/mg/ - maths general

[Anonymous No.10512418]

/ourguy/ edition

Previously >>10494757

[Anonymous No.10512448]

>straight line
>straight line
>CURVED line, WOW
>just a bit more curved line

This always disappointed me. I wish higher degree polynomials did some more interesting stuff than just become more squigly. Odd complaint perhaps, but seeing how radical the change from a straight lined to a curved one is (in my own mathmatical intuition), the line just being curved in different directions seems to be quite dull.

[Anonymous No.10512453]

>>10512418
>Zhu Xiping
isn't he the chairman of china

[Anonymous No.10512463]

What happens when they finish math? Do you guys have a plan B career or...?

[Anonymous No.10512485]

[Anonymous No.10512498]

>>10512453
No, he's one of the guys who made an absolutely risible attempt at stealing Perelman's proof.
>>10512463
I'll work on figuring out how finishing math was possible.

[Anonymous No.10512499]

>>10512485
Yeah, but [math] \zeta : \mathbb{C} \setminus \{1\} \to \mathbb{C} [/math]

[Anonymous No.10512513]

>>10512498
>I'll work on figuring out how finishing math was possible.
All done. Don't steal my proof.

[Anonymous No.10512526]

>>10512499
I'm not sure what you mean.

[Anonymous No.10512542]

>>10512418
What *is* function space [math]Y^X[/math]?

I get that its points are maps [math]f:X \rightarrow Y[/math] and it has the compact-open topology. But is there a way I can "see" it? I know how to visualize product spaces, quotient spaces, etc. But for function spaces, I can't make sense of even a simple example like [math]I^I[/math].

[Anonymous No.10512545]

>>10512526
[math] z_0 \notin \mathbb{C} [/math].
You claim it is; let's look at the definition:
[math] z_0 = -(\widehat{\infty} - b) + iy_0 [/math] where [math] b, y_0 \in \mathbb{R}_0 [/math]
Sure, but any [math] z_0 \in \mathbb{C} [/math] can be expressed as [math] a + bi [/math] where [math] a, b \in \mathbb{R} [/math].
Can you provide a bijection from your structure (basically [math] \mathbb{R}_0 \times \mathbb{R}_0 [/math], let's call it [math] \mathbb{C}_0 [/math]) to [math] \mathbb{C} [/math]?
I suspect you'll have some trouble here.

[Anonymous No.10512549]

>>10512542
Reminder that "maths experts" can't even tell you how big [math]\{0,1\}^\mathbb{N}[/math] is. You think they understand bigger spaces? Lmao

[Anonymous No.10512567]

>>10512542
It's a space whose points are "slices" along X x Y, and it's topology is made by taking all K x U, where K is compact in X and U is open, and then topologizing Y^X by taking a base of "slices" contained in K x U.

[Anonymous No.10512568]

>>10512513
Proof assistants "finish" math in the same sense that assembly lines finish engineering.

[Anonymous No.10512572]

>>10512545
I don't know what you mean by "your structure."

Do you agree that "z" is a complex number if and only if "x" and "y" are two real numbers and
z = x + iy ?

It's seems like you're trying to make a point in the fewest amount of words possible. I'd like to address the point you raise but I cannot quite tell what point you are making. I think the firs thing I need to understand is if you agree that "z" is a complex number if and only if "x" and "y" are two real numbers and
z = x + iy ?

[Anonymous No.10512581]

>>10512568
Not really, I mean when they finish math as in they do all the math that was ever to be done. You know what I mean? One day someone is going to put their pen down and say 'there we go, math is done now'. Humanity will applaud, angels will rejoice, and you will be unemployed. What happens then?

[Anonymous No.10512585]

>>10512581
>One day someone is going to put their pen down and say 'there we go, math is done now'.
no

[Anonymous No.10512589]

>>10512581
This is bait right?

[Anonymous No.10512595]

>>10512581
Hahaha, oh wow!

[Anonymous No.10512600]

>>10512567
>then topologizing Y^X by taking a base of "slices" contained in K x U
Wouldn't the basis set be the set of slices containing K x U as a subset?

Anyway that's more or less just restating the compact-open topology. What I want to know is are there any familiar spaces that arise as function spaces (aside from trivial examples like [math]X^1[/math]). For example, [math]Y^X[/math] is a metric space whenever Y is and X is compact. In particular, this means the path space [math]Y^I[/math] on a metric space is another metric space, which should be fairly down to earth.

[Anonymous No.10512613]

>>10512581
>all the math that was ever to be done
Do you think Euclid or someone made a checklist that all mathematicians ever have been reading off?

[Anonymous No.10512614]

>>10512572
Yes, that is essentially what I am saying, but I wouldn't say it in that exact way.

Saying "z is a complex number if and only if x and y are two real numbers and z = x + iy" is true, but phrasing it as a biconditional isn't even possible. The statement "z is a complex number" isn't a proposition, it's a statement in the metalanguage. A better way to say the same might be "The definition of a complex number is a pair of reals" (+ field structure yadda yadda), or even more succinctly [math] \mathbb{C} := \mathbb{R} \times \mathbb{R} [/math].
Yes, you can define some other structure and call it [math] \mathbb{C} [/math], but then the "complex numbers" you talk about aren't compatible with the complex numbers the Riemann zeta function is talking about (unless your can show that the fields are isomorphic).
On the off chance that this is actually Tooker and not a troll Tookerposting: I don't mean to disparage your work, but have you considered working within a proof assistant (Coq is probably the best one)? You obviously have some amount of mathematical literacy, and if you can prove things formally in a machine-checkable way nobody can dismiss you as a quack.

[Anonymous No.10512635]

>>10512600
Anon, stop thinking about everything in terms of points. It's literally easier to just picture the graphs and interpret them in terms of closeness.

[Anonymous No.10512637]

>>10512448
Well obviously, the 2-variable polynomials of the form y - f(x) = 0 are extremely easy, boring and completely solved. Perhaps you should try adding an exponent to y, or some mixed terms, or perhaps look for something other than real solutions, and look to other fields instead.

[Anonymous No.10512642]

>>10512581
you're shitposting but I do think the idea of math reaching a point where it can no longer progress, either because the theorems are too incomprehensibly complex to be feasible even with machine assistance or simply because everything interesting has been explored is a fun thought experiment

we're clearly nowhere near that though

[Anonymous No.10512647]

>>10512581
Then I'll ask a question that hasn't been asked before

[Anonymous No.10512657]

>>10512614
>A better way to say the same might be "The definition of a complex number is a pair of reals" (+ field structure yadda yadda), or even more succinctly C:=R×R.
No, that is way worse. The better way is the one that I used which appears in the first chapter of every complex analysis book that was ever written.

I am the real me. I have not considered using COQ. I like to do everything 100% by hand.

>nobody can dismiss you as a quack.
lol, they can always do that.

[Anonymous No.10512666]

>>10512585
>>10512589
>>10512595
>>10512613
>>10512642
>>10512647
Listen here you greedy little gremlins, you will not keep up this game forever. One day there will be no more questions to ask, no more equations to solve. It's impossible that it could keep going forever. I know you'd like to think otherwise and try to convince everyone else that you're right so you can keep getting the government funding, but it's clear that one day this game will end. There's only so many meaningless symbols, so many x's and y's that you can jot down, I know it.

[Anonymous No.10512695]

>>10512666
https://en.wikipedia.org/wiki/Hilbert%27s_tenth_problem
Basically, there will always be new Diophantine equations to solve and algorithms to find, so number theorists will always have a job

A similar result for 4-manifolds (uncountability) implies that differential geometers and topologists will always also have a job.

[Anonymous No.10512707]

>>10512666
what do you think math is?

