/sci/ - Science & Math

First for integrable systems

yukariposter

>>12475234
I'm still accepting opinions.

>>12476587
Already had plenty in the other thread, no one can make that decision for you man, just reflect on your own time and go for it, in any case you'll be guaranteed a PhD and a job in the future.

ok so did any of you guys or anyone you know get that "300k starting salary mathematician" job or is it a farce?

yeah me

Tell me about differential geometry.

>>12476732
it's the theory of manipulating indices

How do I stop being absolutely terrible at mathematics? I’m meant to be starting CS major next year and I’m retarded when it comes to maths

>>12476598
I watched Zixi Wang.
She's kinda cute on a small rectangle on the corner of my screen.
The highlight is at 1:09:57.

>>12476744
You'll fit right in with other CS majors then
>>12476732
What do you want to know?

>>12476761
>3DPD

>>12476763
>What do you want to know?
your most interesting theorem, BUT it must be able to be explained to someone whose most advanced math class is calculus two.

>>12476928
>interesting theorem
Hmmm.. I'm pulling a blank here, sorry.

>>12476928
Does Stroke's theorem count?
It basically interchanges integration along a region and integration along it's border.

>>12476685
>guaranteed a PhD and a job in the future
I think you're assuming a bit there.

Yeah, I'll have to make my own decision in the end, but I'll probably be taking and thinking about other's opinions until the last hour.

>>12476928
>>12476941

This Anon is right the Newton-Leibniz-Gauss-Green-Ostrogradskii-Stokes-Poincaré theorem elegant and not too hard too understand. See this normie friendly video for example:
https://www.youtube.com/watch?v=1lGM5DEdMaw

which option is the cheapest /mg/?

>Individual apples at $1.99/lb
>A 2.5 lb bag of the same apples for $3.99
>A 20 lb box of the same apples for $19.99

>>12476928
well the ultimate result in UG diff geo is Gauss Bonnet

>>12476958
the box and before you say anything about packing it doesn't matter because you gave the weights

>>12476941
>Stroke's theorem
That's Calculus III.

>>12476969
but it's not the cheapest anon

>>12476978
yes it is

>>12476976
Do muricans really teach differential forms in calculus 3?

>>12476982
you're paying more for more apples. it's not the cheapest. if it was the cheapest it would be less than 1.99

>>12476988
Most important part of calculus III is Green, Gauss and Stokes, if you didn't learn that in that course then your uni is fucking trash.

>>12476989
what if i want many apples
>>12476988
Most schools in the us do a combined calc iii linear algebra type class and do teach differential forms

>>12476587
have you talked with anyone personally who could be your advisor? it sounds like your doing a lot of at home speculation.

>>12476997
you don't have money anon so you have to buy the cheapest bag, which is individual apples at $1.99/lb. you don't want your apples to rot anyway

>>12477012
How can I make apple turnovers with just one apple ?

>>12476988
he means the 1800s version in R2 with no proof. (engineers )

>>12476994
>>12476976
ignorance is a dangerous thing

>>12477014
do you don't need apple turnovers anon

>>12476698
Of course, everyone in this thread got 300k starting and are swimming in undergrad pussy. What made you think it's a farce?

>>12477024
I'm an undergrad pussy. You are all in a thread with me and likely many others like me. So technically you're swimming in undergrad pussy.

>>12477017
But I actually did learn differential forms in freshman Calc 3, from Hubbard & Hubbard Vector Calculus, Linear Algebra, and Differential Forms

>>12476698
I know a CS guy who made nearly 300k starting from Mastercard and a CS guy who made 60k in summer internship at a famous prop shop (he did systems engineering for them for what it's worth not quant stuff).

>>12477023
Not with that attitude

>>12477008
Not personally because that's impossible right now, but I've sent emails.
The professor from second option was the one to propose it to me in the first place. The guy with a bunch of students said that to me through email, he basically implied that he'd be my advisor if I wanted to, but that he'd prefer that I would choose someone else so that he wouldn't have to use so much time adivising students.

Recently I found out that in practice he has 4 students (the last one didn't contact him in a long while), 2 of those are allegedly finishing their thesis and their scholarships already ended, another's scholarship will end in the middle of next year and the last one's will last until the end of 2022.
I have to focus on qualification next year, so chances are he will have only one of the students he already has now.

I don't like the fact that he wasn't much inviting, but people told me he's very attentious with his students. Sounds like a good person trying to avoid being overloaded without being immoral, I get it.
I don't even want too much time from him, I'd probably be ok with 30 minutes per week... Even though that's more risky for me.
Plus, there are possible backup options there. So right now I'm leaning to first option. Mainly due to subject interest.
I did sent an email in order to check if I understood him correctly though. If he answers even more negatively, I'll probably reconsider.

>>12477137
i'm dying to know what country you're in. can you please tell? for what it's worth I don't think anyone would care enough to dox you. i am going to go out on a limb and say you are from brazil

I found a new test for primality but I'm fairly certain it's just the sieve of eratosthenes with blackjack and hookers

personal favorite beginner (post calculus) statistics?

>>12477152
>brazil
Why that country specifically?

>>12477279
Because of the way he writes (nothing specific just a hunch), the fact that there are good yet understated schools for math in brazil, and the fact that there are many brazillians on 4chan. 2nd guess would be italy for the same reasons

>>12476761
Where did you even find the recordings? I'm blind and can't see them anywhere.

>>12477320
They seem to have deleted the link from the page.
The partial recording is in https://www.youtube.com/watch?v=1adQsqGyVR4

>>12477152
>>12477291
Huh, curious.
At least I think it's pretty obvious that english isn't my first language.

