textbook on topology and differentiable manifolds.

>use answer on stackexchange
>proff graded my answer
>"looks familiar, come to my office or I'll fail you"
>turns out he wrote the answer to catch brainlets
SHHHHIIIIEEEEETTTTTTTTTTTTTT

>>9647655
Why should I care about approximations?

>>9647867
sometimes the best we can hope for is an approximation

>>9647362
>What are you studying right now?
Differential Calculus, specifically with regard to interpreting derivatives to predict function behavior on an interval.
>are you alright?
Mixed feelings. On the one hand, I'm finally studying Calculus which has been my goal for years, but on the other hand, I'm ashamed of studying material that most people learn at 10 years my junior. I just desperately want to get out of brainlet land but I can't skip this material.

>>9647887
>I'm ashamed of studying material that most people learn at 10 years my junior
What age you study it at doesn't matter anon. This isn't a timed race. Keep it up.

>>9647526
Not him, but what kind of problems are you looking for? Are you studying (classical?) algebraic geometry? By yourself?

>>9647526
>Thing is, it always gives me the illusion that the subject is attainable for me.
If it makes you feel better AG is one of the hardest fields of study in all of mathematics.

>AG is one of the hardest fields of study in all of mathematics.

Some modular form help needed.

If [math]f|[\gamma_i(z)]_k=f[/math]
and [math]f|[\gamma_j(z)]_k=f[/math]
then I'm trying and failing to prove [math]f|[\gamma_i\gamma_j(z)]_k=f[/math]
Slash action defined as
[math]f|[\gamma(z)]_k=(cz+d)^{-k}f(\gamma(z))[/math]

Some modular form help needed.

If [math]f|[\gamma_i(z)]_k=f[/math]
and [math]f|[\gamma_j(z)]_k=f[/math]
then I'm trying and failing to prove [math]f|[\gamma_i\gamma_j(z)]_k=f[/math]

Slash action defined as
[math]f|[\gamma(z)]_k=(cz+d)^{−k}f(\gamma(z))[/math]

Some modular form help needed.

If [math]f|[\gamma_i(z)]_k=f\text{ and }f|[\gamma_j(z)]_k=f[/math]
then I'm trying and failing to prove [math]f|[\gamma_i\gamma_j(z)]_k=f [/math]

Slash action defined as
[math]f|[\gamma(z)]_k=(cz+d)^{−k}f(\gamma(z))[/math]

>>9647906
>Are you studying (classical?) algebraic geometry? By yourself?
Yes.

>what kind of problems are you looking for?
Give me anything. I am having a minor panic attack and need to keep my mind occupied. If the guys replying to me here >>9647799 are right, I may have prostate cancer.

Trying to get my head around line bundles and divisors. How come divisors are sometimes written as a sum of weighted hypersurfaces, and sometimes as a sum of weighted points?

>>9647994
Yo prove that [math]|\mathbb{P}^1(\mathbb{Z}/n\mathbb{Z})|=n^3\prod_{p|n}(1-1/p^2)[/math]

that took me forever but is pretty rewarding.

>>9648072
what did I do wrong....

>>9647963
hint: f|(gamma_1 * gamma_2)=(f|gamma_1)|gamma_2
and if j(gamma,z) := cz+d, then j(gamma_1 * gamma_2, z) = j(gamma_1, gamma_2*z) * j(gamma_2,z)

>>9647926
>>AG is one of the hardest fields of study in all of mathematics.
Who are you quoting?

>>9648053
any takers?

If c is the GCD of a and b then does

[math] \Gamma(c) = \langle \Gamma(a),\Gamma(b) \rangle [/math]

>>9648075
I think that 4chan's tex parser has problems and won't always display the syntax correctly if you don't clearly separate the math tags and the latex body by space, like so:

[math] |\mathbb{P}^1(\mathbb{Z}/n\mathbb{Z})|=n^3\prod_{p|n}(1-1/p^2) [/math]

>>9648130
thanks. That's the statement right anyway. Prove that.

>>9648125
Is that the usual Gamma function?

What are the angled brackets?

>>9648134
Gamma here denotes the principal congruence subgroup mod (n)

So for instance:

[math]
\Gamma(2) = \left\{ \gamma \in \text{SL}_2(\mathbb{Z}) : \gamma \equiv \begin{pmatrix}
1 & 0 \\
0 & 1
\end{pmatrix}
\; \text{(mod }2)
\right}
[/math]

>>9648134
Gamma is principal congruence subgroup mod n.

