/math/ general - Archimedean solids edition

>>9008223
>An armistice in the great animeposting debate has been formally established.

The avatarfags killed themselves?

how do i get good at math? i barely passed any of my math classes in high school and that was ten years ago

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>>9008223
Platonic solids > Archimedean solids.

>>9008592
Their imperfections and more subtle symmetries are what make the archimedean solids beautiful

Exercise time:

Let [math] I [/math] be an ideal in a ring [math] R [/math] and let [math] M [/math] be a module over [math] R [/math].
Then [math] {\textstyle M}\diagup_{IM} \simeq M\ {\otimes}_R\ R\diagup_{I} [/math].

>>9008596
No.

>>9008618
do yr own homework brainlet

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>>9008623
This is [math] your [/math] homework buddy. I finished my PhD last year. I only correct homework now.

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>>9008626
You've done a PhD and can't offer anything more interesting than what looks like babby's first exercise out of atiyah macdonald?

>>9008631
I offer exercises appropriate for the level of this general. Every time I posted more difficult exercises in the past they went by unsolved (unless I posted the solution myself)., so...

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>>9008632
>. Every time I posted more difficult exercises in the past they went by unsolved (unless I posted the solution myself)., so...
Sounds like you should be picking more interesting problems then, I'd guess there's plenty of more advanced people in /math/ than myself and I was doing problems like that 3 or 4 years ago

>>9008626
are you a post-doc?

>>9008626
Not the guy you are replying to but I like your posts. That said, I am a filthy sophomore who aspires to be a doctor. How is life as a doctor in mathematics? What do you do irl?

>>9008249
you do more math

>>9008645
>What do you do irl?
it looks like he posts anime on 4chan while attempting to be condescending

I am looking at this math exchange question:
https://math.stackexchange.com/questions/2058905/limit-of-complex-line-integral-over-a-uniformly-convergent-sequence-of-curves

but I want to find that statement as a theorem somewhere in some book. I suppose that if it was a problem then it must be true, but the comments suggest that the problem is not being stated correctly, and then they are vague about how a proof would go. Does anyone who know complex analysis have a reference for this?

I don't necessarily want a proof, I just want a reference to the problem in some book so I can see it stated properly at least.

>>9008657
>it looks like he posts anime on 4chan while attempting to be condescending

I see absolutely nothing wrong with that. Plus, you were the one who was condescending first by assuming he was posting homework problems.

>>9008641
Ok big boy: let [math] F [/math] be a field, [math] p \in F[x] [/math] irreducible, and denote [math] F_p = \frac{F[x]}{(p)} [/math]. Prove that [math] \frac{F_p}{F} [/math] is étale [math] \iff p' \neq 0 [/math].
>>9008645
>How is life as a doctor in mathematics?
Full of sorrow.
>What do you do irl?
Right now, "research" (i.e. I wank a lot).
>are you a post-doc?
Yeah, I have a 2 year research assistant position lined up for me starting this autumn.

>>9008663
>Plus, you were the one who was condescending first by assuming he was posting homework problems.
that's another poster

>>9008666
>Full of sorrow.
> I wank a lot
>satanic trips

What? Why is it full of sorrow?

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>>9008666
You don't have any fun construction problems? Anything more interesting than just proving when some algebraic object satisfies some property?

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>>9008223
>An armistice in the great animeposting debate has been formally established.
Hi guys, I'm new. What does this mean?

>>9008676
It means some faggots wanted to type plebbit.com but the incompetent fucks made 10 typos in a row and ended up typing 4chan.org/sci and then started complaining that people were posting anime characters... despite this being fucking 4chan of all places.

>>9008677
>It means some faggots wanted to type plebbit.com but the incompetent fucks made 10 typos in a row and ended up typing 4chan.org/sci and then started complaining that people were posting anime characters... despite this being fucking 4chan of all places.
you don't have to be so hostile to the newcomers, they'll warm up to anime eventually

>>9008685
I will be hostile to newcomers if they try to impose their cultural norms on top of ours.

We run this place. We made 4chan into 4chan.

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>>9008670
When is life not full of sorrow? (It's extremely hard to get a good position anywhere that would allow you do do anything interesting. Several orders of magnitude harder than getting into a good PhD program. Come september I will have been a glorified NEET for almost a year.)
>>9008673
>any fun construction problems?
Can't think of any on the spot. Can't be bothered to either, because
>proving when some algebraic object satisfies some property
this is what all problems reduce to in the end.

Basically: can you prove it or not you little bitch? I'm waiting.

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>>9008677
Sounds terrible, so let's all do our best to make /sci/ anime again.

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>>9008699
>When is life not full of sorrow?
When you fill up life with things that make you happy, whether it's hobbies or other people or love etc.

>Basically: can you prove it or not you little bitch? I'm waiting.
Maybe, my point is just that it just looks like a generic algebra problem I could find 1000 others like in some textbooks if I wanted to do them, those are the kind I usually skip over

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>>9008704
>my point is just that it just looks like a generic algebra problem I could find 1000 others like in some textbooks if I wanted to do them, those are the kind I usually skip over

>>9008666
If p' = 0, then p has a multiple root in [math]\bar f[/math], hence F_p is not etale over F.
If p' <> 0, then p and p' are coprime (indeed, p is irreducible and deg p' < deg p, hence they cannot have a common irreducible factor in F[x]), hence p splits with distinct roots in [math]\bar F[/math], hence F_p/F is etale.

You could have said separable. In that context, it makes no difference and more people are likely to have heard the term.

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>>9008717
Different strokes for different folks I guess

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>>9008724
>indeed

More problems:
. Let K be a finite field. Count the number of subspaces of [math]K^n[/math] of dimension k for k in {0..n}.
. Let G be a finite group such that Aut(G) acts transitively on G\{1}. Prove that G is isomorphic to (Z/pZ)^n for a certain prime p and and a certain integer n.
. Compute the integral [math]\int_0^{\infty} \dfrac{e^t - 1}{t} dt[/math] (justify every step, please, no bullshit)
. Let [math]f : \mathbb R_{\ge 0} \to \mathbb R[/math] be a surjective function. Prove that f assumes each value infinitely many times.
. Prove that the graph of the exponential function is not an algebraic set, ie. prove that there is no non-zero polynomial P such that [math]\forall x \in \mathbb R P(x, e^x) = 0[/math].

>>9008757
4th assertion is wrong as stated. True though if you assume the function to be continuous.

>>9008786
shit yeah of course it has to be continuous

Adding to the list of problems:

[math] \circ [/math] Prove the variational lemma (2huposter attempted to use something like this last thread):
for [math] u \in {L^1}_{loc}(a,b;X) [/math] where [math] -\infty \leq a < b \leq +\infty [/math], if [math] \int_{a}^{b}\phi(t)u(t)dt=0\ \ \forall \phi\in C_{o}^{\infty}(a,b)[/math] then [math] u=0\ \ (a.e.) [/math]
[math]\circ[/math] let [math] \psi , h \in C[a,b] [/math] where [math] -\infty <a<b< +\infty [/math]. show that if [math] \psi [/math] is non-negative and
[math] \frac{1}{2}h(t)^2\leq\frac{1}{2}c^2+\int_{a}^{t}\psi (s)h(s)ds [/math] then [math] \mid\ h(t)\mid \ \leq\ \mid c\ \mid +\int_{a}^{t}\psi (s)ds[/math]

7 in total should be enough ye?