[Anonymous No.10512718]

>>10512695
Oh so I'm supposed to trust a mathematician that there will always be math to do, when his livelihood relies on that very thing? You might as well listen to truck drivers telling you that driverless cars are never going to be a thing.
>>10512707
Glorified Wolfram Alpha I suppose

[Anonymous No.10512727]

>>10512718
No one's claiming humanity will always need mathematicians, or that men will always be better than machines at doing maths.
We're just saying maths as a subject doesn't end.

[Anonymous No.10512748]

>>10512718
>Oh so I'm supposed to trust a mathematician
you can check the proof yourself

>Glorified Wolfram Alpha I suppose
ever hear of pic related?

[Anonymous No.10512758]

>>10512727
But of course it will end. Even physics tells us that there is a limited amount of information out there
>>10512748
Nice reddit science

[Anonymous No.10512762]

>>10512758
so you cant check it yourself?

[Anonymous No.10512769]

>>10512758
>people who work in a field know more about their field than laypeople
>"MUH REDDIT!"

[Anonymous No.10512790]

Is there something that will generate bibtex output for an OEIS sequence?

[Anonymous No.10512882]

My understanding of the incompleteness theorems is that there will always be things to discover in formal systems.

[Anonymous No.10512944]

>>10512707
>math
This is not well-defined.

[Anonymous No.10512991]

>>10512581
>You know what I mean? One day someone is going to put their pen down and say 'there we go, math is done now'.
If this can happen, we'll be dead before it ever does, I think. I don't think this is possible though

[Anonymous No.10513004]

>>10512613
>Do you think Euclid or someone made a checklist that all mathematicians ever have been reading off?
You must have at least a Bachelor's degree with a >3.0 GPA or equivalent to post on this board.

[Anonymous No.10513010]

>>10513004
all those have been solved, brainlet
or do you not have enough publications to get that newsletter?

[Anonymous No.10513013]

>>10513004
RH SOLVED: >>10512485

Yang-Mills provisionally solved pending formalization:
>The Golden Ratio in the Modified Cosmological Model
>http://www.vixra.org/abs/1807.0136

[Anonymous No.10513049]

I'm wondering how many math majors did undergrad research, what was it about and how involved was it?
The department head said I should look into doing some research but I don't even know where to start.

[Anonymous No.10513087]

>>10513049
Find a prof you have a good rapport with, ask to help them with research, keep reminding them if they don't get back to you or forget, then do what they tell you. The research I helped with was algebraic geometry related and I wrote a bunch of code with another undergrad. I learned a lot. Most of the work was done during breaks between semesters.

[Anonymous No.10513119]

>the proof is elementary

[Anonymous No.10513187]

>>10512448
nigger... do you even know the Taylor series?

[Anonymous No.10513387]

>>10512513
even with proof assistants there is math out there that is beyond us. There might be math that requires all the matter in the visible universe to represent.

[Anonymous No.10513750]

it is easy to see that<div class="like-perk-cnt">&#x1F44C;</div>

[http://math.harvard.edu/putnam(...) !!84u21X0KjW+ No.10513850]

Daily Putnam Problem >>10513842

[Anonymous No.10514032]

why does [math]f=\begin{cases} \frac{1}{x} & x\neq 0 \\ 0 & x=0 \end{cases}[/math] form a closed graph?

[Anonymous No.10514044]

>>10514032
What have you tried?

[Anonymous No.10514069]

>>10514044
For [math]x=0[/math] it is trivial. For non zero [math]x[/math], [math]f[/math], I'm hesitant. Probably has something to do with the continuity.

[Anonymous No.10514128]

>>10514032
does it ?

[Anonymous No.10514151]

>>10514032
it has three connected components, one is just the origin which is obviously closed and other two are the branches of the hyperbola and they are closed since they are given by a closed condition (xy = 1).

[Anonymous No.10514183]

Say something nice about the canonical map from [math]R^2 / [2]^2[/math] to [math]R^2 / Z^2[/math].

[Anonymous No.10514206]

>>10514128
The graph is a singleton union a set that's the inverse image of 1. Remember since the function is continous, the inverse image of a closed set is closed.

[Anonymous No.10514209]

>>10514183
I don't know what that means but I'd like to one day

[Anonymous No.10514213]

>>10514183
What is [2]?

>>10514209
Based

[Anonymous No.10514229]

>>10514213
The subgroup generated by 2, also known as 2Z.

[Anonymous No.10514385]

glad to see mg was not affected by today's tomfoolery

[Anonymous No.10514416]

>>10514183
It is a fourfold covering map

[Anonymous No.10514506]

>>10514385
upvoted,
but seriously guys give me some quick likes so that I can unlock skellingtons on my work computer before I have to go home

[Anonymous No.10514721]

>>10514416
Nice, anon. Anything else you wanna share with the class?

[Anonymous No.10514758]

I feel so stupid... please help...

We have that the closed subscheme corresponding to the closed point [math]q_a[/math] is [math]\text{Spec} K[t]/q_a[/math] and hence the fiber [math]\varphi^{-1}q_a[/math] corresponds to the closed subscheme corresponding to the ideal [math]\varphi^\#(q_a) K[x,u]/(xu)[/math], where [math]\varphi^\#[/math] is the given map [math]t\mapsto x+u[/math]. Hence, [math]\varphi^\#(q_a)=\varphi^\#((t-a))=(x+u-a)[/math] and so the fiber should be the points of the closed subscheme [math]\text{Spec}K[x,u]/(xu,x+u-a)[/math]. Note that the latter ring is isomorphic to [math]K[x]/(x^2-ax)[/math].

When [math]a=0[/math] this is easily seen to be the dual numbers, but I cannot find the isomorphism to [math]K\times K[/math].

[Anonymous No.10514782]

>>10514758
CRT...

[Anonymous No.10514793]

>>10514782
FUCK

[Anonymous No.10514801]

>>10512657
Kill yourself

[Anonymous No.10514917]

THIS IS THE DIOPHANTINE DINO
like this post and solutions to diophantine equations will be divined to you<div class="like-perk-cnt"><img alt="" width="451" height="75" src="//s.4cdn.org/image/temp/dinosaur.gif"></div>

[Anonymous No.10515379]

I never had a problem with linear algebra, number theory, introductory real analysis or group theory, but I'm really fucking struggling with the graph theory course I just took. It's just so new and there are SO MANY FUCKING DEFINITIONS

Any help? :(

[Anonymous No.10515413]

>>10515379
Me too man, I suck at graph theory. I can't keep all the definitions in my head and the moment it gets too complicated for me to just draw a picture and do it naively, I get lost

[Anonymous No.10515423]

holy fuck do i need to read everything on free groups, free products etc to understand van kampen theorem. wtf is all this autism.

[Anonymous No.10515474]

Which math youtubers do you guys use?

I need to learn nth order ODEs and series solutions for differential equations but none of the normal youtubers I use like khan, mathispower4u, or ilectureonline have any videos on these topics. All they have is 2nd ODES and laplace transforms.

[Anonymous No.10515493]

>>10515474
>Which math youtubers do you guys use?
https://www.youtube.com/user/njwildberger

[Anonymous No.10515503]

>>10515493
awww. He doesn't have any diff eq videos. Thank you though, he does have some other cool stuff.

[Anonymous No.10515515]

>>10515503

[Anonymous No.10515519]

Hello, brainlet here. I'm really shaky on trig stuff so I got stuck on this one. I've taken the first derivative, now how do I use it to indicate where it changes positive/negative?

[Anonymous No.10515521]

>>10515519
>>>/sqt/

[Anonymous No.10515538]

>>10512657
It seems like you didn't even understand the basic idea of the point he was trying to make. Please stay out of mathematical discussion if you have nothing to add but schizoposts.

[Anonymous No.10515573]

in this sci wiki for math books https://4chan-science.fandom.com/wiki/Mathematics

im in calc 2 but i feel like i should start out with Challenging Problems in Algebra by Posamentier
because the problems require more thinking than what i learned in school. is this normal? i couldnt do all of them so i think i should start there no?