Angled brackets is group generation.

>>9648125
What have you tried?

>>9648167
I can prove that if GCD(a,b)=1 then

[math] \langle \Gamma(a),\Gamma(b) \rangle = \Gamma(1) = \text{SL}_2(\mathbb{Z}) [/math]

by tiresome demonstration that I can get the generators. There are only two generators for Gamma(1) so this is not possible for bigger values. Even Gamma(5) has 11 generators.

>>9647963
I can't read your latex, but isn't it just by definition? Studying moduli space of complex tori?

>>9648033
What's wrong about the generalization?

>>9647994
It is not an uncommon pain. Sometimes it has to be treated, see a doctor if it is still going on; recently it happened to a friend of mine, he had to take a little surgery and not fap for 1 month, he said it was hell. But at least you are not going to die. Sorry anon.
I still don't know what have you done so far, here are some exercises:

1) Let Y = V(x^2 - yz, xz-x) \subseteq A^3, show that Y is union of three irreducible closed sets (recall noetherianity), describe them and find their prime ideals;

2) assume char \neq 2, Y = V(x^2 + y^2 + z^2, x^2 - y^2 - z^2 + 1), decompose X into irreducible components;

3) Let Y = {(t,t^2,t^3) . t \in K} be the twisted cubic, show that Y is irreducible, has dimension 1 (find K[Y] and compute degree of trascendence of its quotient field, which equals krull dimension of Y) and describe its ideal I(Y);

4) consider the projective closure of twisted cubic, prove that its ideal is (x_0 x_2 - x_1^2, x_1 x_3 - x_2^2, x_0 x_3 - x_1 x_2).

If it is first time doing them they will be hard, the last more than the previous ones. Let me know if you want easier ones, equal ones, harder ones (we can move to surfaces and other stuff), hints or solutions. I'm also new to algebraic geometry, happy to know you.

>>9648214
I proved it in the end. There was just some algebra that managed to trip me up because I was insisting on plugging in (cz+d) without specifying which gamma the c and d were coming from. Plugging in the full formula with c_1 and c_2 and so on, it takes a while but it does just fall out of the definition.

>>9647755
No. I quoted exactly who I wanted to. You don't have to tell me what it is.

On a lighter note, I bought cute notebooks today <3

>>9648233
Good! Technically you should be able to prove it it terms of \gamma if you see modular forms as functions on lattices. See http://www-personal.umich.edu/~asnowden/teaching/2013/679/index.html lecture 13 (just the text below)

>>9648086
please help

>>9648322
Hmm, what is the definition of 2-vectors space? What is a basis of that space? What are the v_i that you are writing about (basis of R^?, just random vectors)?

>>9648333
the question merely assumes that the vectors are linearly independent. nothing else is given

>>9648352
That's enoght to answer then; it should be given by the first two questions I wrote (whose answers should be found in the first page of your book, and probably even in multivectors' page on wikipedia).

>>9648333
A 2-vector is a tensor of type (2,0).

>>9648352
> the vectors are linearly independent
Then it's decomposable.

>>9648387
>Then it's decomposable.
How do you decompose it?

>>9648402
Really carefully, with a lot of care and passion.

>>9648442

>>9647405
>1
This is not well-defined.

Is the category of axioms a small category or a large category?

Riddle me this one brainlets.

How engineering is not well defined but still works anyway?

>>9647994
Are you the Kyoani poster? Don't die if you are him.

>>9648873
we proved the existence of a correct definition of engineering. It's good enough

>>9649009

>>9647753
A 'Zorn's lemma' blocks your path.

>>9648033
What's a hypersurface on a curve ?

>>9647906
>"(classical)" algebraic geometry
No such thing.

>>9648873
>>9648936
Try asking the engineers themselves at >>>/sci/en/.

Can any of you guys give me an input on how you would interpret this equation and solve the derivative
[math]y = ln3x(x - 3)^2[/math]
I thought of it as [math]ln(3x)(x-3)^2[/math] using product rule but professor said it was [math]ln[3x(x-3)^2][/math] I feel like he was being stubborn and didnt want to admit he could have been more clearer writing the problem

How exactly does this imply that every finite dimensional complex division algebra is 1-dimensional?

So uh
What exactly do mathies plan to do out of college?

>>9649681
>>>>>/lgbt/eng/

>>9649591
(log3)x(x-3)^2. Id agree with you more though

what method do i use on this integral?