>>9008757
e^t - 1 is always greater than t if t greater than or equal to zero, by looking at e^t's taylor expasion.

the integral is not bounded.

>>9008811
Fuck I meant from 0 to 1 -.- It really is summer

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When's the first (1st) annual /math/ meetup?

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>>9008677
Remember when posting anime on sci used to get you banned for 'infantile cartoons'? that mod is the reason so many people here still spazz out when you post it.

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>>9008996
>ponies
>anime

>>9008996
To be fair ponyfags deserve to be banned from here as well as life itself.

Hey guys. I will write my math test tommorow about integrals and I dont have an idea how should I do it._. I am really depressed now. perhaps somebody could help me?

I am really bad at math and this is my last test this year... when I write it well I wont fail this subject and I can go to the next class.

>>9009002
>>9009009
did seeing ponies make you go blind, causing you to miss all the anime pics?

also, this was before ponies were banned.

If I say that I am a girl nothing changes, yeah?

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>people still arguing about animeposting
I'll delete this thread and everyone inside it along with their posts

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>Proof: Exercise
>in a journal paper

>>9008659
Bump? No one who knows complex anal has seen this problem/theorem?

>>9008249
khanacademy

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>>9009238
>>9009225
>>9009218
>>9009206
>>9009203
>>9009199
>>9009195
>>9009192
>>9009188
edgy, I like it

>>9008626
>>9008673
>>9008676
>>9008699
>>9008703

Seek professional help. Mental illness will only get worse if it goes untreated.

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Why do you people need a /math/ general when math is a board-wide topic (it's in the board name)?
It makes about as much sense as /co/ having a "cartoons general" or /biz/ having a "finance general".

If there was an excess of math-related posts to the extent that mathposting has to be corraled into a single thread, that might have been a reason to justify the existence of a general, but at this point it looks like pic related is already in full effect.

May I suggest, in lieu of a general, that people simply start new threads discussing math, as and when they have interesting content to discuss.

>>9009225
The irony here being that at least one of those posts is made by someone who just attaches the same images to their every post.

:*

>>9009292
it's just a containment thread for circlejerkers, like every general

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>>9009313
Here's something that will creep you the fuck out: I barely use a reaction image once every 5th post, roughly. We might have interacted on friendlier, normal grounds in the past! Imagine the horror of that!

>>9009336
I was only paraphrasing his claim, the point being that he's made avatarfagging out to be a much bigger problem than it actually is.

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>>9009342
Hold on a second faggot: why are you so eager to elide any trace of your identity and why are you so scared of the identity of others seeping through the veil of your imagined lemming swarm utopia?
I'm not even the only guy who's posted reaction images from Hibike Euphonium, nor is Hibike Euphonium characters my only source for reaction images.

Seriously, kill yourself.

I bet the spammer is the 2huposter. He's mad that no one cares about his physics shit.

It really is the 2huposter and he really is THIS mad! Holy shit this is hilarious!

But I really need help. I can show boobs for help.

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>>9009381
Yo 2hu, why are you so upset tho?

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>2huposter got so btfo last thread that he's now pretending to be one of the anti-avatarfags

>interesting problems, theorems, proofs, textbooks, papers?
http://www.sciencedirect.com.sci-hub.io/science/article/pii/S0001870816317716
>Let [math]X[/math] be a Banach space which is either separable or does not have any
subspace isomorphic to [math]c_0[/math]. Then every operator [math] T:L^{\inty}[0,1] \rightarrow X[/math] is strictly singular.

>>9009347
those thighs tho...

>118 replies
>18 posters
Hmmm

being a pure meth addict is not healthy. pure meth heads need help. maybe a strong masculine engineer can help them.

>>9009602
that's how it goes when someone spills their spaghetti, almost all the posts after this >>9009188
are made by the >"Math" autist

>>9009347
I would have intercrural intercourse with those girls all day long. Those are legs to die for.

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>mfw every time we have a /math/ general it turns to shit at an ever faster rate
So when does the discussion about math begin?

>>9009687
>tfw /mg/ was the solution to the /math/ problem

>>9008808

>variational lemma

Are we allowed to use the fact that [math]C_0^{\infty}(a,b)[/math] is dense in [math]L^{1}[/math]?

>>9009714
You're allowed to use anything pertinent to the proof.

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Ok anon, tell us what's wrong. Did your girlfriend cuck you? Is that why you are upset? Did she cuck you with some math PhD? Physics PhD? Did the guy she cheated on you with like anime or something?

Let it all out man. If you're going to spam the thread, at least turns that into a purgative process for you. Catharsis is impossible if you bottle it up.

>>9009332
>>9009342
>>9009347
>>9009349
>>9009353
>>9009353
>>9009360
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>>9009816
pls kys

>>9009837
Why are you telling yourself to kill yourself? Was your girlfriend cucking you that much of a blow? Are you sure you want to kill yourself? We can help anon, whatever it is you decide to do.

Are you actually schizophrenic or only pretending to be schizophrenic to hide the pain in your heart caused by your girlfriend having the dick of another man inside her?

>>9009898
Were you in the room while the math PhD was fucking your girlfriend? How hard did she moan? Did you masturbate to it?

>>9009877
>>9009898
You don't have a PhD. Stop larping and kys.

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>wake up
>the absolute state of /math/
I wonder what the next /math/ will look like

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Reading "book of proof" and reading proofs on Fermat's library. I'm just warming till I start on my bachelor in a couple of months

Is everyone on stack exchange just mathturbating for everyone to see? It seems like they dont even read the question.
I literally just asked a question, clearly stating that the exercise specifically does not assume *certain definitons/properties*

first two responses:
>have you tried constructing the function using *certain definitions/properties*
>just use that the *categorical nonsense jargon* and then construct the function using *certain definitions/properties*

>>9010204
fuck, dont even get me started about physics stack exchange
>post question
>someone posts a link to another question that is not even tangentially related
>a couple of insults
>tagged as homework
>question locked

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>>9010157
>>9010240
>go on math/physics stackexchange
>"how do I show X is Y?"
>long unreadably verbose post that proves X is Y for generic non-Hausforff non-commutative X and non-compact Dedekind-infinite Lindelof Y as top answer
>"here's a 500 page PDF that talks about X for 5 pages and I'm not going to give you the page number"
>"just look at this one other question that has a link to another question as top answer rofl"
>"if X is Y then [blah]"
>"try reddit lmao"

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>half the thread just disappeared

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>check https://warosu.org/sci/thread/S9008223
>someone spamming from 8 am all the way to 4 pm
someone needs a hobby

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https://en.m.wikipedia.org/wiki/Mathematical_manuscripts_of_Karl_Marx

Theres no need for a math general. I havent seen one worthwhile post in the whole thread and it has nothing to do with a couple of retards spamming gibberish thinking they are so funny

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>>9010392
>Theres no need for a math general.
Do you not see the state of this board?