>>12477495
Is either guess right you don't have to say which

>>12477524
Why are you so obsessed with the personal life of an anonymous in an imageboard?

>>12477551
I'm just curious to see if I am right anon, you're the one posting about your personal life.

>>12477431
Thanks! Or I guess spasiba in this case.

>>12476587
I say 2.

>>12477555
I'm not that guy and you should stop being so interested in gossips about one's private life. No one likes people that likes to play Sherlock Holmes in an anonymous site.

Guys I have a queshon.
If something has a 99.999 percent improbability, is there a word for that?

>>12477551
>imagine being unwilling to relinquish personal information to 4chan strangers in 2020
Yikes.
By the way, my first name is José Gaspar. I was born in Mexico, but I managed to get a student visa to study Electrical Enginnering in the US, and later, since my interests shifted, got into a PhD program for Symplectic Geometry. Since then I've managed to forget all electrical engineering I've ever learned and get married to the most beautiful girl in the world. I'm expecting to finish my program by 25, which is two years from now.

>>12477713
Based José, tu eres una inspiracion para mi

>>12477713
>get married to the most beautiful girl in the world.
if thats true then shes going to cheat on you

>>12477686
yes the word is "impossible"

>>12477030
That’s really hot anon

Why isn't the function x->m for all x in the set of naturals {0,1,2,3,4...m-1,m} a group?

I'm not coming back to /mg/

>>12477947
100 heads in a row denier spotted

>>12477961
>why isn't function a group
because x is the group

>Although he died at age 23, he was already considered one of "the greatest mathematicians of the younger generation" by his professors Helmut Hasse, and Richard Courant
>meanwhile I'm already nearly 22 and still no achievements
I feel I'm never gonna make it bros.

>>12477961
Yes, there's an obvious way to make it isomorphic to the additive group [math]\mathbb{Z}/m\mathbb{Z}[/math].

>>12478016
wouldn't it be m+1?

>>12477947
I was born with 99.999 percent impossibility then. That's pretty freaky if you think about it

After lengthy calculations I decided that it's impossible to get dubs.

>>12478040
Ah right, [math]\mathbb{Z}/(m+1)\mathbb{Z}[/math].

how can I make yukariposter love me

>>12475553
Just do this.
[math]\int^1_{-1}P_n(x)e^{ax}dx=\frac{a^n}{(2n)!!}\int^1_{-1}e^{ax}(1-x^2)^ndx[/math]
Obvious substitution [math]x=\cos\theta[/math] reduces this to modified Bessel function of the first kind. So
[math]\int^1_{-1}P_n(x)e^{ax}dx=\frac{a^n}{(2n)!!}\int^\pi_0e^{a\cos\theta}\sin^{2n+1}\theta d\theta=\sqrt{\frac{2\pi}{a}}\frac{I_{n-\frac12}(a)}{2n}[/math]

>"let w be..."
don't tell me what to do

>>12477961
Because groups need binary operations

Are there any profoundly intelligent(175+ IQ) anons browsing here?

>>12478506
no.

>>12478506
literally all of us
except this faggot >>12478534

> future-in-russia.com

Is this worth doing anons? I'm currently in my third-year undergrad in CS. The program here is very terrible, and I am just self-studying maths through baby Rudin and H&K. Will going to a rusfag uni be worth it? If so where is the best maths program there?

>>12478650
Of your program is bad and you can't study on your own you are going to be raped.

>>12478807
I can study on my own but the faculty here is really clueless.

>>12476744
Hi CS fren! Honestly you’ll do really well with hard work and conversing with your STEM bros during study sessions. When you’re struggling with a math problem, just remember, when in doubt, USE THE DEFINITION of the concept you’re working on. Definitions in math act as lenses to focus your mind on the essentials, so that the process of understanding the problem becomes easier and you can hopefully solve it more efficiently. Try to resist comparing yourself to others while you’re studying and working; just strive to be better than the mathematician you were yesterday. And remember to drop a thread here when you graduate. I want to hear how much math you’ve accumulated in that time. I believe in you!

how do knot theorists rigorously prove anything

>>12479285
bolynomials

How do I combine Teichmüller spaces, Kähler manifolds and Jordan algebras in one for my thesis?

>>12479614
based

>>12479285
This really reads like a post written by someone who doesn't really enjoy knot theory much.
Here's the secret: no knot theorist gives a single shit about rigor and you fucking moron belong in algebra.

>>12478650
I'd say the ones worth going to are MSU, MIPT, SPSU, and HSE (not necessarily in that order). I do not think it would be easy to get in to any of those, and as the other poster said it will be very difficult to stay in. Don't look at the fact that they're somewhat obscure schools in a poorer country and come away with the idea that they're not as difficult and (especially in math) as prestigious as top western universities. Also (this is anecdotal but I've heard this sentiment many times), they put more emphasis on problem solving than western math departments, so make sure you're not behind in that.
Further, do you speak Russian well? Do you think you would be able to adapt to the culture?
If you consider yourself to be capable of getting in to the best universities in Russia, why don't you try for Oxford/Cambridge, UWaterloo/UToronto, or, for that matter, the top universities in the US?

You know how in the proof of incompleteness theorem you form a statement which intuitively reads "Statement x is unprovable", then take its Godelnumber and plug it in? What if we do a little differently and instead take our statment P(X) to be "Statement X is provable", let N be the Godelnumber of P(X) and let G=P(N). Intuitively, G says "I am provable".
Now is G true? I don't see any immediate reasons for it being provable or not, like you could see for the original Godel sentence, arguing from consistency.