>>9649762
dirac delta?

>>9649685
not an answer, faggot.

Have fun working on taxes

>>9649793
>faggot
Why the homophobia?

>>9649591
>>9649762
Have you tried asking in the appropriate thread for such questions? That thread being the engineering thread >>>/sci/en/. Also try >>>/sci/sqt/.
>>9649681
Try asking in >>>/adv/ if you need advice on such matters.

>>9647362
Hey /mg/, maybe I should have posted this here rather than making a thread, but can I get a hand? I swear to god its not math homework.

>>9649695

>>9649883
>statistics
You did the right thing by not posting that in a math thread.

>>9649894
But it IS math...

I spent like, an hour and a half doing calculations and checking everything.
It was math as fuck.

>>9649950
>math
This is not well-defined.

>>9649962
Math (n.) making the numbers do things; esp calculating your father's chances of dying, also party tricks
Ex:
>Did you know e^(pi * i) equals -1? MATH!

i need a resource on proofs and theory of calculus ASAP

>>9649950
>But it IS math...
Nope. Statistics isn't even remotely related to math. Ask in >>>/sci/sqt/ or in an engineering thread.
>doing calculations
And what makes you think that engineering is somehow math?

what the highest form of math I should learn just to have knowledge of it, in college right now taking algebra 2, is that enough? not going into a particular field just want your opinion anons, i enjoy math yet it isn't my niche

>>9650032
>algebra 2

what did he mean by this?

>>9649973
>numbers
There are no ``numbers" in math.

>>9650032
the 2 was a typo

>>9650035
>There are no ``numbers" in math.
define "math"

>>9650032
anything that's not an upper division course

Was there any engineering application for analog mechanical computers ?

>>9648450
https://youtu.be/s1i-dnAH9Y4?t=19m30s
@19:30

If I travel back in time and say I can build a computer that can efficiently approximate the solution any given equation with integral or derivate, who would be interested except pure mathematicians and ballistic experts ?

>>9650125
>who would be interested except pure mathematicians and ballistic experts
Physicists, hope that answers your question

>>9650125
>engineering application
Ask >>>/toy/ or >>>/sci/sqt/. They specialize in that kind of stuff.

>>9650126
I was thinking about more precise problems. But your answer confrims some of my intuitions that finance didn't need those in the past.

>>9650127
Thank you, will try

Hey guys I'm having trouble getting the derivative of this, I just need help with the derivative of the numerator (cos^2(sqrt(Θ))

I get (2cos(sqrt(Θ))*(-sin(sqrt(x))*(1/2*Θ^-(1/2))
Would that be correct? does anyone have a good video of chain rule of triple compositions?

>>9650129
>finance didn't need those in the past.
Why not

>>9649679
What does "factors into lineal factors" mean to you?

>>9650032
number theory

>>9650152
see >>9650127

>>9648878
What's wrong with her hands?

>>9648214
My thanks for the exercises. Feeling pretty chipper today so I'll start to work on them now. (Also thanks to the other guy.)

>>9648878
>Are you the Kyoani poster?
You mean Hibikeposter? No. He also used to post exercises I think. I wish he too would come back.

>>9650334
Basically anything by the Kyoanus studio. Have fun self studying, and don't listen to these babies here. They expect someone to spoon feed them with information, and will therefore call your attempts memes if you try to do it on your own.

>>9650260
>what's wrong with her hands
She's an anime character, so you shouldn't be expecting too much. Especially since anime is of Asian origin, and Asians aren't worth much.

What are some interesting examples of provably non-pointed spaces?

>>9650334
No problem, have fun. If you have questions just ask.

>>9650155
>>9649679
I'm not sure how it corresponds to an algebra being one dimensional.

So we have this non-zero polynomial [math]f(x)=\sum a_ix^i[/math] that has a root [math]d[/math]. We can also write (WLOG, monic) as the product [math]\prod (x-\alpha_i)[/math] since [math]\mathbb C[/math] is an algebraically closed field, and [math]\alpha_i=d[/math] for some [math]i[/math]. In particular, any polynomial [math]p[/math] such that [math]p(d)=0[/math] is divisible by [math](x-d)[/math]. Now what?

>>9649762
sub z^2+x^2=z^2+z^2sin^2t

>>9650590
So you looked at an element d in your algebra.

And it turns out that d is in [math] \mathbb{C} [/math]

For any d that you take.