>>9010406
Whats the point in a general if no one even posts anything meaningful? Thats the kind of posts a general invites. It doesnt foster good discussion, it fosters people trying to craft their own in-thread persona and culture. Its a "hang out" place. Naturally posts in a general are going to be of a very low quality. Just taking a glance at this thread it looks like 50 posts were deleted because someone finally figured out theres a report button

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>>9010415
>Whats the point in a general if no one even posts anything meaningful?
Because occasionally there are good posts, at least better than the rest of the board, I browse this board with every thread hidden except sqt and math

>>9010432
Good for you. Even the activity in this thread is low. It would be better if a really good post had its own thread. I wont report this thread since I already posted in it, that wouldnt be christian. But it sucks ass

>>9008757
4th:
Let p be a point such that f(x) != f(p) for x > p. Then (p,inf) ) gets mapped by f into a half line. Therefore f( [0,p] ), a compact set, fills the other half line. Contradiction.

>>9010467
why

>>9010458
>Then (p,inf) ) gets mapped by f into a half line
How

>>9010491
f( (p,inf) ) is a connected set lying in R \ { f(p) }.

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Could you please give some advices about "how to Galois group" for a novice? Thank you for your response, anon.

>>9010494
where does it say f is continuous

>>9010501
here >>9008789

>>9010506
Even if the image is connected, why do you assume it is a half line instead of a bounded interval. If it was half open half closed then the compliment wouldnt be compact

>>9010509
I said into, not onto

>>9010499
What about them?

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>>9010546
Some literature or guides, I suppose. Where should I start? I studied only common ideas of general groups and crystallographic groups.

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"Green's function" or "Green function"?

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>>9010661
In Russia we use the first variant lol. Фyнкция Гpинa.

>>9008757
>. Let K be a finite field. Count the number of subspaces of Kn of dimension k for k in {0..n}.

let me know if i'm in the ballpark for these first two cases? not used to thinking of vector spaces as being discrete

k=1 take the set of all possible vectors, and for each vector, remove all of its scalar multiples.

so if there are m elements, then m^n unique vectors, and each vector has m scalar multiples, so we take m^n/(m-2) vectors for k=1? m-2 because we don't want to multiply them by zero, and also we want to take out all but one scalar multiple.

k=2 then any selection of two vectors in the case for k=1 defines a 2d subspace. for each pair selected, we would need to remove all remaining co-planar vectors from consideration, so by this method we can construct a basis for every 2d subspaces and count how many there are.

* oops, i think it's m^(n-1) vectors for k=1, or something like that

>>9010709
You're not completely off, but that's not quite right either.
Counting vectors modulo multiplication is a good idea for the case k=1, but I don't think you are seeing it the right way (should you really take *all* vectors in consideration ? do all vectors have m multiples ?)

For the k=2 case, good idea as well, but there are still details to figure out (does any pair of vectors really generate a 2d subspace ?)

>>9010458
succinct (you could have explained why f([p,inf) ) lies in a half line), but correct

>>9010770
>do all vectors have m multiples ?)
not counting scalar multiplication by zero, there should be m-1 scalar multiples. i guess you'd subtract 1 for the origin too. is that what you're getting at, or are they not all necessarily unique?

>(does any pair of vectors really generate a 2d subspace ?)

i'll think more about it

>>9010770
> does any pair of vectors really generate a 2d subspace ?
If this pair is not coplanar (linear independent), you can consider this pair as a basis for a linear 2d subspace. I suppose It's correct.

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>tfw you have shit spatial reasoning
>tfw you don't give a fuck because you do combinatorics
>tfw people think your field is a meme
>tfw

>>9010887
Well yeah, but as you said it has to be a pair of independent vectors. The pairs (0,x) or (x,2x) for some vector x for example don't generate 2d subspaces so they shouldn't be taken into account

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>>9010931
> you said it has to be a pair of independent vectors
I said that they should be LINEAR independent. In case of 2d, It means, that you cant make them equal by multiplication one of them on scalar. In other words, the scalar product of them should n't be equal 0.
The pairs (0,x) or (x,2x) so will be linear independent, if x not equal to 0.

>>9008757
>the number of subspaces of dimension k
1, up to isomorphism.

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>>9008757
>integral
I get the answer in a sum form (picrelated). But I need to think how to calculate this sum.

>>9010937
>In other words, the scalar product of them should n't be equal 0.
two vector are collinear if and only if their scalar product is equal to the product of their norms. 0 means orthogonality.

>>9011021
Oh lol, I get It. Residue, yes?

>>9011024
Ups, I meant vector product, sorry. Angle between two vectors should n't be pi*n.

>>9011031
>vector product
n could be higher than 3. What then?

>>9011036
Okey, I think I made too many mistakes today. Let's see what wiki says.
So, firstly I said the same thing:
>> In case of 2d, It means, that you cant make them equal by multiplication one of them on scalar.

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>>9011040

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https://www.youtube.com/watch?v=S-Xm7s9eGxU

>>9010937
>>9011024

seriously guys, how do you do math without knowing your definitions ? it's not that hard to keep in mind

What's up with the manbabies in these threads?

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Im studying combinatorics with Ralph Grimaldis book that is large och heavy like a fucking tombstone, does anyone know a good and less american sized book on combinatorics that specifically covers inclusion/exclusion, derangements, rook polynomials, partitions, generating functions, homogeneous and general linear recursions, latin squares and the basics of graph theory (i.e. graphs, subgraphs, isomorphisms, euler walks, hamilton paths, dual graphs, coloring, trees, shortest paths, minimal spanning trees, flows and matchings)?

>>9011107
Mate, you need to do the analytic continuation and use the residues. I did do that, but very probably It is the right way to integrate.

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Interesting question: let x and y be linearly independent vectors in R^2, proof they form a basis.

>>9011129
Let [math] v=(v_1,v_2) \in \mathbb{R}^2 [/math]. [math] x = (x_1,x_2) [/math] and [math] y = (y_1,y_2) [/math] form a basis if and only if the system
[math] v_1 = {\epsilon}_x x_1 + {\epsilon}_y y_1 [/math]
[math] v_2 = {\epsilon}_x x_2 + {\epsilon}_y y_2 [/math]
admits a solution for any [math] v \in \mathbb{R}^2 [/math], which happens when the associated matrix is non-singular, which is equivalent to saying that [math] x [/math] and [math] y [/math] are linearly independent.

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>>9011147

>>9011129
what is your definition of a basis

>>9010912
Are you me?

>>9008223
>what are you studying

Finite element analysis.

I had formal coursework in matrix structural analysis, but now I am expanding this knowledge to plate and shell elements.

Currently I am only interested in stress analysis, but I might expand to heat transfer or fluid flow.

>>9010887

every pair of vectors in R^n are co-planar. you mean to say co-linear.

>>9010770
>does any pair of vectors really generate a 2d subspace ?)

any pair of *independent* vectors should, which is what i meant. two co-linear vectors are not a basis for a 2-d space. that's basic stuff.

in the construction for the case of 2d, once you select a pair of *linearly independent* vectors, you have to remove all other linear combinations of those vectors (the set of vectors that are co-planar to your pair). then you can repeat the process starting with the remaining vectors.


for arbitrary k, you'd take the previous collection of vectors and select k linearly independent vectors, remove all possible linear combinations, and then pick another k vectors from the remaining set. the process is repeated until you've counted everything.

for a given k, once you select the k vectors for a sub-space, you know that there are m^(k-1) remaining vectors in that subspace.

from there it should be basic counting stuff if i understand this.