[Anonymous No.10515578]

>tfw in final weeks of undergrad
I'm scared and sad and have a fuckload of writing to do

[Anonymous No.10515584]

>>10515519
Extrema occur wherever f'(x)=0. There are a few ways you can go about this. If you know the end behavior, you can determine extrema to be max or min intuitively. Or, after you've gotten the x value for your extrema, you can test it
>f(x), x values near your extrema on either side will have lower or higher y values than your extrema
>f'(x), x values near your extrema will either all be negative or all be positive.
>f''(x) where a positive or negative value at the extrema suggests concavity.

[Anonymous No.10515601]

>>10515584
for what value of x would cos(x)-sin(x) = 0?

[Anonymous No.10515612]

>>10515601
have you tried wolfram?
pi/4 + any integer times pi

[Anonymous No.10515625]

>>10515601
>interval of [0, Pi]
cos(x)-sin(x)=0
cos(x)=sin(x)
x=Pi/4

[Anonymous No.10515659]

>>10515625
>>10515612
>>10515601
So I've somehow landed on all the right answers, but WHY, could someone walk me through these, I'm having a hard time picturing in my head what's going on here.

[Anonymous No.10515678]

>>10515659
>take derivative
>find where it's zero--this is where the function is either at a (local) min or a max or is flat
>take second derivative
>check if its positive or negative or zero at the previous points, this tells you if it's a min or a max or flat respectively
>check those points you just found along with the endpoints to see where the absolute min and max are

[Anonymous No.10515692]

>>10515659
theres literally no reason to picture this in your head
the point of math is to automate the process of solving a real world problem without putting in all of that effort
and once you hit multivariate calc, there isn't any way to picture it, getting used to picturing things will only handicap you there

[Anonymous No.10515697]

>>10515678
>>10515659
your derivative is just your slope homeboy.
if positive your increasing if negative it's decreasing. if zero your slope is zero. so you can say oh look it's going up, then oh look im not going up or down and then oh it's going down now. so the point between going up and going back down again that's a max. you might just be overthinking it.

[Anonymous No.10515708]

>>10515659
You need to be more specific about what you're misunderstanding.

Remember, your first derivative is describing the change of your original function. In other words, f'(x) describes the slope of f(x). So, where f'(x)=0 (where the slope of f(x) is 0, i.e. where it's vertical), you have an extrema (max or min).

For absolute min or max, you want to find the extrema that have the lowest or highest y value. If you're given a specific interval which includes those points (where [0, pi] includes both 0 and pi, and (0, pi) excludes 0 and pi), you need to test the ends of the intervals as well.

If you're confused about why the trig functions make sense, you need to go back and study what trig functions are. Remember that angle degree measures correspond to radians (ex, pi/4) on the unit circle. The unit circle being a special reference for all trig functions, where cos(some angle) corresponds to an x value on the circle, and sin(some angle) corresponds to a y value on the circle. At 45 degress, cos(45deg)=sin(45deg), because their points on the unit circle are both (sqrt2)/2. In other words, 45 degrees on a circle x^(2)+y^(2)=1, corresponds to the point ((sqrt2)/2, (sqrt2)/2)

[Anonymous No.10515710]

>>10515708
*where it's horizontal

[Anonymous No.10515755]

[Anonymous No.10515759]

>>10515697
yeah but the second derivative tells you that without having to test on both sides of each critical value

[Anonymous No.10515764]

What graphing calculator would anons recommend? Texas Instruments ones are kinda pricey, but are they really worth the price?

[Anonymous No.10515772]

>>10512418
I'm studying accounting, and I really enjoyed business calculus. Anyone have advice for learning more about calculus? I presume I need to go backwards a bit, and can't just buy some calc 2 textbook.

[Anonymous No.10515779]

>>10512418
Is it worth going for an applied math degree. What job opportunities will it open up for me?

[Anonymous No.10515780]

>>10515759
kind of yeah you can easily see by concavity a min or max. but you do have to pay the second derivative tax, which in some cases is not even worth it if you can just plug another value into the first derivative.

[Anonymous No.10515801]

>>10515772
http://tutorial.math.lamar.edu/
this will take you all the way up to differential equations if you really wanna go crazy.
plus it's concise and contains all the topics you may find useful.
calc2 is kinda funny its harder integration techniques some really crazy like the turning a fraction with polynomials into a trig function, integrating that, then referring back to the triangle you made from the polynomials and turning it back into a fraction of polynomials.
then it's series so if you get really really desperate to integrate and you just cant do it. you use taylor and maclaurin to make a polynomial that acts like your function more and more the higher it goes up in order. and just integrating that instead lol.

[Anonymous No.10515964]

>>10512657
LMAO

[Anonymous No.10515982]

>>10515474
>Had an entire week to learn diff eq before my exam
>Now have to finish learning laplace transforms, nth odes, and series solutions all before my exam thursday morning
Why do I keep doing this to myself.

I think I'm confident about laplace transforms because there's a billion crash course youtube videos on them and my professor is letting me use a laplace table on the exam, but there's hardly any fucking youtube videos on nth odes and series solutions.

[Anonymous No.10515986]

>>10515474
>Had an entire week to learn diff eq before my exam
>Now have to finish learning laplace transforms, nth odes, and series solutions all before my exam thursday morning
Why do I keep doing this to myself.

I think I'm confident about laplace transforms because there's a billion crash course youtube videos on them and my professor is letting me use a laplace table on the exam, but there's hardly any fucking youtube videos on nth odes and series solutions.

[Anonymous No.10516346]

is this hooked curved arrow standard notion for denoting a bijection? if so, which field of math is it used in? not sure how to TeX it.

[Anonymous No.10516347]

Which mathematical authors are decent prose stylists in non rigorous contexts?

I'm trying to read about maths in general or as a practice; something on the softer side

[Anonymous No.10516354]

>>10516346
https://tex.stackexchange.com/questions/296151/double-head-and-hook-arrow

[Anonymous No.10516358]

>>10516346
The tail hook means monomorphism
The double barb means epimorphism

[Anonymous No.10516363]

>>10516358
The tail hook means inclusion, anon.

[Anonymous No.10516366]

>>10516363
Not in every category.

[Anonymous No.10516372]

>>10516358
>>10516366
Autism

[Anonymous No.10516374]

>>10516366
No, tail hook is notation for inclusion. Another barb at the back is epimorphism.

[Anonymous No.10516376]

>>10516347
Non-Biographical:
- The Shape of Space, by Yau
- Love and Math, Frenkel

Biographical:
- The Map of My Life, by Shimura
- I Want to Be a Mathematician, by Halmos
- The Apprenticeship of a Mathematician, by Weil
- A Mathematician's Apology, by Hardy
- Who is Grothendieck, by Scharlau (tran. Leila Schneps)

[Anonymous No.10516379]

>>10516358
>>10516363
>>10516366
>>10516372
>>10516374
sooo, yes or no?

[Anonymous No.10516381]

>>10516379
It's not standard, but people will understand what you're trying to say.

[Anonymous No.10516382]

>>10516381
Was just looking for a shorthand is all. So long as there is some truth to it is all that matters.

[Anonymous No.10516437]

>>10515515
There's nothing wrong with Wildbergers lectures, if you can ignore his unreal obsession.

[Anonymous No.10516524]

how is this triangle inequality?

[Anonymous No.10516528]

>>10516524
How is it not? >>>/sci/sqt

[Anonymous No.10516544]

>>10516524
it is used twice

[Anonymous No.10516621]

>>10512614
>Have you considered working within a proof assistant

JFL at even asking this question. Tooker is a total idiot who is absolutely incapable of reasoning correctly about very simple proofs, so no he does not need a proof checker.