>>12479614
kek
I hope you go far anon

>>12479285
Through the techniques of Algebraic Topology.

>>12479626
I guess the theory of 3-manifolds is not rigorous enough for you

>>12479651
>theory of 3-manifolds is not rigorous enough
Topologists don't actually think in terms of proofs, that's a common misconception. Handwavy techniques are all that it it takes. For example, in topology to prove S^n and S^m are not homeomorphic it's enough to say that an embedding of it into R^k separates it into two components only for the appropriate k. You don't actually need to prove it because it's intuitively obvious. We've localized the topological nastiness from of the problem into an extremely particular and uninteresting situation. Such is the goal of topology

>>12479652
Ok, now apply your hand-waving technique to show a non-trivial result.

sci-hub is a great thing but does this woman need to appear every time
i mean put a fucking asian with big boobs there, then i'm gonna read more papers

>>12479652
bait, but let's not forget that this load of shit was meant seriously the first time it was posted

>>12479658
took me ages to notice her shirt was saying "send money" lol>>12479658

>>12478197
Why are you asking us instead of him?
HEY YUKARIFAG HOW DO I MAKE YOU LOVE ME?

>>12479614
Something about classifying the observables in field theories in nice curved spaces

>>12479614
Interuniversal Jordan-Peterson theory.

>>12479799
I recognize that bedroom

look at dis nigga

>>12480406
Im looking at him.

>>12476763
>What do you want to know?
What makes it differential?

>>12480562
the use of differential calculus

Can some mathbros guide me through how to find the vertical tan line of x2y=xy2+1

>be the high school math guy
>go for university math studies
>get reality checked hard by intro analysis
>go screech autistically about real numbers and infinite sets on some anime forum
Many such cases!

>>12480742
>>12480742
fuck, meant (x^2)y=x(y^2)+1

>>12479658
kazakhs are asian and she got fat mammaries even tho she is a bit obese

I've flopped my way into Partial Differential Equations, A's up to DiffEq where I got a B. What should I focus my studies on this next month so I don't fail out of Partial?

>>12480757
Also the A's are pretty much fake community college A's, I'm not great at math can't do long division

>>12480745
You can't even add natural numbers smaller than 10.

>>12480760
>>12480757
>can't do long division
>Passed Calculus
Hahahahahah America is so fucked, we really are living in the end times of US hegemony.

>>12480757
Uhh maybe Partial Differential Equations?

>>12479626
I live fucking rent free in your head, worthless autist.

>>12479652
FUCK YOU! FUCK YOU! FUCK!!!! YOU!!!!
>>12479685
seek help.

>>12478259
Why does the first line follow

>>12481300
>>12481303
Wow. I thought you would have dropped maths by now. How's it going bro?

>>12481303
>FUCK YOU! FUCK YOU! FUCK!!!! YOU!!!!
Clearly a very mentally stable individual.

So we've got a couple more raging autists lately, I see

bros i got filtered by differential forms

>>12481339
just graduated, currently applying to phd programs
finally when i look down on undergrads in this thread i won't be doing so dishonestly
i think i suffer from a communication problem here. i don't mean to suggest that rigor is unimportant. i simply mean to suggest that someone who is being introduced to topology/geometry should first be provided a nearly rigorous intuition for why things work, and then following that they should be assigned to complete proof outlines / full proofs of the rigorous arguments themselves. this is how it should be in undergraduate topology/geometry. similarly, if you're a topologist you probably don't think about your spaces in terms of big chain complexes and homological lemmas (unless you're a pure algebraic topologist). instead you use such things when you need to write down a full proof, or you delegate such things to assistants/grad students. but when you're working on understanding some new piece of math it's not about trying to remember why the jordan curve theorem is true.

>>12481378
Check this dude's channel out: https://www.youtube.com/c/Aleph0/videos

>>12481378
If you got filtered by differential forms this means you got filtered by vector bundles and related constructions which means you got filtered by tensor products which means you need to work on your linear algebra knowledge desu.

>>12481378
k-form = something that can be integrated over k-dimensional space

>>12481472
dumb way to think about it. k-form = something which at any given point takes k tangent vectors and gives you a scalar, doing so multilinearly, and varying smoothly from point to point.

>>12481482
+ antisymmetry condition of course

Should the complement of an integral be called the outtegral or extegral?

>>12481506
it's not called an integral because it's interior to anything
it's called an integral because of the word integrate. you're integrating many small parts into a whole.

>>12481482
all right, and why exactly do we care about these objects so much?

Am I a brainlet if I struggle with the proofs in Spivak's Calc after just covering differentiation and function optimisation in Engineering Math 1?

>>12480771
Long division is gay. It's much easier to understand more abstract stuff, ironically.

>>12481659
It's not easier to understand abstract stuff, it's just easier to get away with pretending you understand it.

>tfw brainlet
>tfw computer scientist
bros......

Who wins in a fight, measure theory or differential forms?

>>12481889
in what fight? what are the parameters you want to compare?

>>12481528
because you can integrate and differentiate them

>>12481655
no, everyone struggles with proofs at the beginning, with time you'll get used to writing and understanding them. just takes practice.

>>12481889
>for purposes of differentiation
differential forms, differentiation of measures sucks
>for purposes of integration
measure theory by a fucking landslide

>>12481889
The rational numbers.