So your algebra is just [math] \mathbb{C} [/math]

You don't have anything else. It's one dimensional.

Is the cotangent bundle well defined for singular projective curves? If not, how do we define the geometric genus for singular curves, as in the wikipedia page for the geometric genus?

>>9650671
It is well-defined if and only if your ambient space is of finite type.

I'm going to try to stop being a socially inept loser and learn how to speak in front of others and make friends. I want to do research damnit, I don't want to limit myself because I'm too scared of teaching.

>>9650794
Good luck with that. People are scary.

>>9650794
Isn't that why the kyoani poster an hero'd? You're brave.

Inb4 "do your own hw undergrad faggot", but does anyone know how to test if large integers are prime?

My textbook doesn't show any ways to do it and google/stack exchange isn't helping. I'd ask my TA like normal but I've just been smashed by post spring break work an

Have pity on a brainlet undergrad.

>>9651228
>does anyone know how to test if large integers are prime?
I don't see how this is a question related to the subject matter of this thread.

>>9651228
>Inb4 "do your own hw undergrad faggot", but does anyone know how to test if large integers are prime?
https://en.wikipedia.org/wiki/Primality_test

>>9651228
How good a test do you need?

If you are wanting something proper then SAGE has a command to check if a big integer is prime.

If you're just using a calculator and pen and paper then do Pollard's Rho.

If you're just scratching something out then check all primes up to the square root.

>tfw.majoring in a discipline(Math) I enjoy but I have no aptitude for
>professor finds it so perplexing that I work so much harder than all the other students but don't even do better than the students who don't care or are forced to take the class
>thinks I have a metal disability
>forced to retake nearly every test I do
>everyday just feel like shit knowing I'm objectively not smart enough for this and shouldn't have stuck to it with sunk.cost fallacy back in first year
>regret falling for the do what you love meme

I don't know what I'm doing with my life
It's not fair. Why did I have to be born like this

How do I not blow my brains out? I graduated high school I was so good at chemistry and history but instead of that I chose to do Math because that's what fascinated me

Well fascination isn't enough. My brain is too fried to ever do chemistry again either after all these proofs

>>9651372
delete this please

>>9650154
why yes

I have only optimization problems in mind... Damn ! It's really hard to figure what problems pre-computer civilization had...

Are /mg/ posters the niggers who avatarfag and post cringey anime-fashwave type bullshit in other threads? If so, please stop. If not carry on.

>>9651654
>niggers
Why the racism?

>>9651671
*roodypoos
Why do you shitpost?

>>9651671
the term nigger is not racist on 4chan

>>9650631
ok that makes sense, was having a retard moment thanks

can someone show me Hölder summation in action please?

so what happened to p=np proof guy? Did he ever get his proof accepted? How come we haven't heard of him in the news yet?

>>9651789
The German guy? His proof had a mistake. He said he's working to patch that up.

>>9651654
>in other threads
Where? My personal answer depends on the location of these threads.

>>9652214
kys

>>9652267
That is not a board.

i'm a freshman at college
currently taking algebra classes
they're easy enough
i'm an engineering student and i'll have to take calculus
can any of you explain calculus to me in such a fashion that an idiot could comprehend it
not how to solve calculus problems, but what calculus does and how it applies to the real world
thanks!~

>>9652373
Reduce problems to a form where you have a set of pieces which tell the whole story. Solve the pieces and add those pieces up to solve the whole problem. This is the essence of infinitesimal calculus.

>What are you studying right now?
Probability
>Do you have or know of any interesting articles you'd like to share?
No.
>Are you alright?
No.

I am getting the right answers when I think things through, but whenever I try to apply any of the formulas or theorems given to me, I just get totally fucking whack answers. You know, it's great that I can think for myself and get the right answers, but what the fuck? What the fuck is going on here? I can't even understand what's happening right now.

I try the problem by reasoning through it. Boom. Easy.

I try the problem by applying the theorems they give me. Fucking nonsense.

Send help.

>>9652373
Rate if change.

>>9652424
Of, not if.

>>9652373
>how it applies to the real world
I recommend asking a thread titled something like "engineering general".

>>9652440
how can a mathematician not know how his logic applies to the real world

>>9652442
Don't reply to the spammer.

>>9652442
Why would a mathematician care about "logic" in the first place? And so-called "real world" "applications" are irrelevant to most mathematicians.

