/sci/ - Science & Math

>>12491864

>>12491873
Yawn, get new material.

I have more than 60 exercises to do and I still didn't even start it. I'm so fucking pathetic...

>>12491886
if they are proof based you're fucked

>>12491927
Around 20 are.

>>12491864

Does anyone know of an example of a program (preferably in Python) for visualizing the image of a set under a conformal map?

More specifically, I'm looking for a program to help with problems like "given a set A and a set B, construct a conformal map f:A->B." I want to be able to plot A in one window, input a function, and then get f(A) in another window.

thanks chads

Stein's proof of Cauchy's integral formula for higher derivatives looks fishy. (From his famous complex analysis book.)

The proof is basically by calculating the limit of the derivative definition of the integral formula for [math]f^{(n-1)}[/math]. He shows that the integrand tends to the value we need and just assumes implicitly that we can insert the limit under the integral.

I'm trying to fill in the gaps but I don't know how to proceed:

We need to show that
[eqn]\lim\limits_{h\to 0} \int_C F(\zeta, h)\, d\zeta = 0, [/eqn]
where [math]F(\zeta, h)[/math] is defined as
[math]F(\zeta, h) := f(\zeta)\frac{1}{h}\left[ \frac{1}{(\zeta-z-h)^n} - \frac{1}{(\zeta - z)^n}\right] - f(\zeta)\frac{n}{(\zeta - z)^n} [/math]
is well defined and holomorphic (on both variables) on [math]C\times \overline{D}_\delta[/math] for some real number [math]\delta > 0[/math]. [math]z[/math] is inside the closed curve [math]C[/math] which is inside an open subset of the complex plane where [math]f[/math] is holomorphic.

By trying to bound the integral by something that goes to zero, we need to show that
[math] \lim\limits_{h\to 0} \sup\limits_{\zeta\in C} |F(\zeta, h)| = 0[/math]. For each [math]h[/math] there is a maximizing [math]\zeta_h \in C[/math] for [math]|F(\zeta, h)|[/math], and as I mentioned, we know that [math]\lim\limits_{h\to 0} |F(\zeta, h)| = 0[/math] for any [math]\zeta\in C[/math]. But there's no clear way to show that [math]\lim\limits_{h\to 0} \zeta_h[/math] converges.

I just tried some ideas of picking converging subsequences since those are compacts, but runned into other complications.
Any ideas?

>>12491874
seethe

>>12491864
You are given a bowl of 50 noodles. You randomly select two noodles and tie them together. Repeat this until you run out of noodle ends to tie. What is the expected number of loops (i.e. noodles tied to themselves) you end up with?

My approach is to say one experiment corresponds to a 50 x 50 permutation matrix, where the 1's tell you which noodles are tied. This would mean the number of loops in an experiment are the number of fixed points of the corresponding matrix thought of as an element of [math]S_n[/math] under its standard action on [math]\{1,...,50\}[/math]. Burnside's Lemma then implies that the average number of fixed points is 1.

However, after running thousands of experiments in Python, I believe the real answer is 0.5. I must be doing some double counting here, but I can't see how to fix my argument. Thoughts?

>>12492140
You aren't looking at all the permutations, just the even ones.

Reminder that being good at maths makes you an honorary Aryan, and then you are honorarily almost as cute as Kähler.

>>12492140
Do you randomly select noodle ends, or do you randomly select noodles and then randomly pick their ends?

>>12492256
The former

>>12492044
Correction, [math]F[/math] is defined on [math]C\timed (\overline{D}_\delta\setminus\{0\})[/math].

>>12492044
Correction, [math]F[/math] is defined on [math]C\times ( \overline{D}_\delta \setminus\{ 0 \})[/math].

I'm getting ready for differential geometry course next semester but I don't have much free time. Which topics in linear algebra, multivariable calc, and topology should I be reviewing to make the most of my time?

>>12492278
Cycles in permutations contains a direction, which is not exactly clear here.
Consider assigning a direction to each noodle, so that each noodle has a head and a tail. Now then the permutations only actually correspond to the experiments where every head is tied to a tail and vice versa.
The experiment of tying ends together clearly corresponds to permutations of 2n, thinking of tying the first two ends together, the next two, and so on.
In each pair, there is a 1/(2n-1) chance that the two ends are from the same noodle, so linearity of expectations gives n/(2n-1) as the expected total.
The difference from 0.5 becomes more pronounced as the number of starting noodles decreases.

>if [math]f(x)[/math] is written as a polynomial then [math]f(1)[/math] is the sum of the coefficients of [math]f(x)[/math].
Why is this blowing my mind so hard

Whenever I see his smile, I am inspired to do mathematics.
>>12492926
Exercise: try to find a simple expression for the sum of all the coefficients at odd indices.