>>12476958
Getting one individual apple is the cheapest, it’s less than 2 bucks

>>12481402
yeah i figured... im reading about vector bundles now

>>12480748
Differentiating both sides with respect to x, we get

(2x)y + (x^2)(y’) = (1)(y^2)+(x)(2y y’)

by the product rule on both sides and using the chain rule for the y squared on the right. Then we isolate and solve for y’ using quick algebra. Get the y’ terms on the left and the other terms on the right.

(2x)y + (x^2)(y’) = (1)(y^2)+(x)(2y y’)

(x^2)(y’) - (x)(2y y’) = y^2 - 2xy

y’ (x^2 - 2xy) = y^2 - 2xy

y’ = (y^2 - 2xy)/(x^2 - 2xy)

How many of you are bald or balding?

>>12482863
0

Give me books that will make me a good proof guy I am absolutely dog shit at proofs. I tried Lang but I think geometry is boring as shit.

>>12482964
Try Fuchs Fomenko

>>12481528
First of all think about everything visually as an embedded manifold in R^2n (this is always possible anyways (Whitneys Theorem)). Think about the tangent space of a manifold at a point. Very roughly speaking its something like a linearization or "approximation" of the manifold locally. Suppose you have a fine grid on the manifold, you get by taking small squares on your coordinate chart. To integrate you want to sum up the little squares, but theres a problem! A little square in your chart will pull back to something like a curvy(!) parallelogram on your manifold (think about the sphere example)! So what do you do? You approximate your curvy parallelogram by taking tangentvectors, making it into a flat parallelogram. Now all that you need is a notion of signed area for k tangent vectors, but that is exactly what a differential form is, a way to asign signed area to k tangent vectors! (Think about why this is the case if you don't know, in particular the connection between determinants and differential forms)

>Theorem: R^n and R^m are of different dimension when n ≠ m
>Proof. Trust me nigga
Why do mathematicians be like this?

>>12483296
mathematicians are not like this

>>12483299
they really do be like that tho

>>12483302
prove it

>>12483308
trust me nigga

>>12483310
nice circular reasoning

>>12483308
proof: by inspection

>>12483308
Steinitz lemma

>>12483322
>*bijects ur R^n to R^m*
nothin personnel, coordinatist

>>12483296
Define dimension of a manifold by the dimension of its charts. To show this is an invariant you show that Rn is not homeomorphic to Rm. This can be shown by removing a point from both spaces and comparing their homology.

>>12482964
Just give up and do something you are actually good at. If you don’t have the talent you are in for a world of pain.

I like COVID.
>can attend conferences without having to travel
>if a talk is shit, just mute Zoom and open 4chink or work on something for a while
>can still have poster sessions with Zoom breakout room feature
>becoming more common for seminars to be recorded and material to be posted online so you can go back and check stuff more easily later

Just handed in my take home differential geometry final lads
been working on it for ~ 6 hours now
probably could have done it in half that time if I wasn't retarded

>>12483704
>implying one can easily measure talent with barely any experience data as it seems to be his case
Maybe you're the one with no talent, huh.

>>12483877
My next course will be given through google meet.

Any suggestions on how can I record classes for later reference? Would help not needing to take notes etc

>>12483936
IIRC the lecturer would have to either 1) be the one recording, or 2) tick some box that says 'enable recording feature'.
Or were you thinking of using some kind of screen capture software?

>>12483950
I can't count on him enabling recording, so I want to know how is the easiest way to record it myself through some software.

>>12483960
Sorry anon, try asking /g/ maybe

>>12483936
Ask /g/.
>>>/g/sqt

>>12483424
>proof by abstract nonsense
lmao pure math majors are joke

You can only reply to this post if you got straight A's in your math courses this semester.

disregard this post, i am copying and pasting something from archive so i could read Tex.

A map [math]\varphi:V \to W[/math] between vector spaces is linear if [math]\varphi(au+bv) = a\varphi(u)+b\varphi(v)[/math]. It's called linear because it preserves linear combinations (the term in the bracket). A corollary of this is that it maps lines to lines. A line is something like [math]p+tv[/math], apply [math]\varphi[/math] to see that the image is also a line.

In our case, [math]V = W = C^{\infty}(\mathbb{R})[/math], the set of all smooth functions on the real line, [math]\varphi = \tfrac{d}{dx}[/math]. The map eats a function and gives back another function. It's linear because we know that [math]\tfrac{d}{dx}(af+bg) = a\tfrac{df}{dx}+b\tfrac{dg}{dx}[/math] from calculus, that's literally the fact that derivative preserves linear combinations of functions.

Linearity of the derivative has absolutely nothing to do with the fact that the derivative is related to the slope or whatever. Integral is also a linear operator and integral is about areas and not about lines.

eqn] \frac{d}{dx} f(x) = \lim\limits_{h \to 0} \frac{f(x+h) - f(x)}{h} [/eqn]

[eqn] \frac{d}{dx} a \cdot f(x) + b \cdot g(x) = \lim\limits_{h \to 0} \frac{a \cdot f(x+h) + b \cdot g(x+h) - a \cdot f(x) - b \cdot g(x)}{h} = \lim\limits_{h \to 0 } \frac{a \cdot f(x+h) - a \cdot f(x)}{h} + \lim\limits_{h \to 0} \frac{b \cdot g(x+h) - b \cdot g(x)}{h} = a \cdots \lim\limits_{h \to 0 } \frac{f(x+h) - f(x)}{h} + b \cdots \lim\limits_{h \to 0 } \frac{g(x+h) - g(x)}{h} = a \cdot \frac{d}{dx} f(x) + b \cdot \frac{d}{dx} g(x) [/eqn]

>>12484228
>>12484239
Use http://mathb.in/

>>12484245
oh cool. i see what is supposed to do but it doesn't work, the same raw latex is displayed on the right.