Easy challenge question: for any 3 points in the plane, not all collinear, how many lines are there that are equidistant to all 3?

>>9011532
Hard challenge question:

Show that there exist infinitely many positive integers that are not expressible in the form [math]n^2+p[/math], where [math]n[/math] is an integer and [math]p[/math] a prime

>>9011538
Brainlets beware: Analysis is scary tier:

Evaluate the following integral: [eqn]I=\int_0^1 \ln x\ln(1-x) dx[/eqn]

>>9011532

in R^2?

each equidistant line must be parallel to a line drawn between two of the three points. so two points are on one side. for any selection of two points, there is one line with the same distance from the first two and the third. so [math] {a \choose b} [/math] lines?

>>9008223
What is the best definition of an ∞-category?

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>>9011553
Extend to [math]z \in \mathbb{C}[/math] then we see that the conformal map [math]w = f(z) = \ln z[/math] maps the entire plane into the strip [math]f(\mathbb{C}) = \{z \in \mathbb{C}\mid \operatorname{Re}z \in [0,2\pi],\operatorname{Im}z \in \mathbb{R}\}[/math], which means that the preimage of the interval [math][0,2\pi][/math] is the unit circle [math]S^1 \subset \mathbb{C}[/math]. Thus we have [eqn]I_{\mathbb{C}} = \int_0^1dz \ln z \ln(1-z) = \int_{f(S^1)}dz \ln z \ln(1-z) = \int_{S^1}dz f^*(\ln z \ln (1-z)) = \int_{S^1}dz (\ln \ln z + \ln \ln (1-z)) = \int_0^{2\pi} d\phi \left(\ln(i\phi) + \ln(1-e^{i\phi})\right).[/eqn]
Pretty sure I can keep going but I got bored.

>>9011538

n^2 - (n-1)^2 = 2n-1

so the gap between squares grows linearly. isn't there also some result that states the distance between consecutive primes grows at some rate or something?

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>>9011664

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I didnt fail calculus 2 got a C!
yay me!
drinks are on me boys

now im worried about what comes next since i was close to failing
what could probability and statistics with prerequisite calc 2 be?

>>9011669

don't be a smartass

>>9011669
>Yeah. I was actually the one who discovered that.

>The more primes you have, the less new primes you need to keep making numbers

Wow, such a deep discovery. Have you checked your mail? I'm sure we already called you for your fields medal. Will you attend to the ceremony and recieve your prize, doctor?

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>>9011674
but theres already anime pics which is the same thing

>>9011669
>discovering a result from 1931

>>9011684
like, maybe 5 or 6 right now, my dude

>>9011625
im assuming you mean 3, in which case correct

>>9011644
literally wrong

>>9011656
>>9011538
hint: argue by counterexample: express p as a difference of squares

>>9011705
suppose only a finite number are expressible in that form. let m be the largest integer expressible in the form

so m = n^2 + p

pick (n+1)^2 + p.

Holy shit can you people just stfu and do math?

>>9011206
Isn't a basis V a linearly independent spanning set of vectors in V.

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that actually wasn't very hard

>>9011702
has that fag ever been right about anything?

>>9011817
Fuck you're right I won't make that mistake again.

>>9011838
if you're on a /sci/ board and pro trump you're either here for your homework help or are trolling

>>>/trash/

I can no longer report any more posts. This faggot actually paid money for a 4chan pass to spam the thread. Report his posts. Hopefully he gets permanently banned.

>>9011902
do you kiss your mom with that mouth

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>physics isn't rig-

Seeing as no one has yet solved my hard questions, here's another slightly easier one:

>Let [math]0<\epsilon<1[/math]. Prove that there are infinitely many integers [math]n[/math] such that [math]\cos n\geq 1-\epsilon[/math].

>>9012247

if this
>>9011538
was your question, it was not very hard
>>9011743

>>9012247
>>Let 0<ϵ<1. Prove that there are infinitely many integers n such that cosn≥1−ϵ.

i guess this would be the same as proving you can always make a multiple of 2*pi arbitrarily close to an integer by increasing the multiplier.

>>9012302
* considering only integer multipliers

>>9012302
>>9011743
>that are not expressible in that form

>>9012302
prove it

>>9011671
Expect continuous random variables.

>>9012319
>prove it

is that a property of any irrational?

>>9011743
>>9011705

suppose that m is the largest integer not expressible as n^2+p


then m^2 = n^2+p for some n and p

p = m^2 - n^2

p = (m+n)(m-n)

so many deleted replies

>>9012482
let's complete this

then p = m +/- n because p is prime

so that m = p +/- n

i.e. m^2 = p^2 +/- 2pn + n^2 which is not the same as n^2 + p

contradiction.

this one isn't that hard, to whomever asked the question.

>>9011553
https://www.wolframalpha.com/input/?i=integral+from+0+to+1+lnx*ln(1-x)dx

i can safely say i wouldn't have gotten this

>>9008699
Zero college debt high school math teacher here. I make $89k plus god tier health insurance and can retire in 20 years and get 2/3 my final salary.

I’m better at financial math than you even though I’m a brainlet by comparison.

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Whatever happened to that anon who claims to have proven RH or whatever?

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Touhou is dead and belongs in museums not on my math general.

>>9012597

it's already a contradiction. p is supposed to be prime, so you can't put it in the form (m+n)(m-n)

>>9008757
>. Let G be a finite group such that Aut(G) acts transitively on G\{1}. Prove that G is isomorphic to (Z/pZ)^n for a certain prime p and and a certain integer n.

could you explain some of this notation?

>>9012319
this seems related to how you can find any string in pi which Im pretty sure is an open problem

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>>9011021
What contour did you pick?
Also we could analytically continue
[eqn]\frac{1}{n!} = \frac{1}{\Gamma(n+1)} \rightarrow \frac{1}{\Gamma(z+1)} = \frac{1}{\pi}\Gamma(-z)\sin(\pi (z+1)) = \frac{1}{\pi}\sin(\pi (z+1))\int_0^\infty dt t^{-z-1}e^{-t}[/eqn]
Now the recurrence relation only holds for non-integer values of [math]z[/math] so we have to use Riemann-Stieltjes integral to pass the summation over n to an integral [math]\sum_{n=0}^{\infty} \rightarrow \int_0^\infty d[x][/math] where [math][x][/math] is the integer part of [math]x[/math].
What we have then is [eqn]
\sum_n \frac{1}{nn!} = \int_0^\infty d[x] \frac{1}{x\Gamma(x)} = \frac{1}{\pi}\int_0^\infty d[x] \frac{\sin(\pi (x+1))}{x}\int_0^\infty dt t^{-x-1}e^{-t} = \frac{1}{\pi}\int_0^\infty dte^{-t} \int_0^\infty d[x]\frac{\sin(\pi (x+1))}{x} t^{-x-1} [/eqn]
What you can do is then divide up [math][x] = x - (x)[/math] where [math](x)[/math] is the fractional part of [math]x[/math] and then do the integral with [math]x[/math] first.
Good luck.