[http://math.harvard.edu/putnam(...) !!84u21X0KjW+ No.10516663]

Daily Putnam Problem >>10516658

[Anonymous No.10516928]

>>10516376
Thanks

[Anonymous No.10517528]

>>10516347
me

[Anonymous No.10517672]

I've read that differential equations (both ODEs and PDEs) have motivated lots of research in mathematics. Why is that? What's so special (and hard) about them? What kind of questions are so hard to solve than tons upon tons of research is done on the subject?

[Anonymous No.10517716]

>>10517672
>What kind of questions are so hard to solve than tons upon tons of research is done on the subject?
https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existence_and_smoothness

[Anonymous No.10517802]

Yeah sure, let's make an entire branch of mathematics that mainly consists of definitions with no useful proofs or applications (unlike topology). That'll be great.
this post has been brought to you by the continuum gang

[Anonymous No.10517804]

>>10517802
>topology
>useful

[Anonymous No.10517828]

>>10517802
>this post has been brought to you by the continuum gang
i can tell your a fuckn normie. kys

[Anonymous No.10517837]

>>10517672
Literally every physical process can be described by a DE.

High level differential geometry is glorified PDEs on manifolds. Literally anything with a smooth structure benefits greatly from studying DEs on them.

Although I think there's so much research because it's probably the best funded field due to the nature of its (real-world) applications

[Anonymous No.10517838]

>>10517802
>that mainly consists of definitions
>(unlike topology)
fuck off clopen nigg

[Anonymous No.10517906]

>>10516437
i don't wanna watch his diff geometry videos and catch his rational autism, and then find out about the autism later because i didn't know any better.

[Anonymous No.10518032]

>>10517838
>mainly consists of definitions WITH NO USEFUL PROOFS OF APPLICATIONS

have you ever read a book? for fuck's sake

[Anonymous No.10518353]

>>10516363
>implying every category is concrete

[Anonymous No.10518394]

Grothendieck has some cool writings with varying degrees of lucidity.

[Anonymous No.10518397]

>>10512418
Yeah... this red graffiti around here makes Mochizuki look like a cunt. I thought they were doing opposite day in those threads about
HM vs SS

[Anonymous No.10518406]

anyone else here taking the GRE this upcoming weekend?

I am; I did mediocre on my first practice test and have been studying from a prep book. The format and questions are just more annoying than anything else.

I wish I didn't get saddled with the absolute shittiest time for this relative to my schedule. I was swamped with exams all of last week through the start of this week, and having to cram this test format is really burning me out after all this.

I'll probably be called brainlet for admitting I did mediocre on my practice test, but fuck it. It's a pretty shitty test and I'm hoping to get high enough on it to not have to worry about it again.

Good luck to anyone else taking it

[Anonymous No.10518408]

>>10518406
I'm talking about the math subject test, btw, if that wasn't clear

[Anonymous No.10518410]

There's got to be another finite simple group out there. I can feel it

[Anonymous No.10518530]

Someone please recommend some videos/guides to me of how to find roots for polynomials?

I'm trying to practice nth order ODEs but but honestly I feel like a complete retard trying to figure out some of these roots. The diff eq part of the problem is incredibly easy but some of the tricks to finding these roots is shit I'd never think of.

[Anonymous No.10518531]

Someone please recommend some videos/guides to me of how to find roots for polynomials. I'm trying to practice nth order ODEs but but honestly I feel like a complete retard trying to figure out some of these roots. The diff eq part of the problem is incredibly easy but some of the tricks to finding these roots is shit I'd never think of.

[http://math.harvard.edu/putnam(...) !!84u21X0KjW+ No.10518558]

Daily Putnam Problem >>10518553

[Anonymous No.10518667]

>>10518531
This is a bit more of psychological advice than mathematical advice, but know that if you ever need to factor a polynomial of degree 3 or more as a student, there are going to be obvious roots.
People that make these problems usually do not assume that students know the formulas for degree 3 or (god forbid) degree 4 polynomials.
Here, -1 is an "obvious" root for example.
If you ever have to do something like this, start by checking if -2, -1, 0, 1, 2 are roots.
Now obviously, this should not deter you from actually learning how to solve equations of degree 3 or 4.
An algorithm is given here: https://en.wikipedia.org/wiki/Cubic_function#Cardano's_method
There are other tricks like palindromic polynomials: https://en.wikipedia.org/wiki/Reciprocal_polynomial#Palindromic_and_antipalindromic_polynomials , but as a general rule there is no method, so keep this in mind.

[Anonymous No.10518811]

Am I being stupid here?

Isn't [math]\mathbb C[x]/(x^2+1)\cong \mathbb C[/math] since it is an algebraic extension?

[Anonymous No.10518814]

>>10518811
C[x]/(x^2+1) is the ring of complex polynomials modulo (x^2+1), anon.

[Anonymous No.10518817]

>>10518814
That's an algebraic extension, but there are no proper algebraic extensions of algebraically closed fields like C.

[Anonymous No.10518818]

>>10518814
right, im dumb, i forgot x^2+1 is not irreducible in C

[Anonymous No.10518820]

>>10518817
Anon, it's not an extension, it's a modulo. You're saying give me all complex polynomials and equal x^2+1 to zero.

[Anonymous No.10518870]

[eqn]\frac{\text d }{\text dx} \frac{1}{x}=\frac{\not{\text d}}{\not{\text d}x}\frac{1}{x}=\frac{ }{ x}\frac 1x=-\frac1{x^2}[/eqn]

[Anonymous No.10518877]

>>10518870
Enjoy your ban

[Anonymous No.10518918]

>>10518870
Good point.

[Anonymous No.10519229]

>>10518406
I'm retaking it on Saturday. I took it last semester and did abysmally but I applied to grad schools and go into the Master's programs I wanted to get into. My friend's and my shitty performance on the exam prompted my undergrad advisor to create a one unit GRE prep course where we do practice problems and discuss strategies. So I'm going to try and improve my score. When I go for PhD later it'll be good to have a better score to send (though I've also heard that many PhD programs don't even ask for GRE subject scores).

[Anonymous No.10519278]

What's

[math] \dfrac {d^k}{d^k x} \left( 1 + \dfrac {x} {n} \right)^n [/math]

expanded, in terms of n and k.
I can see that

[math] \dfrac {d^1}{d^1 x} \left( 1 + \dfrac {x} {n} \right)^{n-1} [/math]

[Anonymous No.10519364]

>>10519278
apply leibniz rule to (1+x/n)(1+x/n)^n-1

[Anonymous No.10519702]

Mfw found all the explicit solutions/hints to my homework.

[Anonymous No.10519744]

>>10519702
with sites like this and stackexchange uni profs homework is essentially pointless desu (besides learning how to LaTeX and redact maybe?)

Most of the answers to my abstract algebra homework assignments were available in mathstack exchange. I only got one B but because I was really fucking lazy.

[Anonymous No.10519831]

>>10519744
it's' stupid when they count for so much, it doesn't make me wanna do the problem on my own. one mistake fucks me, or i could just google the "catch" and make sure i get all the points.

[Anonymous No.10519949]

>>10518811
it's not a field

[Anonymous No.10520021]

>>10519949
yes, i realized my mistake here >>10518818
no need to remind me

[Anonymous No.10520053]

Which is generally harder to learn, series solutions for differential equations, or variation of parameters/method of undetermined coefficients.

I'm going through and trying to review power series but I don't remember any of this shit and I'm wondering if my time would be better spent going back over stuff like variation of parameters/method of undetermined coefficients.

[Anonymous No.10520084]

Homological algebra is so fucking bad, holy shit.

[Anonymous No.10520097]

>>10520084
Idk why you would think that, HA is about the nicest math you can hope for. It's just suped up linear algebra. What is "good math" to you?

[Anonymous No.10520101]

>>10520097
Anything that isn't category theory.

[Anonymous No.10520104]

>>10520101
But anon, everything is category theory

[Anonymous No.10520109]

>>10520104
I don't have any problem with applying category theory, but pure category theory is a corpse of a subject that reads like a dictionary.