>>9652452
math epitomizes logic

>>9652423
>Probability
refer to >>9652440

>>9652453
Unfortunately for you, that's not how it works. Logic is a separate field of study discussed mainly at >>>/lit/ and other similar boards.

>>9652460
don't believe you

>>9652467
Mathematicians don't tend to bother themselves with the opinions of vulgar peasants.

>>9652460
Math is literally logic

>>9652471
pure math is literally the most artsy field out of stem m8
neck yourself

>>9651372
No, no, NO.

TRY A DIFFERENT APPROACH. Trust me, please.

Don't give up on shit that's hard. It's hard, yeah, but if you fucking love that bitch, you do whatever it fucking takes. Try different methods, approaches. Go to a psychologist, see what's up, maybe he opens up new views you've missed. Just try.

Success is not final, failure is not fatal. It is the courage to continue that counts.

Please don't give up anon, please don't. I fucking believe in you even if it seems impossible to you. You only fail if you give up.

Just you thinking that your brain is fried makes you believe less in yourself, which in return makes you worse at math. Just stop putting yourself down my man. Fight that motherfucker like that nigga did those snakes on the plane. FUCK THAT SHIT UP. If it fucks you up, you'll just be another one who failed and no one will care or remember it, but if you succeed, you're not another 'failed one'. You'll be remembered, you'll know you made it. You will show that you could and that you did.

you love math? make love to that bitch as passionate as you can. if she's that girl you always wanted to get but never tried/could, you fix yourself. You fix the shit that's putting you down and you go fuck that bitch and make her yours.

ANON, don't succumb to a mere state of mind, you got this.

>>9652474
Are you utterly thoughtless? How can something like this be said about a field which is completely disjoint from math? Maybe you should try discussing your "deep" insights at >>>/lit/? I'm sure they would appreciate your contributions.
>>9652476
I don't expect your kind to understand reasoning.

>>9652489
yeah dawg i just finished my second semester analysis class
my kind would not understand at all

>>9652488
What can I even do?

I work so hard already
My proofs suck. I suck .
I graduate in a year

>>9652520
How is finishing an engineering class relevant to the thread? Please take that kind of garbage to >>>/sci/sqt/ or >>>/lit/.

>>9649762
>Griffiths
Oh, the memories

>>9652524
what? who the fuck thinks real analysis is an engineering course?

>>9652527
Don't reply to the spammer.

>>9652527
Any mathematician does. Any non-retarded engineer does as well, if such beings exist, that is.

>>9652547
????????????????????
there's almost no applications outside pure math from analysis. unless you're being retarded and think calculus = analysis

>>9652547
>mathematician
Not well defined.

>>9652521
At this point, do you think of what you do just brute work or do you try and abstract what you do? Do you try to do it intuitively?

If you're just brute forcing it so you just finish it, that's the issue. I cannot tell you what to fix as I do not know. Two people may have same problems, but it does not mean that one solution will work on both. You must find it yourself, you just do.

Think. What caused the decline?

>>9652551
>there's almost no applications outside pure math from analysis
This barely makes sense in English. Try writing down your thoughts more coherently.
>unless you're being retarded and think calculus = analysis
They're the same thing as physics or psychology as far as this thread is concerned.

>>9652572
uhhhhhhhhhh
why are you even in this thread? i'm skeptical that you've even done any math outside first or second year applied courses. anywho because you're a pedant and a dunce imma just leave you to yourself and the convincing comments you post

>>9652578
>why are you even in this thread?
To discuss math, which is the thing this thread was created for in the first place.
>math
>applied courses
No such thing.

>>9652565
What do you mean decline? I was never ever strong in math. I was barely average . I just like math.

I never inclined enough to have a decline.
I'm not brute forcing . I read through very slowly I always go to office hours I try to do problems. I give it my all. Like spend 12 hours a day reading and studying for a class all.

My professor just looks so sad for me in his eyes. Man.

>>9652578
He's a shitposter, stop replying.

>>9652597
Could you point me to what exactly is wrong in any of my posts?

>>9652597
>He's a shitposter, stop replying.
I'm not a "he".

>>9652599
>Could you point me to what exactly is wrong in any of my posts?
The burden of proof is on you.

>>9652588
do you consider yourself a logical person? are you asking yourself whether or not something is true when you do it?

>>9652588
How about you speak to your professor about it? Maybe he has an idea on what's going on. I really recommend talking to someone who has experience in this, like a psychologist. Not a generic one, but one with experience. You gotta figure out why does it take you so long to process this stuff.