>>9012688
Sure:
. Aut(G) is the set of automorphisms of G, ie. the set of isomorphisms (invertible morphisms) from G to itself. It forms a group under composition.
. Saying that Aut(G) acts transitively on G\{1} means that, for any two elements x,y in G different from the unit element 1, we can find an automorphism g of G such that g(x) = y.
. (Z/pZ) is the group of integers modulo p. (Z/pZ)^n is the direct product of n copies of Z/pZ, ie. it is the set of sequences of n elements of Z/pZ with addition defined componentwise (it is still a group).

>>9012597
>>9012482
this doesnt prove anything

this just shows that m^2 cannot be expressed in the form n^2+p for the SAME n and p, but there might exist some other l and q such that m^2=l^2+q

>>9011705
>>9011538
I'm just gonna answer this one cos retards cant read or understand the question

Consider integers of the form [math](3m+2)^2,
m=1,2,...[/math].

Suppose that [math](3m+2)^2=n^2+p[/math] for [math]p[/math] prime and [math]n\geq 1[/math]. Then [math]p=(3m+2-n)(3m+2+n)[/math].

Since [math]p[/math] is prime and [math]0<3m+2-n<3m+2+n[/math], we must have [math]3m+2-n=1, \;3m+2+n=p[/math].

Solving for [math]m[/math] and [math]n[/math], we get [math]m=\frac{p-3}{6},\; n=\frac{p-1}{2}[/math], so that [math]p=3(2m+1) [/math]. As [math]p[/math] is prime, we must have [math]m=0[/math], which contradicts [math]m\geq 1[/math].

>>9012646
I'm still here a couple times a day to see if anyone solved any of the problems posted or if they need some hints. And I didn't claim to have proved the Riemann hypothesis, I claimed to have found a way to prove that it is false using sheaves in [math] \mathbb{R}^3 [/math] which would allow me to construct whole regions with non-trivial zeros. It's not definitive yet and I may turn out to be completely wrong. I'm still working on it.
If I can get anything substantial out of it by the end of summer I'll write up an article on my method, irrespective of any conclusive result on the RH.

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Beside bruteforce, how could I approximate n when given M?

>>9012983
Fourier series.

>>9012987
I don't see how, care to explain please?

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https://arxiv.org/abs/1707.00282
Might extend CFT techniques to supersymmetry.
>>9012966
Sounds interesting. I await your progress.

>>9012983
We can write [math] M = \sum_{k=1}^{\lfloor \log_5 n \rfloor } \frac{n}{5^k} + \epsilon_n \log_5(n) [/math] for some [math]\epsilon_n \in [0,1)[/math].
Simplifying, we get [math]M = \frac{n}{4} - \frac{n}{4\cdot 5^{\lfloor \log_5 n \rfloor}} + \epsilon_n \log_5(n)[/math]. Finally, since [math] 1 \le \frac{n}{4\cdot 5^{\lfloor \log_5 n \rfloor}} < 5[/math], we get [eqn]\frac{n}{4} - \frac{5}{4} < M < \frac{n}{4} - \frac{1}{4} + \log_5(n)[/eqn]

>>9011553
First use power series expansion on ln(1-x) (legit since we are integrating over [0,1) ):
[eqn]I = \int_0^1 \left(\sum_{n \ge 1} \frac{(-\ln x) x^n}{n}\right) dx[/eqn]
We are integrating a nonnegative function so we may use Tonelli's theorem:
[eqn]I = -\sum_{n \ge 1} \frac{1}{n} \int_0^1 x^n \ln x dx[/eqn]
Now, we compute the inner integral separately.
Integrating by parts, we get:
[eqn]\int_0^1 x^n \ln x = [x^n(x\ln x - x)]_0^1 - n\int_0^1 x^{n-1}(x \ln x - x) dx = -1 - n \int_0^1 (x^n \ln x - x^n) dx[/eqn]
Putting two and two together, we realize that the same integral appears on both sides:
[eqn](n+1)\int_0^1 x^n \ln x dx = -1 + n\int_0^1 x^n = -\frac{1}{n+1}[/eqn]
Finally:
[eqn]\int_0^1 x^n \ln x dx = -\frac{1}{(n+1)^2[/eqn].
Reinjecting in the previous expression, we get:
[eqn]I = \sum_{n \ge 1} \frac{1}{n(n+1)^2} = \sum_{n \ge 1} \left(\frac{1}{n(n+1)} - \frac{1}{(n+1)^2}\right) = 2 - \frac{\pi^2}{6}[/eqn]

>>9013032
beautiful

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Mathematics majors have the highest average age when it comes to losing their virginity. Why are mathematicians so pure?

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>>9013637
Wow, I never thought of life like that.
Using age of the first time you had sex as some form of measurement of a person.
I feel so enlightened.

But srs, what makes someone who lost there virginity at 16 so different than someone at 18?

>>9012966
>prove that it is false
Do just want to set the number theory on fire or what? How many thousands of papers would just get BTFO'd at once?

>>9013648
Found the soiled one.

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>>9013637
>Mathematics majors have the highest average age when it comes to losing their virginity.
Really? There were around 10% girls in the math classes of my old undergrad and 1% girls in the physics classes.
Really makes you think doesn't it?

>>9013637
Because they're losers.
It isn't a surprise they're also anime faggots.

>>9013729
The key to your puzzlement is that you're not obliged to have intercourse with the members of the concave sex attending your classes.

>>9013730
Oversexed math majors turn into philosophy majors which turn into baristas.

Nofap masterrace.

t. Former neet Phil major

http://www.gnxp.com/blog/2007/04/intercourse-and-intelligence.php

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>>9013787
>concave sex

One requirement to graduate from my uni is to take 6 analysis classes starting right away when you get there as a freshman.
I'm starting in August !5th but in reality I'm not super good with proofs and I can't tackle Baby Rudin.
How fucked am I and what should I do to avoid getting buttfucked when I get there?

>>9013898
holy fuck thats a lot of calculi

>>9013921
Ik, intro to RA, more RA the next semester, Measure Theory, Complex Analysis and finally Functional Analysis

>>9013787
Exactly, go pump and dump a bunch of slutty gender studies majors who aren't going to amount to anything anyway.

You don't have sex with the female math/physics majors, those are the girls you marry.

>>9013898
>>9013928
Where in the hell do you go, ENS? Cause if it's measure theory at the level of Folland then that's not typically an undergrad class. If you want to get better at proofs there are books like polya that can help you, after that Tao is pretty easy to handle, you could also do rudin just make sure to thoroughly understand the proofs, keep note of how the theorems are used, the techniques used there will be the same techniques used to solve the problems. After that Barry Simon's new 3500 page analysis series covers all the analysis you'll ever need, even basic real/complex analysis at very easy (but in depth) level

>>9013977
I don't know for sure how in depth the courses are going to be, I just spoke to some other students I met while I was looking the uni.
I'm not going to ENS but I applied for the top program in my country without hope of getting accepted but somehow I passed the examinations.
Quite a few from here have been accepted into PhD programs at ENS, Polytechnique, Princeton
I feel I'm not smart enough to be there ;_;

>>9014070
Classic case of impostor syndrome anon, look, if you got in that means chances are you're good enough, provided you keep diligently working to improve, even if the examination was a fluke you can improve. My advice would be to email the instructor of the course and ask what sort of material will be covered in the class a few months prior so you can prepare, that way at least even if the pace would normally be too much for you you'll be able to do well in the class. Plus don't stress about some students going to Princeton for grad school, those kind of students are at every school, they're also usually the most passionate and hardworking individuals there, if you work just as hard you'll probably also get pretty far. it's been working for me. If you really find that proofs aren't your thing I'd also suggest for you to check and see if your uni has any proof methods courses and try and read the material for that class. If it doesn't there are other universities with proof courses and look at the books, notes, and problems sets provided by the syllabus and website like

http://www.math.ucla.edu/~heilman/teachingMPP.html
https://www.math.princeton.edu/undergraduate/course/mat214/
https://math.berkeley.edu/~hutching/teach/proofs.pdf

These may also help
https://mathoverflow.net/questions/62629/textbook-recommendations-for-undergraduate-proof-writing-class
https://math.stackexchange.com/questions/38854/basic-book-about-mathematical-proofs
https://math.stackexchange.com/questions/166603/book-for-proof-writing
https://math.stackexchange.com/questions/62212/good-book-for-self-study-of-a-first-course-in-real-analysis

There's more stuff out there as well to learn proofs or for easy analysis texts

Algebraic geometry is the best!