>>12484245
>http://mathb.in/

>>12484269
>>12484272
apparently you need to enclose formulas in $$
that sucks.

I think the best way is to copy from warusu and paste to the math thread, it is math after all and others can learn something.

>>12484287
You'd be correct if that post had actual insight, but it's basically just spoonfeeding a retard and only relevant in context.

>>12484296
hey that post was reply to me.
also you can blame 4chan for retarded non-standard tags like [math] and [eqn], instead of using something like $$ so you could copy and paste on 3rd party web sites.

>>12483936
Get a tape recorder

>>12483960
OBS is your friend, friend

>>12477034
>CS
everyone knows CSfags are making a lot of money, just wait until the CS bubble pops and they will be earning less than burger flipper

>tensor
>operator
>spinor
a lot of thinking, still don't get it

>>12484046
homology is not abstract nonsense. if you don't have an intuition for homology you need to go back to undergrad.

>>12484942
What is your intuition for homology?

>>12484816
What did you think about?

>>12485051
>inscribe a boundary of a triangle into your space. is it possible to fill the inside? if not, it's because there's a hole inside.

>>12482593
an individual apple could be like 20 lbs though

>>12485090
This is only applicable in the most trivial cases. I wouldn't call that intuition of homology when most of the time it's useless. Does it help you in any way to intuitively understand the universal coeffient theorem or Kunneth theorem?

>>12485073
i thought about lines and surfaces

If I'm asked to differentiate some function:

[math] 2/(4(x^2 - 1))[/math]

Could I rewrite that as

[math] 2/4 * (x^2 - 1)[/math]

Before differentiating?

>>12485185
>knows tex

Hi /mg/!

>>12485185
you should tell your lecturer or whoever gave you that problem that using / in a mathematical context is plain retarded

anyway, in this sense, it's clearly [math] \frac{2}{4(x^2-1)} [/math] so no, you can't rewrite it

>>12485234
Yes, that's what I was attempting to write. So I can't rewrite it as a fraction multiplied by [math](x^2-1)[/math]?

>>12485222
fuck off

>>12482964
Linear algebra is good for that
It's prettier with some geometry but still

>>12484942
>homology is not abstract nonsense
Yes but abstract nonsense is homology

>>12485222
Who is this Norwood 3 ass mf

>>12476536
How do I stop being a such a brainlet at math? I was good at it in school, but the complex stuff escapes me now that I can't coast by on innate ability.

I do not get it.
I am trying to use CLT to show the connection between a binomial variable and the normal distribution.
But my variance comes out wrong.
[math]
\begin{aligned}
X &\sim B(x; n, p)\\
E[\bar{X}] &= E\left[{\sum X \over n}\right] = {1\over n}\sum E[X]
= {1\over n}n E[X] = E[X] = np\\
Var[\bar{X}] &= Var\left[{\sum X \over n}\right]
= {1\over n^2}Var[\sum X] \overset{idp}{=} {1\over n^2}\sum Var[X]\\
&= {1\over n^2}n Var[X] = {1\over n}Var[X] = {1\over n}np(1-p) = p(1-p)\\
SD_X &\overset{???}{=} \sqrt{p(1-p)}
\end{aligned}
[/math]

am I mixing up the n of the binomial distribution with the number of samples in the average?

>>12485482

i am doing fine in uni but i struggle with summing/subtracting anything more than two digits or multiplying a single digit numbers that aren't 1 or 10 or 0. it literally takes me like a minute to figure out that something trivial with fractions like 4/8 + 1/2 is 1. is this normal?

>>12485520
Damn this is dark, regret that I asked

>>12485525
Dyscalculia and or low working memory. Not great but not suicide-tier

>>12485518
perhaps I should convert the binomial variable to a bernoulli one or something

Why is [eqn]i^{i}[/eqn] approximately 0,20?

>>12485516
Practice more

Have any of you lads read Bernhard's "The Loser"?
I feel like most of you could relate to it.

>>12485581
>I feel like most of you could relate to it.
Why do you think so?

>>12485573
Wait, there's more. What is this sorcery?

>>12485581

can't bring myself to read fiction, seems like a waste of time

Why the hell is it so hard to simply read and understand a math book?

>>12485594
Because most of my profiling of the mathematicians of this board comes from things like animeposter offhandedly mentioning that he already plans on giving up on academia, people discussing dropping maths to become quants and general despair, and that's the kind of person who'd relate to the Loser.

>>12485518
oh right I am dumb
it is the thing I suspected about mixing up the n's
(1/N)*N cancels out and E[X] remains
with Var, (1/N) remains as does np(1-p)

it is not exactly the same thing as in the theorem, but I guess somewhat related.

>>12485518
>>12485631
it actually is CLT after all
I just have to divide by n to turn the binomial X into the average of n bernoulli variables
the expected value and the variance get the desired form that way.

sorry for my triple dumb

Do you guys have any lectures on real analysis that you can recommend? Also, can any americans explain to me what difference there is between calculus and real analysis, where I'm from we don't the have calculus/analysis split, we just call it analysis. I'm not sure if this just means it's calculus but renamed.

>>12485266
You can rewrite it as 1/2 * (x^2-1)^(-1).

>>12476988
Meritard here. My school didn't even mention differential forms in calc three. Never proved a single thing in calc three. Only triple integrals and word problems.