Think of math as your dream waifu. You're still fighting for her. You like her. She is very hard to impress and get, but giving up definitely won't win her over. Repeating the same shit, over and over is stupid, so that's why you must test other methods and ways. See what is fucking you up.

Hey guys! I'm a CS major currently, but I plan to graduate with a minor in math. I've taken all the core required courses that you'll need for any upper level math courses. I just need to decide electives.

I'm going to be taking differential geometry in the Fall, but my university has a course called Topics in Geometry offered in the Spring. I thought the course would really interest me just from the course title and I would have taken a diff.geo. course previously. However, after reading through the schedule and homework, it looks like high school geometry. Is this normal? Should I be wary? Is it even worth taking? Do other universities do this? You can find the syllabus here: http://www.pitt.edu/~sysoeva/math1290/m1290.html .

Also, if it helps, I plan on making a career out of computer vision.

As a side note, do you guys rank Pitt math?

Does /mg/ like problem books?

Pls help me on this
>>9653060

>>9652936
nah, I'm way too lazy
I can barely force myself to do a couple of the problems in a regular textbook

Can someone link me to some Putnam resources or previous problem sets?

>>9652894
Sounds like it covers axiomatic geometry. It would probably be fun and insightful but it probably won't be very rigorous. You should take another class and study axiomatic geometry on your own if it interests you.

>>9652894
Thats a proof course. Its going to be considerably harder than high school. Thats why it has intro to theory math as a prerequisite.

Also that prof seems like a complete cunt. I wouldnt take him

should you take it? if you want. not particularly useful for your major.

pitt math isnt ranked in t200 as far as im aware but once you get outside t50, it starts to blur anyway. every uni professor is an expert at their subject so its not like youll be getting a shit education

I'm learning Coq. Am I wasting my time ?

>>9653197
>Am I wasting my time ?
No, now you're actually doing mathematics, and not just writing "proofs"

>>9653197
Wrong thread on the wrong board.

>>9653265
What
>>9653256
What makes you say that? I'm still early but I question the application

>>9652597
It's a tranny, not a human

>>9653197
Make way for the superior theorem prover

>>9651654
/sci/ is /mg/'s bitch. Deal with it.

Is obstruction theory worth learning? If so, what would be a good source for someone with somewhat limited intellectual capabilities?

Is there a metric, topologically equivalent to the standard metric in [math]\mathbb{R}[/math] such that [math]\mathbb{R}-\{0\}[/math] is complete?

>>9653451
No

>>9653451
what is your definition of equivalent metrics ?

>>9653475
Define the same open sets.

>>9652936
Of course, but I would like more one with exercises for a person who already had a bit of exposure to the subject, like first chapter in Hartshorne but a tad easier and a lot more in number. This particular book is cool because it makes you prove the theory and gives simple exercises to motivate it, but most of them feel too easy as proper exercises, illegal pic related. Also, I will ask, dou you know other nice exercises book?

>>9653479
then yes, [math]\mathbb{R} - \{0 \}[/math] is homeomorphic to the complete metric space [math]\mathbb{R} \sqcup\mathbb{R}[/math]. use this homeomorphism to induce the metric on [math]\mathbb{R} - \{ 0 \}[/math]

>>9653484
nevermind, you were asking something different

>>9653439
>obstruction theory
First time I hear of this.

Ok which one of you memers was this?
>>>/lit/10964713

What are french universities like for maths?
I'm thinking of going on exchange and I wouldn't mind doing it in France but I have heard they are quite old fashioned. My current university is already pretty good so I don't really want to go somewhere a lot worse.

>>9653490
I've been bumping into the phrases "follows from elementary obstruction theory" and "an obstruction theoretical argument shows that" quite often lately. I wonder if it's worth the time or if I should just find some results and apply them when the situation permits that.

>>9653518

>>9653313
I can't read it , it's too transparent

>>9653439
>is <mathematical subject> worth learning
is a meaningless question without context.
If you have enough time, then the answer is trivially yes. Nobody knows your interests.

>>9653952
Wow! What a smart answer! Feels good to be surrounded by intelligent people.

>>9654095
At least gives us a bit more detail anon. You should do it though.