>>9014470
but what is it?

>>9013977
Not him, but I had 7 obligatory analysis courses during my undergrad: 3 general calculus/mathematical analysis courses, a real analysis course, a complex analysis course, a functional analysis course and a measure theory course.

I imagine it's the same in every other country that follows the French model..
The difference is made up by the fact that you get a lot less elective courses. Overall you finish your undergrad with a more rounded overview of mathematics compared to American universities.

>>9014649
>7 obligatory analysis courses
Correction, 8 courses. I also had to take an obligatory numerical analysis course.

>>9014649
What uni do you attend? We might be going to the same uni

>>9014649
>>9014652
By "3 general calculus" do you mean at the level of american uni calculus? Also what level for the real, complex, functional, numerical, and measure theory courses (like, what kind of books? Folland? Rudin? Conway? Ahlfors)? Just curious. I actually really love the french style of teaching mathematics, I was really mad when I found out that ENS has a program for international 2nd/3rd year students to apply to study there and I was half way through my 3rd year.

>>9014658
>By "3 general calculus" do you mean at the level of american uni calculus?
If the calculus courses from American universities available on youtube are any indication, my courses were a lot more theoretical. Slightly higher level I'd say.
>>9014657
Unlikely. I graduated in 2012.

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How many more decades/centuries until we have even a moderate understanding of L-functions?

>ENS
there are people here who seriously think they had a shot at getting in?
I'm impressed. you're either really smart or really gutsy.
it's by far the most selective university in the world.
MIT, Princeton, Harvard, Cambridge you name it: these are brainlet-tier compared to ENS. is doing research as an undergrad mandatory at any of those other schools? no? if you want to get your diploma from ENS you'll have to publish as an undergrad.
and, since you're expected to publish, you're also paid a monthly salary (on paper you're actually an employee). or in short, the ENS math department treats its undergrads as if they were doctoral students.
unsurprisingly, there are less than 50 students per year in the math department.

It's not for nothing that it has the highest number of physics nobel laureates and Fields medalist per alumnus in the world. seriously, the ENS is scary.

>>9013011
OK, but doesn't that give me an approximation of M knowing n? What I'm looking for is n = f(M).
Of course some information is lost due to the flooring, but there may be a way to extract a value of n +/- 2.

For instance, with n = 256, we have M = 63. So we'd have f(63) = 257 +/- 2.

>>9014928
I'm well aware how difficult ENS is, people always talk about math 55 without realizing that every course at ENS is more difficult than that class, but that sort of difficulty makes it very attractive, at least to me, since I really love spending a solid 7-8 hours a day doing math the prospect of being taught by those who have a deep understanding and love for field while also being surrounded by similarly driven people, being pushed to excel, how does it not sound exciting? The idea of publishing doesn't turn me off, if anything that makes it even better, I've been working as a researcher for about a year and a half and have actually been able to publish results in pretty good journals, is any of it at the level of ENS students? Probably not, but I still imagine it to be quite an amazing place nonetheless, and somewhere I'd like to visit, at least once, just to see the place where great talent is breed.

>>9014945
Continuing from
>>9012987
>>9012990
You'll have to go in circles for a bit.
[math] \lfloor \frac{n}{5^i} \rfloor = \frac{n}{5^i} - frac(\frac{n}{5^i}) [/math]
The trick is understanding that the fractional part of a number is a periodic function, and any real periodic function can be expressed as a trigonometric Fourier series.

You rewrite [math] M [/math] in terms of that series, and invert it the result to obtain [math] n [/math] in terms of [math] M [/math].

>>9014970
>tfw Gibb's phenomenon

>>9014928
>if you want to get your diploma from ENS you'll have to publish as an undergrad.
No you don't (besides, it doesn't deliver a diploma anyway). Students are required to study some advanced topic in-depth in their first year there and produce some sort of synthesis, but it's not like actual research. I mean it's really a great school but there's no need to spread myths.
It is also not really an undergraduate uni. They recruit their students at the end of the undergrad cycle and teach them everything they have to know in a semester or so in order to move on to the grad classes as soon as possible. It really is conceived as a grad school that happens to have undergrads attending.

>>9014999
>They recruit their students at the end of the undergrad cycle
This is not true. Some of the international students attending have already finished 1 or 2 years as undergrads somewhere else, but as a rule you only need to have finished high school (most students have attended a CPGE after high school though).
>It really is conceived as a grad school that happens to have undergrads attending.
This is true and exactly my point, in terms of intellectual intensity, otherwise it's an undergraduate. The ENS also has a graduate school for masters and doctoral students.
>it doesn't deliver a diploma
This is false.
>Students are required to study some advanced topic in-depth in their first year there and produce some sort of synthesis
I'm talking about the whole cycle, not just the first year.
>it's not like actual research
Actually, it is.

>>9014998
Here that's only a problem when n is divisible by 5, which you can treat separately.

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>>9013637
>Why are mathematicians so pure?
Nice one. I'm going to use this next time someone asks me why I don't have a girlfriend.

>>9013637
To master the topics of mathematics one must not waste his libido, the main source of willpower into vain pleasure games like sex. Is the power of virginity that gives us the drive to succeed.

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How do you know when to be really satisfied with a proof?

https://en.wikipedia.org/wiki/Grunwald%E2%80%93Wang_theorem

>Grunwald (1933), a student of Hasse, gave an incorrect proof of the erroneous statement that an element in a number field is an nth power if it is an nth power locally almost everywhere. Whaples (1942) gave another incorrect proof of this incorrect statement. However Wang (1948) discovered the following counter-example: 16 is a p-adic 8th power for all odd primes p, but is not a rational or 2-adic 8th power.

>Some days later I was with Artin in his office when Wang appeared. He said he had a counterexample to a lemma which had been used in the proof. An hour or two later, he produced a counterexample to the theorem itself... Of course he [Artin] was astonished, as were all of us students, that a famous theorem with two published proofs, one of which we had all heard in the seminar without our noticing anything, could be wrong. - John Tate

Consider x = sqrt(2)
Therefore x^2 = 2 and (x^2) - 2 = 0
According to the rational root theorem, this has the following possible solutions: 1, -1, 2, -2
None of those satisfy the equation above, therefore the sqrt(2) is irrational.
Is this a legitimate proof that sqrt(2) is irrational or am I making a weird assumption?