[Anonymous No.10520115]

>>10520101
>category theory
Category theory is irrelevant to most of mathematics

[Anonymous No.10520213]

>>10520053
nevermind, answered my question. I've spent past 2 hours trying to learn series, it only took me 20 mins to learn undetermined coefficients.

[Anonymous No.10520296]

>>10520115
Only because algebr*sts haven't invented Algebraic Category Theory.

[Anonymous No.10520312]

>>10520296
Well, you *can* work over a class of morphisms where an operation is sometimes defined and subject to certain axioms, and then use the existence of a composition to track down objects, i.e. if (a, a) exists then a behaves like a map a: A->A. But that's essentially the same as working over the usual category.
And categorical algebra does exist.

[Anonymous No.10520317]

Let's say you have compact orientable 2-manifolds A, B, C such that A x C is homeomorphic to B x C, is A homeomorphic to B? A, B, C are all either spheres or connected sums of tori. I'm convinced to death that they are homeomorphic, but this is generally not true without the conditions of being compact orientable 2-manifolds...

[http://math.harvard.edu/putnam(...) !!84u21X0KjW+ No.10520892]

Daily Putnam Problem >>10520885

[Anonymous No.10520903]

the SQT and ENG threads turned up nothing, maybe the savants of mg can correct my brainlet math

what in the ever loving fuck am i doing wrong?

I even put this equation in symbolab and still got the same apparently incorrect answer

I have a heat transfer exam tomorrow and this is the only thing i've been trying to figure out for the past hour

[Anonymous No.10521161]

>>10512581
bad b8 m8 0/8

[Anonymous No.10521163]

>walk out of exam
>immediately discover all the holes in your proofs
What area of mathematics do I go to for this feel?

[Anonymous No.10521166]

>>10520903
My guess is that the error is that the solution you posted is using degree sine when it should be using radian sine.
If you recompute this with sin(1.432 radians) you get the tau you expect.

[Anonymous No.10521190]

>>10521163
algebraic number theory

[Anonymous No.10521229]

>>10521190
Yeah. All the holes. It was genus all along

[Anonymous No.10521333]

>>10520115
Cope harder. Category theory makes the relations between all you favourite structures much more insightful.
You don't want to stay pedestrian forever do you?

[Anonymous No.10521421]

>>10521190
Good intermediate books? I went through Stevenhagen in a course but found Neukirch and Serre (local fields) too hard for self study.

[Anonymous No.10521518]

>>10521229
Kek

[Anonymous No.10521533]

>>10512418
Name your favourite mathematicians...

[Anonymous No.10521585]

What are the top 3 rings? I'm assuming Z_(p) is the localisation and I think the two top left are Z/Q p-adics, but i have no clue what C_p is

[Anonymous No.10521594]

>>10521585
I think you're right, in which case [math]\mathbb C_p[/math] is the completion of the algebraic closure of [math]\mathbb Q_p[/math]

[Anonymous No.10521604]

>>10521585
Either Gaussian integers modulo the [p] ideal or >>10521594
>>10521533
The usual. Milnor, Gromov, Serre, Poincaré, Banach, Hilbert, Artin, and so on.

[Anonymous No.10521616]

>>10521421
Marcus

[Anonymous No.10521618]

>>10521533

[Anonymous No.10521620]

>>10520317
Bumping this :<

[Anonymous No.10521623]

>>10521533

[Anonymous No.10521629]

>>10521533
Riemann, Grothendieck, Weyl, Noether, Voevodsky, Baez.

[Anonymous No.10521635]

>>10521620
>>10520317
It's probably true for compact manifolds but I don' know much about that

I know it's true for stable equivalences of vector bundles over compact base spaces however

[Anonymous No.10521662]

>>10521533
Hard to say. Among the most relevant to what I do, probably Tits, Steinberg, Mumford, Zariski, Serre, Grothendieck, but there are just so many

[Anonymous No.10521681]

>>10521604
>>10521623
>>10521629
>>10521662
T-thank you anons. This will do...

[Anonymous No.10521685]

>>10512418
This is a stupid question but ill ask it anyway, ignore at pleasure.
[math]\sum_{i=1}^{3} 1 = 3 [/math]
[math]\sum_{j=1}^{3}\sum_{i=1}^{3} 1 = 3 * 3 [/math]
[math]\sum_{k=1}^{3}\sum_{j=1}^{3}\sum_{i=1}^{3} 1 = 3^3 [/math]
[math]\sum_{l=1}^{3}\sum_{k=1}^{3}\sum_{j=1}^{3}\sum_{i=1}^{3} 1 = 3^4 [/math]
[math]\sum_{m=1}^{3}\sum_{l=1}^{3}\sum_{k=1}^{3}\sum_{j=1}^{3}\sum_{i=1}^{3} 1 = 3^5 [/math]
...

Why are exponents the "last step" when summing up sums? Is there a particular reason?

[Anonymous No.10521690]

>>10521685
Oh wait i see now nvm. The sum sign is the exponent itself. That's kinda cool

[Anonymous No.10521696]

>>10521685
what do you even mean?
You are just doing 3 x 3 x 3 x 3 x 3 in a convoluted way, of course it's the exponent you dumbass

[Anonymous No.10521717]

>>10521696
I have this plan of inventing a new area of math which is designed to be cryptographic. You write a simple equation as convoluted as possible, for no good reason at all. The math problem is to figure out what the hell it's saying.

Similar to this: https://en.wikipedia.org/wiki/Brainfuck or this https://github.com/TheRaz/DerpPlusPlus

[Anonymous No.10521743]

>>10521717
trying posting instead in the /eng/ thread then

[Anonymous No.10522412]

Anyone know how to compute something like [math](\sqrt2 x-\sqrt 3 y)\cap\mathbb Q[x,y][/math]? It can't be the zero ideal since [math]2x^2-3y^2[/math] is in it

[Anonymous No.10522422]

>>10522412
Does [math]( \sqrt{2}x-\sqrt{3}y)[/math] read as the field generated by that, or as the algebra over Q?

[Anonymous No.10522424]

>>10522422
As in the principal ideal generated by it in [math]\bar{\mathbb Q}[x,y][/math]

[Anonymous No.10522440]

>>10522424
Righty.
If you compute (2x^2-3y^2)^2 you obtain [math]2x^2-2 \sqrt{6} xy + 3y^2[/math].
Since taking anymore powers always will keep a component with a sqrt part, and we can't cancel them out because the i and j the x^j y^i keep growing.
I'm sure there's an easy proof, but I'm not feeling inspired right now.

[Anonymous No.10522553]

>>10522412
Write [math]P = (\sqrt{2}x - \sqrt{3}y)Q[/math] with [math]P \in \mathbb Q[x,y][/math], [math]Q \in \bar{\mathbb Q}[x,y][/math]. Note that, under that assumption, [math]Q \in \mathbb Q(\sqrt 2, \sqrt 3)[x,y][/math].
Let [math]\sigma[/math] be the automorphism of [math]\mathbb Q(\sqrt 2, \sqrt 3)[/math] such that [math]\sigma(\sqrt 2) = \sqrt 2, \sigma(\sqrt 3) = - \sqrt 3[/math].
[math]\sigma[/math] extends naturally to an automorphism of [math]\mathbb Q(\sqrt 2, \sqrt 3)[x,y][/math] by setting [math]\sigma(x) = x, \sigma(y) = y[/math].
Applying this automorphism to both sides of the initial equation, we get [math]P = (\sqrt 2 x + \sqrt 3 y)\sigma(Q)[/math].
Hence, both [math]\sqrt 2x - \sqrt 3y[/math] and [math]\sqrt2x +\sqrt 2y[/math] divide [math]P[/math]. Since both are irreducible and [math]\bar{\mathbb Q}[x,y][/math] is factorial, the product must divide [math]P[/math].
Hence, we may write [math]P = (2x^2 - 3y^2)R[/math] for some [math]R \in \bar{\mathbb Q}[x,y][/math]. Since both [math]P[/math] and [math]2x^2 - 3y^2[/math] have rational coefficients, so does R and therefore [math]P \in (2x^2 - 3y^2)\mathbb Q[x,y][/math].