>>9653197

FUCK COQ

>>9653313
what makes lean superior

>>9654243
>>9654247
see >>9653265

>>9654254
What are you saying

Please give resources to learn Haskell

>inb4 wrong board
>inb4 learn coq instead

>>9654475
>>>/g/

>>9653367
get your own anime pics retard
i used that pic last thread

>>9654475
Refer to >>9653265

>>9654527
>>9654483
How is it the wrong board or the wrong thread?

>>9654532
It's the wrong thread on the wrong board for trivial reasons. A good reference is >>>/g/.

>>9654475
learn agda instead

>>9654567
see >>9653265

>>9654534
What is wrong with you? It's not related to g

Have any of you fags ever taken the Putnam? Was it fun. It kind of looks like it.

>>9653439
>Is obstruction theory worth learning?
Yes.

>>9654896
And what would be a good source material?

>>9654807
Don't reply to the spammer.

>>9654810
>Have any of you fags ever taken the Putnam?
Twice, it was fun both times

>>9654903
Read up on Donaldson theory, Hypercohomology, Hochschild cohomology, Cech cohomology, Kodaira-Spencer morphism, etc. These are the places where obstruction theory is useful.

>>9654931
Thanks, but I didn't ask for applications. I asked for a source.

>>9654903
Your own notes on the subject. They have to be written first, of course.

[math]\xi[/math] is a trivial line bundle. Why does the existence of a vector field imply that the tangent bundle of the manifold is a direct sum of a plane bundle plus a trivial line bundle?

>>9655102
I have none.

>>9655115
Because the Euler characteristic is 0.

>>9655180
yeah i know, but what is the name of this result, or at least, a reference i can look at?

>>9653925
https://leanprover.github.io/

>>9654247
I have never actually used coq so I was mostly claiming that to start a conversation.

The main cool thing that Lean does is that you can write automation for Lean (tactics) in Lean itself rather than a metalanguage. So for example there is a tactic `ring`, written in Lean itself, which resolves equality arguments using ring axioms.

Lean syntax seems to be cleaner than coq from what I have seen but I'm sure there are things which are nicer in coq.
Coq probably does something similar but the visual code Lean extension automatically compiles your work as you write, and gives you a list of goals and a list of things you know from your current position in a proof.

>>9655274
Coq does the same shit
You have prolog/lean we have ocaml/gallina

>>9655277
The special part is that you do it in Lean.
You only need to learn one language and it is easy to use Lean to reason about the automation you write.

>>9655258
>>9655274
>>9655277
>>9655291
Refer to the >>>/g/hetto/.

>>9655321
Have I hurt your non-constructivist feelings?

undergrad brainlet here. help me understand proofs.

is there a method you use for constructing them? i really want to go to grad school but i vant get a handle on these fuckers. and every proof i write is bloated and clumsy. i never know how much i can assume in a proof. haaalp

>>9655339
What does constructivism have to do with my post? Refer to the >>>/g/hetto/.

>>9655364
>axiom of choice
>>>/x/

>>9655375
Who are you quoting? How is the axiom of choice relevant to my posts? Proceed to the containment zone located at the >>>/g/hetto/.

>>9655380
What did he mean by this?

>>9655291

its not like there are that many resources on this stuff anyway. Should I not learn Coq? I'm sorry

>>9655533
Use the >>>/g/hetto/ if you want to discuss this.

>>9655533
Just learn it m8, I was only having a bit of fun.
You can always try them both out and see what you prefer.

>>9655540
refer to >>9655537

>>9655533
>>9655540
>>>/g/

>>9655540
I want to be a hacker cyber vegan, can you help me with that? I want to hack Shodan. I need your help.

>>9655383
>What did he mean by this?
I'm not a "he".

>>9655359
you can assume as much as they give you

the method for constructing them is to use classical logic to deduce from a series of tautologies

>>9647526
It seems to me that the biggest obstacle in AG is that there is an extremely big gap between really easy and incredibly hard, almost nothing being really in between those extremes...

>>9649190
Even Grothendieck's EGA is called "classical" nowadays.

>>9656266
How do you call algebraic geometry without schemes, i.e. affine/projective algebraic geometry as in Shafarevich I? Pre-something AG?

>>9647887
Currently in the same boat except I don't see why you feel the need to dress it up that way. You don't need to make it any more fancy than "we wuz lernin bout dem curvy curves n shiet"

Who are you trying to impress?

You're never gonna stop feeling the way you do if you keep comparing yourself to otgers and for every person that makes you feel that way a million other people just barely managed not to drown themselves in the bath tub this morning so you are probably fine.