>>12492376
>topology
euler characteristic
that's the main connection
>multivariable calc
you'll use a lot of it if they teach it like I learned it. It's a lot of directional derivatives and vector/diff form calculus
>linear algebra
Can you tell if a matrix is full rank?
Do you know what a subspace is?
I think that's 80% of the linear algebra used

you might also see the definition of geodesics presented as a partial differential equation, but you rarely use that directly, so diff-eq isn't that relevant
They might frame things in terms of tensors, or they might not. brush up on tensors if your syllabus mentions them.

t. just finished differential geometry

>>12492926
Like how the value at [math]k=0[/math] of the Fourier transform of [math]f[/math] is its integral.

Here's some thing fun for you making use of your insight:

A: Think of an arbotrary oder polynomial [math]p[/math] with coefficients in the positive integers.
B: Done.
A: What's [math]p(1)[/math]?
B: *tells*
A: What's [math]p(p(1))[/math]?
B: *tells*
A: [math]p[/math] is ...

Semirelated is the Gödel beta-function.

arbitrary order*

>>12492044

>I just tried some ideas of picking converging subsequences since those are compacts
>https://en.wikipedia.org/wiki/Iterated_limit#Sufficient_condition

I put these two together and it worked, if anyone is interested. (Probably no one, but I ought to close my monologue for autistic reasons.)

Define the factorial function "[math]n![/math]" in set theory, i.e. as a set of pairs
[math]\{(0,1), (1,1), (2,2), (3,6), (4,24), (5,120), \dots\}[/math],
formally

Hiya /mg/!

>The Department of Mathematics at the University of Western Ontario solicits applications for its MSc and PhD programs. We have up to 20 fully funded positions available, and applicants from any country are welcome.
>Our faculty members supervise research in a variety of areas:
http://www.math.uwo.ca/graduate/supervisors.html
>More information about our program, including the application procedure, is available at
http://www.math.uwo.ca/graduate/

>>12493489
I take orders only from mom.

>>12493503
Can I fuck you in the ass?

>>12493503
Is that uni any good. Would you recommend Americans to apply?

>>12493527
Not before Thursday, sorry. I spent a few hours in London (the real one, not that Canadian one) and now I am in quarantine for 3 days. Then we can meet up for that, but you will have to fight a beefy guy first and the winner can claim me.

>>12493534
I don't study there, so no comments on either of those. However, the list of potential supervisors' topics seemed good, and mr. Jardine is, dare I say it, quite based (at least his and Goerss's book on simplicial homotopy theory is!). It was just something I noticed when going through my email and thought I could share.

>>12493558
based plague bearer tranny

>>12493558
How old are you?

>>12493572
Sadly, both the NHS version and the test I had at the local airport were like me, negative.

>>12493623
A well-preserved [math] | \langle a, b, c\ |\ a^2 = b^2 = (ab)^2 = c^7 = 1, aca = c^6, bcb = c\rangle| [/math] year-old (in a few days, yay). How old are you?

>>12493643
Answer in a string of strokes pls.

>>12493527
There are high schoolers in these threads, please don't post inappropriate things.
>>12493656
By Lagrange's theorem, his age is divisible by two and seven, so we can estimate him at twenty eight.

What is the most complicated proposition ever used in a published paper? Complicated in terms of the arithmetical hierarchy.

>>12493643
>28
Would you say Sam Hyde was right about your intelligence cristalizing at 25 and it becoming much more difficult to learn new things?

>>12493683
Well applied Lagrange.

>>12493724
No. 24 is the age giving up.

>>12493748
Knowing that I could end up like you makes me irrationally angry at you.

>>12493753
Learning can become more difficult at any age if you believe in such claims and let them dominate your life. I, personally and hence anecdotally, have not noticed any change related to getting "old", however diet, sleep and exercise do affect it by my experience. If you feel like you are becoming an obnoxious degenerate like me, then feel free to track me down and show me pain that will make Tartarian horrors seem like a joke.

/gnmg/

>>12491864
How do you not get BTFO'd by textbook. Feels like I’m overwhelmed by an endless stream of definitions.

>>12493809
What is your IQ?

>>12493851
Uh oh

>>12493724
I don't remember Sam Hyde being that much dramatic. He said that it becomes hard after 30s and that you should have finished your "training" by 27.

Personally I think that your mind won't get any better after ~30 years of age, this is the beggining of the decline. But that doesn't mean you must stop learning. It's just that it's more convenient to learn all your basics before this mark and starting aplying and reaping after that, instead of preparing to do something only in the long future after you're 30.

>>12493809
I'm a brainlet but I just kinda try to do the proofs and the like by myself

>>12493851
Idk, I tested somewhere around 120-125 when I was in high school.