[Anonymous No.10522914]

>>10522553
This is all well and good, but either you're wrong or I'm wrong, since what I'm looking for is this:

The field extension [math]\mathbb Q\hookrightarrow \bar{\mathbb Q}[/math] induces the morphism [math]\text{Spec}\bar{ \mathbb Q}[x,y]\to \text{Spec}\mathbb Q[x,y][/math] mapping a prime [math]\mathfrak p\mapsto \mathfrak p\cap \mathbb Q[x,y][/math].

As such, your answer should be a prime ideal but it isn't, r-right?

Literally as I typed that last sentence it dawned on me that I'm probably wrong

[Anonymous No.10522926]

>>10522914
>that last sentence it dawned on me that I'm probably wrong
The true inner beauty of formal reasoning.

[Anonymous No.10522936]

>>10522553
It reads like a shitpost, but I give it a 1% chance of actually being correct.
>>10522914
He did give a prime ideal lad.
Anyhow: the preimage of the ideal [math]\sqrt{2}x - \sqrt{3} y[/math] doesn't have zeroes in Q, so it's just the 0 polynomial.
Which is nonempty, I guess.

[Anonymous No.10522963]

>>10521533
Only Euclid. Now, I am going to resume drawing circles in mud.

[Anonymous No.10522973]

>>10522936
>>10522412
>can't be the zero ideal since 2x2−3y2 is in it

[Anonymous No.10523012]

>>10522973
Right, my bad.
The preimage doesn't contain any elements of the form (ax+by), for obvious reasons. It also doesn't for (ax^2+by) or (ax+by^2), and that's a matter of showing that [math](2x- \sqrt{6}y)(ax+b)[/math] hasn't integer coefficients, and similarly for the other way around.
We show that it has nothing of the form ax^2+by^2+cx+dy+exy other than multiples of 2x^2-3y^2. We do so by setting [math](2x- \sqrt{6}y)(ax+by)=2ax^2 - b \sqrt{6} y^2 +2bxy -\sqrt{6}axy=2ax^2 -b \sqrt{6} y^2 + [2b-a \sqrt{6}]xy[/math], exhausting its solutions, and using the closure of a to show that we only need to check for those cases.

[Anonymous No.10523269]

>>10521533
Teichmuller

[Anonymous No.10523273]

>>10521629
Nice taste, friend

[Anonymous No.10523376]

>>10521533
fermat & euler

[Anonymous No.10523475]

>>10521533
Riemann, Serre, Hilbert, Grothendieck

[retard No.10523541]

I can’t help but feel like a tool when i’m taking classes. That said, I’ll probably wrap my degree in the next couple years. It’s hard to go back because I’ve self studied out of where I am. I don’t want to pay money retake analysis and abstract algebra. Are i like schools a joke? Are there CHEAP regionally accredited options available? PhD sounds ideal, but doing two tedious and expensive years of undergrad school sound bad. Cheap power leveling toward post grad via li gen + youtube sounds way more comfy.

[retard No.10523543]

>>10523541
>Are i like schools
*online, I want something like Open Uni but regionally accredited

[http://math.harvard.edu/putnam(...) !!84u21X0KjW+ No.10523590]

Daily Putnam Problem >>10523587

[Anonymous No.10523593]

>>10512448
> hasn't played with secret sharing schemes

[Anonymous No.10523625]

>>10523541
>don’t want to pay money retake analysis and abstract algebra

I'm in a similar situation. I won't be going to a university with a proper math program (juniors are taking introductory proof courses) so I just decided to major in philosophy while taking upper division math courses that interest me. Maybe it's not the best decision, but I really don't want to sit through two years of busy work. I think I'd go insane.

[Anonymous No.10523723]

>>10522926
Worst part is that I was stuck on it for 2+ hours because I was convinced that it wasn't a prime ideal from the get-go

[Anonymous No.10523770]

>>10522936
>It reads like a shitpost
rude
>As such, your answer should be a prime ideal but it isn't, r-right?
It is though. The polynomial [math]2x^2 - 3y^2[/math] is a polynomial of degree 2 in x. If it is not irreducible, then it has a root in Q[y]. But we know its roots already and we know that they are not in Q[y]. Hence it is irreducible, hence prime since Q[x,y] is a UFD

[Anonymous No.10523823]

Last night I had a dream that I, very generously, posted a download link of my textbooks here but accidentally posted some that had snippets of my name and one of you dicks doxxed me

Fuck you guys, I trusted you

[Anonymous No.10523998]

>>10523823
Sounds like you lost your dream job

[Anonymous No.10524036]

>>10523823
Textbooks of what subject?

[Anonymous No.10524048]

>>10524036
All of them, I have thousands of textbooks, all GTMs, UTMs, and other TMs, Theses, etc. I had the idea that my name was in one of them since I actually got the Princeton companion as a prize for my math at uni (albeit it has a card stuck on the inside rather than in actual print)

[Anonymous No.10524060]

>>10524048
If you're still thinking about it, I'll recommend looking up how to remove metadata.

[Anonymous No.10524086]

>>10524060
I'd never share my textbooks because I'm dumb/compute-illiterate enough that I'd get caught or fined

and you can find the torrents easily on /t/ or just go on libgen desu..

[Anonymous No.10524104]

>>10524086
but what if I don't know what to look for?
You could always just upload them to mega if they're under 30GB.
Also, no one is checking textbooks like they do for honeypot torrents of popular shows.
If nothing else, please upload a document with the file tree: https://www.digitalcitizen.life/how-export-directory-tree-folder-windows so we can see what to look for.

[Anonymous No.10524124]

>>10524104
>but what if I don't know what to look for?
then you shouldn't be mass-downloading textbooks, and instead checking math over/under flow or asking a prof
>Also, no one is checking textbooks like they do for honeypot torrents of popular shows
I know enough to note take advice from a website that will just as excitedly tell me to delete system 32
>If nothing else, please upload a document with the file tree
https://file.io/51hlKU

[Anonymous No.10524142]

>>10524124
huh idk why it 404'd
https://file.io/xIHyx2

[Anonymous No.10524298]

Okay lads. I'm officially retarded.
How is this as massive of a fuckup as it is?
What am I doing wrong here?
Why doesn't it work?

[Anonymous No.10524413]

>>10524142
>https://file.io/xIHyx2
That one 404ed too.
I'd personally recommend only putting on mega the stuff you can't find on libgen.
By the by, all the Quillen Homotopical Algebras on libgen are some pretty bad scans. Please post it if you have a nice version.
Literally just go on >>>/g/sqt and ask "how do I clean a .pdf to put it online", or use libgen's guide on the forum.
>>10524298
>the entire thing in the middle
I'm sorry, but I don't really remember any notation that resembles that.
I also don't follow what you're trying to do overall.

[Anonymous No.10524423]

>>10524413
I'm trying to subtract row 1 from row 2 and 3 in order to remove X from both of them.

[Anonymous No.10524434]

>>10524423
All the operations seem correct.
Just iterate the process for the two last rows to remove one of the remaining variables, swap it back in, and you're done.

[Anonymous No.10524439]

>>10524434
You have no idea how mad I am right now
I must have typoed something, because last time I solved the bottom one it gave me something else entirely.

[Anonymous No.10524565]

>>10521533
Weierstrass

[Anonymous No.10524594]

>>10513004
>implying those are the only open problems
They are the most well-known but far from the only open questions.
For instance, Quartertonic Analysis is something that's relatively unstudied and is actually a bit rich.
https://hal.archives-ouvertes.fr/tel-01833951/document
(abstract & main results are in english as well as french)

[Anonymous No.10524609]

>>1052153
Borel, Lesbesgue, Fourier, Carathéodory, Cauchy.