>>9647362
Define "math"

>>9647362
>>What are you studying right now?
Math rock
>>Are you alright?
Never felt better

>>9656363
analytic geometry

>>9656363
If all you do is work over C, schemes are mostly just a middle ground you don't really directly work with. Spaces of interest will be either Varieties or Stacks.

>>9655359
One thing that helps me keep it lean it to write the assumptions, definitions, etc that I used on every line of the proof. If something is too obvious and adds bloat, cut it

>>9647362
>>9647362
hey /mg/,
>What are you studying right now?
kindergarten math :^(
>Do you have or know of any interesting articles you'd like to share?
quantum mechanics, fluid dynamics, physics in general. Need calculus though and descrite math but that requres unerstanding the fundamentals and i don't.
>Are you alright
no :^(

So here's the thing about me /mg/, i understand algebra, dscrete math, etc like the back of my hand, but i cannot for the life of me add 2 single digit numbers, and i forgot basic facts like how all even numbers are the sum of 2 primes and such. So now i'm stuck in this wierd position where i'm reviewing kindergarten math whils't fully comprehending calculus, vectors, etc.

Is there any hope for me?

>>9655533
Learn Isabell instead

Can a Hausdorff space with a countable number of points be connected?

>>9656965
I cannot give a satisfying answer to your question but each continuous real function on such a space must be constant.
That excludes many spaces.

>>9656965
Yes, see 'prime integer topology over N', namely the one you use in the topological proof of Euclid's theorem. There is a generalization of the same to rings, see Clark commutative algebra if interested.

>What are you studying right now?

Im taking third quarter complex, differential Geometry, and intro to c++. Pic related it should be my syllabus rn. We're doing riemann Roch theorem which seems interesting

>>9657401
What book are you using for diff geo?

>>9657499
We're using Walter A Poor's Differential Geometric Structures. The image is our syllabus. It's a second year class

>>9647362
Can anyone recommend a website online/Jewtube where I could learn Linear Algebra on its full expansion without a book? Thanks
T. broke fag.

>>9656835
Refer to the >>>/g/hetto/.

>>9657401
>C++
see the above message.

>>9657597
secon yead g-graduate, right?

>>9657877
I sure hope not. This is first/second year undergrad material.

>>9657877
Yes of course! There's no assignments what so ever. I'm in my senior year so it's comfy

>>9657860
It's required at UCLA to graduate as a pure math major. I had no choice.

>>9657597
https://www.youtube.com/watch?v=NpcjWwlOj8o

>>9658032
>I had no choice.
You had a choice in mentioning it in this thread.

>>9648072
[math] |\mathbb{P}^1(\mathbb{Z}/n\mathbb{Z})|=n^3\prod_{p|n}(1-1/p^2) [/math]

>>9650032
Hatcher's book on algebraic geometry should be enough, but you might need more.

>>9654911
What did you get? I got above median when I took it (I got 2 points).

>>9657401
How is the attendance for Tao's lectures compared to Garnett's? I am sure that it has at least doubled.

>>9657857
Read Axler.
Pirate it you mong

>>9658664
Yeah, the 245 TA showed up in Tao's - there are a lot of people in there just for Tao. I actually only took the sequence because I like Garnett as a prof

>>9658657
>What did you get?
I never checked

>>9649132
No need for axiomatic set theory here. There are more intuitive non-constructive existence proofs out there. For example, most proofs relying on the pigeonhole principle or the probabilistic method. Especially, many probabilistic proofs couldn't be replaced by explicit proofs, yet (for example, lower bounds for Ramsey numbers).

>>9658637
>Hatcher's book on algebraic geometry
what did xe mean by this?

>>9658793
If you haven't heard of it then clearly you have not done enough mathematics.

>>9658914
>If you haven't heard of it then clearly you have not done enough mathematics.
If you have heard of it then clearly you have not done any mathematics.

>>9658032
>Yes of course! There's no assignments what so ever. I'm in my senior year so it's comfy
Eh, a second year ug course with cohomology as prerequisite sounded too strange, but then there are some crazy universities out there. No assignment is ok, but don't forget to do exercises!

>>9658975
>Eh, a second year ug course with cohomology as prerequisite sounded too strange
Yeah, that's pretty strange. It's like listing the ability to read as a prerequisite.

>>9658793
Are you sure that you don't mean Hatcher's "Algebraic Topology" or Hartshorne's "Algebraic Geometry"?