>>12485528
>low working memory
Not him but yeah, it fucking sucks

>>12485786
Calculus seems to be nonrigorous analysis. Just learning the mechanics of integration and differentiation. Usually a HS course.
My country also calls it analysis. The level of rigour really just depends on your major (its not usually a hs topic around here)

>>12485051
Homology is holes.
Cohomology is cuts.
Do some examples and see how the two relate to understand things like universal coefficient theorem and Poincaré duality.

To me it makes more sense with coefficients mod 2 since then your chains directly represent inclusion/exclusion of components. Torsion is weird and I'm not sure there's an intuitive explanation for it beyond a "twist" in the space.

>>12484185
I gets As in all my courses. The only course I didn't get an A in was because it was assessed terribly. I ended up tutoring that course and writing the assignments.

Why no one here ever talks about mathematics or anything interesting?

>>12486000

>>12486014
Boring desu.

>>12486000
Why don't you?

>>12476536
What academic fields are you interested in outside of mathematics? I am into biology and computer science.

>>12486036
On my phone right now otherwise might have posted cool graphics and animations.
>>12486064
Computer Science, Economics and Statistics. Not sure if the last one counts as "other fields" here.

>>12485573
Use oiler's formula.

Where do you guys go to find old exams? I would like to write some exams just to test myself.

>>12485149
you don't need to understand those to understand why R^n and R^m are not homeomorphic. you need to understand excision or mayer-vietoris. that's about it.

>>12485605
i mean all of those are just i^(i^n) which is either i^i, i^1, i^(-i), or i^(-1). so this shouldn't be particularly surprising to you.
i^i is about 0.2 because i = e^(i*pi/2) and e^(i*pi/2)^i = e^(i*pi/2 * i) = e^(-pi/2).

>>12485786
real analysis kind of means three things in terms of courses:
1. calculus
2. metric space topology and proving a bunch of calculus theorems about riemann integration / differentiation
3. measure theory and lebesgue integration

>>12486064
been into computer science for a while. more recently physics, specifically the quantum side of things. i like dispersive pde and operator algebras so i should have been doing physics a long time ago.

next year i'll be a pure math major basically not remembering anything from high school.
just did it because i have no interest in anything and the things you guys say in this thread sound really cool. wish me luck bros.

>>12486691
Hey I did the same thing four years ago.
I hate my life but it's (probably) not math's fault.

Good luck bro

>yukarifag fucked off again because he got no (You)s with any substance to them
I'm unsurprised and feel nothing.
>>12486259
Professor's pages.
Misha has a bunch of tests on his page, for example.
http://verbit.ru/
>>12486274
Also Banach/Hilbert and topological vector spaces, on rarer occasions.
Large chunks of Royden's Real Analysis and Simon's Real Analysis are dedicated to those:
https://bookstore.ams.org/simon-1/

daily reminder

>>12487727
Ted K was a fag and he can suck my balls.

>>12487752
he is right about math being a risky career

>>12487788
You can say that again.

>>12487661
>also banach/hilbert/top vec spaces
just because a book titled real analysis includes those doesn't mean they aren't functional analysis. i suppose then you'd take issue with me calling measure theory real analysis, so i guess i should have specified i meant construction and analysis of the lebesgue measure on R^n.

>>12487920
>i guess i should have specified i meant construction and analysis of the lebesgue measure on R^n.
I was actually planning on also taking issue with topology and abstract metric spaces if you went for this angle, but I'm glad we both agree not to have this argument.

>>12485518

Why would the number of bernoulli trials in each of your Binomial variables be the same quantity as the number of Binomial variables in your sample mean?

>>12485605
You didn’t put the parenthesis toward the correct direction. The parenthesis go inside the exponent to make the power tower.

>>12486064
Physics, Computer Science, Chemistry, Biology, Economics

>>12486064

The CIA, Mossad and reptilians

>>12488073
Dangerously based.

>>12487953
I don't mean general topology, just metric space topology. All metric space topology is real analysis because metrics are real valued. Except when the metric space is specific enough to be called something else. Like if it's a metric for a normed complete vector space. Then it's not real analysis. Then it's functional analysis.
I too am glad that you concede that you are wrong.

>>12486000
The only people here who actually know any math are autistic trannies larping as anime girls.

>>12488160

>autistic

the new buzzword now is schizo

>>12488098
math is not metal music

>— I want to make the strong claim that in the foundations of mathematics, one should replace topological spaces with condensed sets (except when they are meant to be topoi — topoi form a separate variant of topological spaces that is useful, and somewhat incomparable to condensed sets). This claim is only tenable if condensed sets can also serve their purpose within real functional analysis.

>— if it stands, the theorem gives a powerful framework for real functional analysis, making it into an essentially algebraic theory. For example, in the Masterclass, Clausen sketched how to prove basic results on compact Riemann surfaces or general compact complex manifolds (finiteness of cohomology, Serre duality), and one can black box all the functional analysis into this theorem. Generally, whenever one is trying to mix real functional analysis with the formalism of derived categories, this would be a powerful black box. As it will be used as a black box, a mistake in this proof could remain uncaught.

>— while I was very happy to see many study groups on condensed mathematics throughout the world, to my knowledge all of them have stopped short of this proof. (Yes, this proof is not much fun…)

>— I have occasionally been able to be very persuasive even with wrong arguments. (Fun fact: In the selection exams for the international math olympiad, twice I got full points for a wrong solution. Later, I once had a full proof of the weight-monodromy conjecture that passed the judgment of some top mathematicians, but then it turned out to contain a fatal mistake.)

>— the Lean community has already showed some interest in formalizing parts of condensed mathematics, so the theorem seems like a good goalpost.