[Anonymous No.10524817]

>>10512418
>oooo
>rooky rooky
>pererman proof
>me rikey rikey

[Anonymous No.10524830]

What am I looking at here?
Are they supposed to be matrices?

[Anonymous No.10524834]

>>10524830
Fuck

[Anonymous No.10524843]

>>10524830
>>10524834
Yeah, obviously. What did you expect, pre-Latex sandwich notation?
A= (-3 6)
......|-2 3|

[Anonymous No.10524850]

>>10524843
I was thrown off because they show a 3x3 below with straight brackets. And it's late.

[Anonymous No.10524851]

>>10524850
That's usually the determinant.

[Anonymous No.10524954]

>>10524851
How aboot giving me another hint too?
AX = X + AB, A and B are known matrices.
How would I go about this one? All I need is a starting place

[Anonymous No.10524961]

>>10524954
Try to isolate X like you normally would. Is (A-I) invertible?

[Anonymous No.10524964]

>>10524961
Indeed it is

[Anonymous No.10524968]

>>10524964
So isolate X normally and instead of dividing you can multiply by the inverse.

[Anonymous No.10524972]

>>10524968
Oh man that's good.
Matrix operations really are better than sex

[Anonymous No.10525096]

Holy fuck, Görtz-Wedhorn Schemes part I literally has all of Atiyah-Macdonald and much more commutative algebra and field theory summarized in 20 pages in the appendix.

[Anonymous No.10525447]

There are hundreds of people that have not posted a single post on 4chan(nel) ever that are reading this thread right now. I find this to be scary.

[Anonymous No.10525755]

>>10525447
>hundreds reading this thread
It's not clickbaity enough

[Anonymous No.10525822]

>>10521533
Kontsevich, Manolescu, Witten, Freed, etc.
Fuck Grothendieck
>>10521629
Weyl is a physicist.

[Anonymous No.10525840]

is yukariposter single?
asking for a friend

[Anonymous No.10525841]

Let [math]\left(X,\tau\right)[/math] be topological space, and [math]Y\subset X[/math] a countable subset and the topology [math]\tau_{Y}=\{ V\cup E\; |\; V\in\tau,\; E\subset Y\}[/math]. Is It true that if [math]\tau_{Y}[/math] is first countable then [math]\tau[/math] is first countable?

[Anonymous No.10526074]

>>10515379
I've got no advice for understanding the matter
But to keep in mind the dozens of definition you could try using Anki

[Anonymous No.10526113]

Maths is so fucking cool

[Anonymous No.10526399]

>>10525755
moot said iirc that 80% of people on 4chan never post and just lurk

[Anonymous No.10526493]

>>10525841
It is not true. Let X be the wedge sum of countable many circles and let Y={y} be the point that connects all the circles. Then t_Y is first countable but t is not.

[http://math.harvard.edu/putnam(...) !!84u21X0KjW+ No.10526647]

Daily Putnam Problem >>10526643

[Anonymous No.10526798]

>>10525822
If Weyl is a physicist then Witten is one too.

[Anonymous No.10527311]

>>10525840
please respond

[Anonymous No.10527380]

>>10527311
Married to maths

[Anonymous No.10527443]

>>10527380
o-oh

[Anonymous No.10527591]

Test

[Anonymous No.10527598]

Something just dawned on me. Since there are no homomorphisms from the zero ring to any Nonzero ring, when we consider exact sequences of rings do we exclusively consider them as modules?

[Anonymous No.10527673]

>>10512666
nah, there is an uncountable number of true and false statements because there is an uncountable number of statements.

and there will be higher and higher truths to consider always.

the "end of mathematics" will come when it changes form, but there will never be an end to discovery of new truths and forms themselves.

right now our sense of form is restricted by what we can realize as meaningful. it requires 3 years of training to understand a lot of the meaning in one subfield of mathematics, and even more to do innovative work.

as we increase the rate at which meaning can be inferred from statements, we will then begin to view the structures of formal systems in "3D". In other words, you can conceive of 3D as very quickly moving 2D images that are being perceived in combination, over time to create an emergent object which is the "3D" object. this is how computer graphics works for instance - it's a bunch of very fast and coordinated 2D images.

as we increase the rate at which we perceive meaning from data (possibly with ai-assisted neuro-engineering), the object which will form from the conglomeration of the erstwhile thin slices of mathematical reality we must now work years to be able to understand, is simply beyond our comprehension. at that point "mathematics" as we know it will probably look like monkeys counting on their fingers. but this doesn't mean that there will be an end to discovery or questioning or truth within the confines of formal systems. even if we exhaust all possible formal systems in every possible way at our level of reality, you haven't considered the emergent forms which are right now beyond our comprehension.

[Anonymous No.10527679]

>>10525822
>math-phys
spy

[Anonymous No.10527758]

Help me out /mg/, I feel like a brainlet.
I'm trying to derive a matrix equation, but I think the dimensions don't match up along the way.
Here's somebody who had the same problem on Stack exchange: https://math.stackexchange.com/questions/2387495/how-do-you-differentiate-a-matrix-equation-with-respect-to-a-vector
They say [math](y-X\beta)^T X[/math] is a scalar, but I don't get that. y is an n-vector, X is an nxp matrix, [math]\beta[/math] is a p-vector, so I think [math](y-X\beta)^T X[/math] should be a 1xp vector (row vector), which is not a scalar. Where did I fuck up?

[Anonymous No.10527769]

I want to start calculus rigorously. I've heard that the two major calculus/analysis introductions are Michael Spivak's book and Tom Apostol's. Which is preferred, and what are the differences mainly?

[Anonymous No.10527774]

>>10518406
Just reporting in to that test today was omega shit

Literally won't even going to be mad if I do god awful, I wasn't going to study a bunch of the shit that came up today regardless of time.

The combinatorics questions I've seen on past exams were always so straightforward; this time they actually reminded me of the questions I used to do in high school.

Also, a question that was on the form integral (log x) ^m - integral (log x) ^n? What the fuck was that? I looked it up after the exam and saw there was a formula for it, but I literally have never seen that equation come up in my math career to be familiar with it, and a year away from graduating with a BA/MA.

I didn't know that an exam that was supposed to be assessing my mastery of college level mathematics was going to ask me about 5 questions on Euclidean geometry (not even things you do in precalc, literal high school geometry, which I admit openly to being terrible at) and it would suddenly decide to ask some non-trivial algebra questions.

I like algebra a great deal and like to think I'm at least decent at it, but the questions it asked to day certainly werne't so easily done in the all of ~3 minutes per question you have.

Anyway, if any of you took it and thought it was easy, good for you; I'm just bothered that I even studied for this, seeing as with what I was asked, I literally would have scored identically without pouring into past exams/study resources.

[Anonymous No.10527777]

>>10527774
*literally won't even be mad if I do god awful
*the contest questions I did in high school
*of the form
*I'm a year away
apparently I had a fucking rage stroke writing this sorry

[Anonymous No.10527917]

can someone explain some advanced properties of prime numbers to me? obviously i know all the basics but i think i found an extremely useful property that involves factorials.

[Anonymous No.10527967]

>>10527917
if you take any two prime numbers r and s, they form a group under the operation of division

[Anonymous No.10527980]

>>10527967
wat

[Anonymous No.10527992]

>>10527980
if you take any two prime numbers, they form a non abelian group under multiplication

[Anonymous No.10527997]

>>10527992
how? 2*3 = 6 which is not prime

[Anonymous No.10527999]

>>10527997
keep in mind i said non abelian.

[Anonymous No.10528003]

>>10527997
He didn't say that. He said that any two prime numbers inherit a B-Teichmuller type structure which naturally induces a non-abelian group operation under division.