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>>9015127
>Is this a legitimate proof that sqrt(2) is irrational
yes

>>9015136
How come this method isn't used to prove that a root is irrational?

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>>9015147
>How come this method isn't used to prove that a root is irrational?
But you just used it?

You can prove it from scratch without appealing to other theorems though, which is probably why it's not the most common proof

>>9015154
I see. Thanks for the clarification.

>>9015011
>This is not true.
Dude I study at an ENS (not *the* ENS, but I also know a bunch of people there) and I can tell you no student there got in after high school. There have been exceptional instances of extremely bright students who got in after a year of CPGE, but it's a one in a decade type of thing. The curriculum is clearly designed for people who already have a solid grounding in linear and bilinear algebra, real analysis, topology and ODE at the level expected of the best CPGE students. It's not just a matter of being bright enough, it's also about knowledge and technique. Of course, nothing keeps you legally from taking the entrance exam at the end of high school, but chances are you wouldn't even understand what it's about.

>otherwise it's an undergraduate.
I'm not sure I expressed myself very clearly but what I meant is that it really is a grad school (especially at the ENS Paris, where most students start their masters in their first year).

>This is false
Yeah, not sure about that one, but at least until very recently it didn't.

>Actually, it is.
Okay, my bad, that's right. But my point was that you don't *have to* produce original research in order to graduate. Some students might, it might even be typical for a cohort to have a bunch of its students to produce original research by graduation, but it's certainly not a requirement.

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http://empslocal.ex.ac.uk/people/staff/mrwatkin//zeta/physics.htm
>number theory and physics archive

>>9015297
>I'm not sure I expressed myself very clearly but what I meant is that it really is a grad school
No. Formally it is an undergraduate program. The Licence program is equivalent to a Bachelor's degree within the Bologna system. It's just way more advanced and geared on research from the get go.
>I can tell you no student there got in after high school.
I know that. Not of those currently enrolled in any case.

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>>9015113
>How do you know when to be really satisfied with a proof?
When you understand it.

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*sips tea*

http://www.math.harvard.edu/~gaitsgde/GL/

>>9015941
>Not reading Lurie's thesis
Ya gotta read the classics anon

Any undergrads in REUs or summer seminars here? I've got one lined up in August but I have no idea what to expect.

>>9016225
I'm going to one about Toric Varieties

>>9015954
Lurie is not the only approach to derived geometry

>>9008677
I chuckled controllably while reading this

>>9016235
>algebraic geometry

Been trying to avoid that for as long as possible because I'm a brainlet. Mine's on knotted surfaces in 4-space.

>>9016255
Toric geometry is a bit different from standard algebraic geometry. Very combinatorial.

>>9008223
I'm not very good at a field theory, is the algebraic closure of a field an extension of its perfect closure?

>>9016308
Yes. If your field has characteristic 0, then it's already perfect, hence it is its own perfect closure, hence the claim is obviously true.
Otherwise, you have to realize that the perfect closure is an algebraic extension (you add all p-th roots, then do it again, and again, infinitely many times and taking the increasing union, you get the perfect closure, which is a compositum of algebraic extensions)

>>9016255
What were the prereqs for your REU?

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EUDOXUS > EUCLID > ARCHIMEDES

WHEN WILL YOU GUYS LEARN!

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>>9016773
>[math]\mathbb{R}[/math]
No such thing, anon.

>>9015824
So you're never satisfied with a single proof?

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>>9016820
Yeah but I am satisfied with multiple proofs.

>>9012646
Why would anyone claim to have proven something false?

>>9008757
>[math]\mathbb{R}[/math]
Anon, there is no such thing.

>>9013655
Maybe they'll just find a weaker but true form strong enough not to obliterate countless well-established theorems?

>>9016899
>well-established theorems
How can these """theorems""" be ""well-established"" if the Riemann hypothesis is obviously false?

>>9008757
If i only know how to do adding and subtracing and a little multiplying how long will it take me to do these kind of problems?

>>9016930
[math]|\mathbb{R}|[/math] seconds

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>>9016940
>[math]\mathbb{R}[/math]
No such thing.

>>9016911
clearly it's not obviously false, even if it turns out to be false

>>9016952
It's actually pretty obvious if you think about it. A lot of people already know, it's just that nobody has bothered to write it down yet.

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>The axioms of a 2-DMF's and rational 2-DMF's look pretty complicated. It is by no means clear that they define interesting objects worth any serious attention.
Top kek.

>>9016955
[citation needed]

>>9016964
No one has bothered to write it down. We're waiting for the brainlet who thinks he's the first one to solve it.

>>9016956
>Top kek.
Kill yourself.
>>>/b/

what is math even good for?

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>>9016970
Calm down autismo.

is it true that 23 is a special number?

>>9016977
Yes.
4,8,15,16,23,42 are all cursed numbers.

>>9016971
absolutely nothing

>>9016979
Wow those are all Numberwang.

does gematria count as math?

>>9016968
can you stop being a fucking gay retard niggerfaggot for a second

>>9016975
>reddit frogs
Kill yourself, retard.
>>>/b/

>>9014970
Thanks, I'm starting to understand where this is going.

Isn't it a problem that [math] frac(\frac{n}{5^i}) [/math] will always be in {0, 0.2, 0.4, 0.6, 0.8}? Is that periodic enough?

(I'm obviously not very fluent in math yet, but this can be fixed)

>>9017027
>but this can be fixed
Probably not.

>>9017032
R E K T

>https://en.wikipedia.org/wiki/List_of_savage_centers_in_the_Savage_States

r/bestof here we come!

>>9017037
>R E K T
>r/bestof
>>>/b/

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>>9017008

>>9017051
see >>9017008

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what books do i need to read to understand this?

currently reading Elementary Lingear Algebra, Discrete Mathematics and Intro to Abstract Algebra. would into to number theory be needed too?

>>9017077
some algebraic number theory wouldn't hurt

eisenbud's commutative algebra is literally designed to cover the algebra background for hartshorne

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>>9017054
I'm not familiar with the site, what other memes are from reddit?

>>9017077
Why do you want to ? Did you fall for the hype as well ?
Anyway, you will need some (but that much) topology and a lot of commutative algebra to understand the arguments. To understand the motivation, you might want to read a book on Riemann surfaces or algebraic number theory concurrently

>>9017097
see >>9017008

>>9017081
oh i was talking about like basic number theory, like Elementary Number Theory: Primes, Congruences, and Secrets. i'll look into eisenbud's commutative algebra though. im only a 1st year so my current knowledge is fairly low.
>>9017098
yeah pretty much. it seems pretty popular among grad students and im not a math major, but i wanted to get my mental faculties in order to grasp gradual level concepts pertaining to algebra and some implementations of dedekind cuts to it possibly.

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>>9017108
if you want the ultimate babby-tier AG book that you could already start working through, take a look at pic related

>>9017112
thanks i appreciate it. is it enough that i know calculus I and some linear and discrete (relations,induction)

>>9017116
for the start of the book at least, yes. whatever else you're missing is introduced through the text so it's pretty self-contained (it's on libgen too if you want to dl it)

>>9017119
yeah that's where i got it. it was just a regular version not the late draft. is there a big difference?