>— If achieved, it would be a strong signal that a computer verification of current research in very abstract mathematics has become possible. I’ll certainly be excited to watch any progress.

>>12480745
>get reality checked hard by intro analysis
>go screech autistically about real numbers and infinite sets on some anime forum
Yeah, that's me. Analysis I was a fucking bitch.

>>12487727
Computers might end up being smart enough to solve any problem we give them but they will never be able to come up with new problems

>>12488483
In case anyone's wondering what is it about, see https://xenaproject.wordpress.com/2020/12/05/liquid-tensor-experiment/

>>12488942
didn't ask

>>12488942
Thanks anon, love me some based Kevin

>>12489063
ok boomer

>>12489205
Wait actually it was based Peter

What's the simplest way of talking about all integers of the form am+bn where a,b are predefined specific integers and m,n are any integer?

>>12489314
[math]\langle a, b \rangle[/math]

>>12489331
That's already in use

>>12489353
Okay mister sophomore.
There's also [math]\mathbb{Z}a + \mathbb{Z}b[/math].

>>12489314
point on a grid on a tilted plane in R^2 going though zero?

>>12489314
Ideal generated by the gcd of a and b

>>12489314
[math]gcd(a,b)\mathbb{Z}[/math] or simply [math](a,b)\mathbb{Z}[/math]

>>12487661
>>yukarifag fucked off again because he got no (You)s with any substance to them
this happens to literally every good poster
we're stuck in an eternal summer in /mg/

>>12487661
>yukarifag fucked off
good riddance

>>12488483
>a *top mathematician* says we should include a *highly abstract concept* into foundations
>he claims that this will let us reduce *few fields of math* into triviality
shit like this makes me uneasy bros

>>12489536
I don't understand why he thinks that. He even says his theorem doesn't have any applications yet.

>>12489393
>this happens to literally every good poster
yukarifag was not a good poster.

I dunno guys, this book is a bit daunting. I understand what he's saying and how he writes, but I can't do the proof exercises for shit. I've asked around and apparently this is because I need to know the structure of proofs first, with people recommending me some proof materials and books.

For context, I am in 2nd year Engineering.
The thing is, the way he writes makes the problems seem so trivial and obviously true when he writes them, but when I am asked to prove some statement it's like my brain just shuts down.

I'm not required to use or write proofs in my course, I'm just doing it out of interest.

>>12489677
>engineering
I think >>>/lgbt/ is more your speed.

>>12489723
Ouch
How will I ever recover?

>>12489393
You genuinely can't blame this one on us, we didn't actually have anything to work with.

>>12489677
2nd year and just now doing single variable? And yeah as a fellow homo some exercises are tough

>>12489677
For this book think of the proofs as a step by step explanation, where each step you can use a definition, or a theorem, or some algebraic manipulation. But that's it. Each step must lead into the next.

Pay attention to the order of quantifiers (for all, there is,..). Don't expect to write a fully formed proof in one go, always have a page for rough work. If you're stuck try working backwards from what you're trying to show.

>>12476536
Anyone have the link to the lie theory discord? I got my main account banned.

>>12476698
SHAHAHAHAAH

>>12476698
issa joke nigga

>>12490037
https://discord.gg/rhE3fsTnUV

>>12490308
Thank you

>>12489677
I mean you just need to do it and try your best. It will feel very awkward and forced at first, and you'll always feel like you're doing it wrong. And slowly you'll get used to the feeling of it and it won't feel as weird.
Usually the most important thing is extracting "what am I actually trying to do?" Sometimes you're trying to find a delta that makes an inequality true. Sometimes you're trying to show some function preserves structure. Identifying what it is you need to do, saying "we need to find/do this," and then finding/doing that just like you would in any math problem is a very common way to write a proof.

[math]\mathcal{WHY~}\mathbf{THE~} \mathbb{FUCK} \text{ IS THE } \tt{\COLOR{}} \text{ FUNCTION }\mathbb{BROKEN}\text{ FOR /SCI/ } \LaTeX \tt{-POSTING~} [/math] [math]{{YOU}^{\displaystyle NEED}}_{\displaystyle TO} FIX^{\displaystyle THIS} RIGHT [/math] [math]{FUCKING^{\displaystyle NOW}}[/math]

>>12485581
I have it, but didn't read it yet.

>As to the “Jewish question,” Hitler, thought Kähler, had the insight to see that there was a “Jewish question.” How Hitler handled the Jewish question may have been wrong—and Kähler thought Kristallnacht was wrong—but this did not negate Hitler’s insight. Having said this, he immediately attempted to mitigate the wrong by commenting that much worse things were happening in Lebanon [in 1988]. Indeed, there were only two things that made Kähler doubt Hitler’s politics: his handling of the Jewish question, and his marching into Prague in March 1939 (because it meant he had lied when he said the Czech Sudetenland was all he wanted—Kähler acknowledged the Bible as a strong early influence in his life). However, he made the point, a familiar one from the German right, that none of the extermination camps was on German soil, but all were in the East, as if to argue that the German people would not have tolerated them. Furthermore, he pointed out that Auschwitz was liberated by Russians; news of Auschwitz came from Russians and was intended to defame the Germans. For Kähler, the destruction of the Jews (which he seemed to admit was wrong) is used internationally as a “wooden hammer” (Holzhammer) to end any serious analysis or discussion of the German question (this, of course, was said in 1988, prior to the reunification of Germany).