[Anonymous No.10528004]

>>10527999
non-abelian means non-commutative, what does that have to do with what i said?

[Anonymous No.10528008]

>>10527758
>They say ... is a scalar
Source?

[Anonymous No.10528011]

>>10527917
the factorial of a prime number p is the greatest common divisor of 2p and p-1

[Anonymous No.10528015]

>>10528008
The two answers in the stack exchange link I posted
They both say something is a scalar which isn't if you look at the dimension (unless I fucked up somewhere)

[Anonymous No.10528019]

>>10528004
the non abelian group formed by division among the primes inherits a B-Teichmuller type structure which clearly induces a non abelian group operation under division

[Anonymous No.10528030]

>>10528003
>>10528019
interesting!
>B-Teichmuller type structure
where can I read up on this? google is not being particularly helpful

[Anonymous No.10528033]

>>10528030
https://www.pornhub.com/gayporn

[Anonymous No.10528038]

>>10528015
The answer proposed by steven gregory is brainlet tier

[Anonymous No.10528039]

>>10528033
that doesn't look very non-abelian to me...

[Anonymous No.10528045]

>>10528039
Yeah, that anon's messing with you. Gay porn is clearly abelian.

[Anonymous No.10528048]

>>10528039
this is why you wont make it you dumb aspie

[Anonymous No.10528055]

>>10528038
So how do you do it properly?

[Anonymous No.10528066]

>>10528055
What? The textbook does it just fine kiddo. The only one who says it's a scalar is the aforementioned stackexchange brainlet.

[Anonymous No.10528075]

>>10528066
>The textbook does it just fine kiddo.
The textbook only gives the solution, I want to know how to get to the solution
Along the way I get matrices of different dimensions being added together which is obviously false

[Anonymous No.10528080]

>>10528075
No one in /mg/ is gonna take a derivative of a quadratic for you.

[Anonymous No.10528085]

http://www.kurims.kyoto-u.ac.jp/~motizuki/papers-english.html
Is Mochimochi a child at heart?

[Anonymous No.10528089]

>>10528080
It's a derivative using matrices which I'm having trouble with. I can derive a normal quadratic equation obviously.
Where do you suggest I look for help then if this is not the right place?

[Anonymous No.10528101]

>>10528089
*snubs out cigarette*
here you go kid. https://eli.thegreenplace.net/2015/the-normal-equation-and-matrix-calculus/

[Anonymous No.10528106]

>>10528101
Thanks anon, I'll take a look at it.

[Anonymous No.10528196]

what the most powerful is it prime calculator on the internet?

[Anonymous No.10528223]

>>10525841
yes

[Anonymous No.10528227]

>>10525841
Take a point in the subspace. Take a countable neighborhood basis, restrict, and check if it's also a neighborhood basis for the subspace.

[Anonymous No.10528308]

>>10527917
[math](p-1)! \equiv -1 \mod p[/math]
every finite field is isomorphic to [math](\mathbb{Z}/p^n\mathbb{Z}, +, \cdot)[/math] for some[math]p, n[/math]
for [math]p > 2[/math], [math]p \mid 1^{p^n} + 2^{p^n} + ... + (p-1)^{p^n}[/math]

[Anonymous No.10528331]

So, this proof is intuitively obvious. But this doesn't feel like a formal proof at all. It feels like something pulled out from the ether. What is the proper justification for "when we sum the degrees of the vertices, edge e gets counted twice"?

Fuck discrete maths and their "intuitive counting" proofs.

[Anonymous No.10528351]

>>10528331
Is this bait? You can formalize it in two lines, it's just not worth the effort.

[Anonymous No.10528359]

>>10528331
What is this from? Looks like khan, but I can't recognize the logo on the bottom right corner.

[Anonymous No.10528424]

>>10528351
Please. I'm desperate. I need to know what's the underlying math behind these arguments. Are there some implicit bijections I'm not getting?

>>10528359
Sarada Herke, graph theorist, her videos are great tbqh

[Anonymous No.10528432]

>>10528424
>her
dropped

[Anonymous No.10528601]

>>10528331
its already formal tho
every edge has 2 and only 2 vertices

but yeah combinatorics is fucking gay

[Anonymous No.10528731]

>>10527673
> nah, there is an uncountable number of true and false statements because there is an uncountable number of statements.
You keep using that word. I don't think it means what you think it means.

The number of possible statements may be infinite, but it's countably infinite (enumerable, having the same cardinality as the natural numbers). In mathematics, "countable" means that you can number statements 1,2,3,... and so on. It doesn't require that the counting stops at some point. The natural numbers, integers, rationals, constructible numbers, algebraic numbers and even computable numbers are all countable. The reals are uncountable.

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

[Anonymous No.10528738]

how the fuck do i become a math god, i just finished linear algebra but i still dont get the hieroglyphics you guys post is it mostly higher algebra and topology?

[Anonymous No.10528741]

>>10528731
Wait, is this bait? There is an incountable number of incorrect statements. I'm shocked that you would think otherwise.

[Anonymous No.10528756]

>>10528738
Most of it is just logic and set notation. Read on how to do formal math proofs for a start.

[Anonymous No.10528764]

>>10528738
>formal math proofs
Here you go
https://cheng.staff.shef.ac.uk/proofguide/proofguide.pdf
All I had to do was google "formal math proofs".

[Anonymous No.10528792]

>>10528741
If you're talking about finite statements in a language with countably many symbols you're wrong.

[Anonymous No.10528803]

>>10528741
infinite and incountable arent the same

[Anonymous No.10528892]

>>10528792
Choose some [math]q\in{\mathbb{R}\setminus{\mathbb{Q}}}[/math]. We define the following statement [math]P_{q}[/math] to be [math]1=q[/math]. Let [math]P=\{P_{q}|q\in{\mathbb{R}\setminus{\mathbb{Q}}}\}[/math]. [math]P[/math] is uncountable.

[Anonymous No.10528922]

>>10528741
It's not bait. It's an attempt to explain what countable means (hint: it's not the same as "finite").

[Anonymous No.10528927]

>>10528892
>[math]P[/math] is uncountable.
That's one statement hunnie.

[Anonymous No.10528931]

>>10528927
[math]P[/math] is a set of statements tho. Not sure why I thought that they must be incorrect from your earlier post, but my point still stands

[Anonymous No.10528936]

>>10528931
>set of statements
So you think "q = 1 for all q in R" is |R| many sentences? Holy shit that's hilarious LMAO
>tfw people invoke uncountably many statements whenever an [math]\epsilon-\delta[/math] proof is written
>tfw Aquinas, Descartes and all classical analytics BTFO

[Anonymous No.10528945]

>>10528936
I constructed a set of statements with an infinite cardinality and for which there exists no bijection to the naturals. I'm sorry you are so upset by this.

>sentences
Perhaps you meant sentences, not statements, originally? In which case, you'd be correct to state that, given a countable alphabet, there are only countably many.

[Anonymous No.10528947]

>>10528331
think of it as a holomorphic line in a 3 dimensional vector space. Because all graphs inherit a B-Teichmuller type structure, the surjective function that relates the amount of vertices to edges is actually a non-abelian group of the polynomials with the operation of division. The rest of the proof is a simple matter of a substitution

[Anonymous No.10528952]

>>10528331
baka

[Anonymous No.10529111]

>>10528892
>We define the following statement...
Not a statement. You can't even write it down lmao.

[http://math.harvard.edu/putnam(...) !!84u21X0KjW+ No.10529144]

Daily Putnam Problem >>10529139

[Anonymous No.10529171]

>>10529111
>Not a statement
By what reasoning?

[Anonymous No.10529182]

>>10529171
You can only "state" it for countably many choices of q. In the context of limited nature of maths your statements are meaningless because they're not something a human being can actually write.