>>9017125
>is there a big difference?
probably not (i used the regular version)

>>9017077
Just use Cox lmao

>>9017130
?

>>9017139
Maybe he means "Ideals, varieties and algorithms" idk

>>9017195
oh wait he also has a book "Using Algebraic Geometry" which is probably more suited to the topic at hand

>>9017077
Ravi Vakil's online notes are very good as well, you might want to try them out, they're free online here http://math.stanford.edu/~vakil/216blog/index.html

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what math books make for comfy reads?

pic related

>hey

>always wanted to math
>same with my friend
>doing soft dev as a backup plan
>get internship in big tech company
>when i say i am gonna be a math major everybody laughs but as soon as i am also focusing on soft dev i get "good thinking"
>wtf why is this happening
>go back to school
> friend is still working on math degree.
> i take more soft dev oriented classes as well as upper math classes
>time to decide to do grad or job
> my grades are phenomenal and i have professor recs but i have no money.
> i have a gf and need money to establish myself
>best friend is in same situation
> i decide to look for jobs he goes to grad school
>calls me a brainlet pussy
>5 years later
>senior engineer with 6 dolalrs figures
>wasnt easy
>married to gf
>have nice car and nice house in nice city
>go to school to apply for masters
>find friend he doesnt say hi.
>find out through people her gf broke up with him and he has free college but does not really life.
>barely any money left after fellowships and scholarships
>he works at burger king ad a side job
>finally talks to me
> he says he is about to get his phd
>but he has to wait more years to get tenure
>calls me a quitter
>i ride away in my 2017 susuki
>he walks home in the rain
lmao

>>9017077
All you need is basic Topology and Commutative Algebra.

Atiyah-MacDonald is good resource on commutative algebra.

>>9017543
> he says he is about to get his phd
Nice! Send him my regards next time you meet him

When is it /too late/? I'm 22 and don't know a lick of real anal yet, and won't graduate until 24-25. I've recently began studying math in my liesure though, and enjoying it, so I expedct I will be vastly ahead of my classmates who only studied the required material. I know my only chance of making it is to double, or even triple, down on my study time and intensity.

Will I ever get live the /comfy/ life of Perlememe, with my time spent mainly sutdying?

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>>9017582
Forgot pic.

I know I won't ever be as recognized, but it's the lifestyle I'm after.

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>>9017543
Your friend sounds like my type of guy. I'd definitely do hormone therapy and chop my dick off for him.

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>>9017582
>>9017586
It's never too late to become a bohemiathematician. Come, join us in the Kingdom of Mathematical Heaven!

>>9017582
if u havent finished real analysis and algebraic structures by sophomore year with an A, you ll just be a waste of space in th4 math world

>>9017604
>>9017574
yeah he is fun yo hang around. always acting nice. He showed me how my life would have evolved if i had chosen to go with what i love rather than money.i left 100 dollars on his doorstep at the dorms he lives. Hope he is able to eat something now.

>>9017623
The way I read his posts, he doesn't seem to be looking to become a professional mathematician.

>>9017626
so? why do any math if you cant dominatr the most basic concepts in undergrad?

>>9017630
For the pleasure of it. Every chunk of math you understand is a message from God. Not everything needs to be a contest. Especially not math. God has enough love for everybody, the extent of His Words is vast and deep.

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>>9017604
And here I was thinking the math general was full of autists like me but the anime posters are just sexually roleplaying homos....
Just another day in my life.

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>>9017643
>he uses the term 'autism' ironically

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>>9017658
Do you think you know what true autism is about?
When was the last time you suddenly started rolling on the floor trashing yourself out so much your mother had to help stop you from hurting yourself?

>>9017665
You're not autistic. You're an attention whore.
Only replying since the thread is close to reaching bump limit.

>>9017643
>he hasnt realized anyone that likes math is the most unlikable person
face the truth now and save yourself soem headdaches

>>9017672
No, you're an idiot who uses the term ironically ironically. And it is funny to read this coming from someone who was playing with avatars just hours ago, and also misusing the quotation function.

>>9017676
Here's your (you).
(I never avatarfag.)

>>9017642
Ramanujan is that you?
Anyway what you said is beautiful.
Wish i could IM you or contacr you somehow. I need guidance. I am lost

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None of you are alltists, because alltists don't recognize they're alltists. It's usually politically motivated idiots who get into this kind of "i have a genuine mental condition" "no i".

>>9017672
>>9017658
Do you have autism?

>>9017684
the fuck are you talking about

>>9017689
I want answers.

>>9017623
So what, if I'm off your arbitrary schedule by 365 days I'm screwed? I'm positive I'll get an A in that class, I just haven't taken it yet.

>>9017626
All I want is to be able to study all day. Is that being a "professional" mathematician? Or is that being a hobbyist mathematician?

>>9017672
https://www.youtube.com/watch?v=yTU8WbTbZMI
Does this kid look like an attention whore to you?
Literally sperging out is one of the symptoms.

>>9017687
I'm just going to recycle what I said in another thread:

There is no such thing as autism. It's an outlier phenotype where certain traits are pushed to extremes. To say there is something sui generis about people with "autism" is the same as saying there is something sui generis about very tall people, or very fast people, or people with very big hands and so on. Autism is nothing like gigantism even.
Autism is largely not functionally impairing except when it is "co-morbid" with a low IQ, suggesting that the impairment autistics suffer is not due to autism.

>>9017696
He looks like a retard.

>>9017700
Just like you then.

>>9017698
Answer the question. Why are you avoiding it?

>>9017692
lmao u ll be nothin in math. NOTHiNG. I alreafy did grad courses in sophomore.

>>9017705
I already answered. There is no such thing as autism. I am merely extremely introverted, extremely disagreeable, extremely curious, and mildly neurotic.

>>9017719
Nice blog.
Where can I subscribe?

http://escholarship.org/uc/item/1zk1g4c0#page-1

"Research suggests studying personalities of individuals with Autism Spectrum Disorder (ASD) could give insight into the heterogeneity that exists within ASD. The present study aimed to: (1) determine the extent to which the Five Factor Model of Personality (FFM) and its facets account for variability in ASD symptomatology (2) verify differences in average FFM personality profiles of adults with and without ASD and (3) to identify distinct behavioral phenotypes that exist within ASD. A sample of 828 adults completed an online survey consisting of an autism diagnostic questionnaire (RAADS-R) and an FFM personality questionnaire (IPIP-NEO-120). Results indicate that IPIP-NEO-120 facet scores account for 70% of the variance in RAADS-R scores. Neuroticism positively correlated with RAADS-R scores, while Extraversion, Openness to experience, Agreeableness, and Conscientiousness negatively correlated with RAADS-R scores. In addition, four distinct FFM personality subtypes emerged within adults with ASD based on k-means cluster analysis."

>Results indicate that IPIP-NEO-120 facet scores account for 70% of the variance in RAADS-R scores.

>online survey
Yeah because everyone is so honest with themselves on those online tests. They're really reliable, and it is definitely worth the risk basing serious medical research on what someone you don't know you can trust tells you on a report.

>>9017735
There is plenty of corroborating research. Baron-Cohen is increasingly leaning in the same direction. Help put a nail in the coffin of the autism myth: https://maths.autismresearchcentre.net/