>>12489599
The definitions of topology, by its simple base axioms, incidentally through out a lot of the nice order theoretical properties that this subset of the powerset would have.
I think he's making a valid case that the simple topology axioms are a ruse, since most theorems end up demanding particular properties anyway (e.g., most notably, being Housdorff and others), so it's a ruse to say "oh topology is so simple, look at those nice 3 axioms."
There's many fields of mathematicans which go on to cast "ostensible topology" into metric theory, combinators, graph theory, lattice theory, locale theory to to their thing anyway.

But David Rodgers in the comments seems to be also a bit triggered that he's not giving pretopoi it's due, which already seem to capture half of the abstraction. I don't know enough about it.

>>12491240
Fucking nazi. That's why all differential geometry should be banned.

>>12491240
Can we change the names of theorems that have his name in it?

>>12491348
Agree 100%. Although most differential geometry originated in France. Fucking frog eaters.

What is the name of the comp problem where you have a bunch of different vectors (say, 800 of them in six variables) and you need to find all of the points that can be reached by summing them in various combinations?

>>12491502
This guy will say this but will not say anything about Marx' letters to Engels which outlined the utter contempt Marx had for black people.

You can rename things and erase history and attempt to not see, but truth is one.

>>12491502
Why? What's wrong?

>dont know how to link my algebra tinkering to the result
>"thus follows"
>rewrite the theorem
>write QED underneath
>mfw

I haven't taken a course on game theory but from what I've seen these people care more about diescrete, finite and stochastic game.
What about a continuous time game such as a cat and mouse chase? I'm trying to formalize this from an approach where the cat and mouse can have a strategy and then a solution to the game solves a differential equation. Pic related is more of a quick sketch but does anyone get what I'm trying to do here? Is this kind of structure being studied already?

>>12491602
>we abuse notation, writing S((t,gamma,rho)) =: S(t,gamma,rho)
now this is autism

>>12491602
I kinda get it but the sequential nature of that game smells ill defined as time is continuous, so a sentence like

>the direction the cat will decide to move in after having itself moved along gamma and seen the mouse move along rho

does not seem very clear unless you go more rigorous and explain things better. Just my opinion tho.

>>12491613
It's actually relevant here because we could NOT just define S on the product [math] R_+ \times P_t^\alpha(x) \times P_t^\beta(y) [/math] because as you can see the latter arguments domain depends on [math]t[/math]. Carelessly using the notation [math] S(t,\gamma,\rho)[/math] would suggest that this is possible. I think formally [math]S[/math] is a sigma-type.

>>12491615
well that's the thing the game is not sequential, it is truly continuous time in every sense. The phrase you quoted was intuition, this is done rigorously in the definition of a solution because there you say a path for the cat and a path for the mouse form a solution if the cat and mouse did INDEED move according to the strategy at every point, i.e. the gradient is what the strategy predicts.
My formalization is a bit awkward still... maybe I should work with [math] C^1([0,\infty),\Omega) [/math] paths instead of tuples [math] (t,\gamma) [/math].

>>12491631
what I mean is that discrete time games allow for observation of the opponent and strategy adjustment according to some criteria. How is this translated to continuous time? That's what I don't 'get' from your sketch.

>>12491602
hope omega is path connected, bud

>>12491639
The cat observes the time t, its own path [math]\gamma [/math] and the mouse's path [math]\rho[/math]. Then the strategy gives the gradient the cats consecutive path should have at this time.

>>12491646
Still skeptical. I feel it's also possible to obtain nondifferentiable paths in this way, so it makes no sense to talk about derivatives.

>>12491655
Yea so in this idea you don't end up with a situation where you give two strategies for the two players and boom you get a trajectory for how the game goes, but instead given two strategies you get a kind of PDE which might have solutions which might be unique and might have certain regulartiy, or not.

>>12491655
It's a lot more about differential equations than it looks at first. I think one could formulate this in a way where a picking a strategy basically means picking a differential equation from a certain family, and then two strategies where the mouse catches the cat would correspond to two differential equations where the solution paths end up meeting.

>>12491537
Which theorem takes Marx's name?

>>12491661
ohh reminds me of dynamic programming. Not an expert though. You should read some material because there's a lot.

>>12491675
>>12491661
To be more specific, your sketch looks really like a rudiment of some kind of Hamilton-Jacobi-Bellman problem of optimal control of two agents.

>>12491602
Ok so this is a simplified way to formulate this (the agents decisions are only based on their current positions, not the complete previous trajectories) and it looks a lot like something that methods already exist for.
>>12491675
>>12491685
Probably you guys can recognize this.

>>12491602
>>12491700
Stop underlining.

>>12491704
underlining definitions is good style my friend

>>12491700
yeah this really looks like dynamic programming with infinite time horizon

>>12476536
What is the interpetation for exponenting a number by i, similar to how multiplying by i is rotating by 90 degrees? Also, what is 1 to the power of i? Since 1 is equal to e to the power of i times 2pi times k where k can be any integer.

>>12491728
I don't know from which direction you're looking at this but if you want to exponentiate numbers other than positive real numbers by a complex number then this is defined via the complex logarithm, and that involves branches.

>>12491743
Go on anon.

>>12491728
radius becomes angle and angle becomes minus radius

New >>12491864

>>12491866
i will not be posting in a nazi thread

>>12489314

[math] \mathbb{Z} \setminus S [/math], where [math] S [/math] is the finite list of integers not expressible as [math] am + bn [/math].

>>12491931
Bye. We won't miss you.

>>12483936
ffmpeg in the worst case

>>12486064
literature, radio science, language

>>12491602
This sounds like control theory.