>>12491975
Use google before asking this stupid question

>>12493907
Sorry bud the cutoff for maths is 130. Try to be born with better genetics next time.

>>12493914
What can I do to cope?

>>12493572
Why do you call him "tranny"?

truth is -- infinity just werks

>>12493939
because (s)he is a finnish algebra tranny. ask it if you don't believe me. easy to recognize from the style

>>12493928
Develop schizophrenia and publish your disproof of the Riemann Hypothesis.

>>12494006
So my only chance is to go full tooker mode? Is there truly no hope?

>>12493809
Yeah you're supposed come up with some examples using the definitions on your own if they're new to you. Especially if the textbook doesn't give you any.

>>12492955
Thanks for your input

>>12493489
How do you recover the codomain of a function encoded as a set of pairs?

After learning measure theory everything is so easy bros.

>>12494570
Explain. Are you a probability person?

>>12493503
>http://www.math.uwo.ca/graduate/supervisors.html
>only one real-analyst
>it's Sinnamon
nice

/gmmg/

>>12494641
So, not the quantity but the quality of the analcysts in this case?

>>12494570
IUTeich next, then! Should be easy to learn.

>>12493956
>ask it
>it
Meow.

what sorta jobs can you do with a math degree?

>>12494688
mathematician. If you can't do that you're fucked, unless you teach or get a phd.

>>12494688
Learn stats and basic CS, get job as quant.

>>12492278
Is this what you're looking for?
https://math.stackexchange.com/questions/2209/expected-number-of-loops

Just testing it out ∈∈∈

>>12494688
you can teach math!

>>12494688
cashier

>>12494688
Trans rights activist.

>>12491864
So, uhm got any recommendations for advanced complex analysis books? I have a solid grasp of the basics.

>>12494775
Is stats with CS godtier for financial security?

a nazi thread overtaken by trannies
i guess that's a good thing

>>12495419
Overtaken?? What do you mean?

how do I solve the wang conundrum?

>>12495352
i don't know what "advanced" is supposed to mean but alfohrs and stein & shakarchi are the classics.

>>12495419
No brown-eyed "people" allowed, though.

>>12494619
Analysis + PDEs + MathPhysics. I only need to make sense of topological wankery and I will know everything.

>>12495518
hint: compute [math]A_1, A_2, A_3[/math] and then add them

>>12495633
wow very insightful, /mg/ does it again

Okay, topologists young and old: YTM 2021 is now open for registration
>The registration form can be found here: https://forms.gle/KxdgTSGxLKjEyGTJ9..
>The registration deadline is March 31, 2021
>Depending on how the pandemic develops, it might not be possible to hold a physical conference. If this is the case, then we plan to hold an online conference instead with the same lecture series. We plan to make a decision about this by the middle of May at the latest. You can indicate on the registration form whether you would be interested in participating if the conference were to be held in-person, if it were to be held online, or both.
>We strongly encourage participants to give a talk or present a poster. It does not have to contain original research results; expository presentations are also welcome.
Give a talk and shine as the brightest of stars, anon.

>>12495633
Prove it!

how I into geometry?

>>12494688
Go into finance, make dosh. Or CS, and make dosh.

>>12495832
Which? You better not say analytic or synthetic geometry, but that's just reading a textbook and doing your homework

>>12495854
Not him but yeah where do you learn basic bitch shit like that

>>12495877
Just search for books for that and use libgen retard. It doesn't matter which one you chose as it is basic shit.

>>12495927

>It doesn't matter which one you chose

Wouldn't recommend this for undergrad level books. They tend to overdo on the exercises section and an immature learner will feel the need to do all of them which is a huge waste of time.

>>12495877
https://4chan-science.fandom.com/wiki/Mathematics

http://gen.lib.rus.ec/
https://b-ok.cc/

>>12492938
[math]\frac{f(1)-f(-1)}{2}[/math]
right?
>>12493241
Is this solvable in general?
anything like [math]p(x)=x^n[/math] will have [math]p(1)=p(p(1))=1[/math] and will be indistinguishable

>>12491864
Does anyone think when you started learning mathematics it was like uncovering the work of God but as you progressed it was like you were executing the work of Satan?

>>12496617
only the truly irreverent seek absolute truth detached from god
you were a fool to imagine it holy to begin with. this is the most sinful discipline
several demons and fallen angels in the lesser key are noted as avid mathematicians

>>12496644
I am scared to progress further. I want to stop. What I am doing is evil and insane. Reason and logic were never meant to be given to man.

>>12496617

>work of Satan

I didn't mess with category theory beyond my required courses

>>12496617
Nope. I'm not mentally ill.

>>12496664

>finnish algebraist weeb tranny
>of sound mind

huh let's not kid ourselves here

>>12496664
>he hasn't started algebraic topology yet

>>12496681
Most rude, yet maybe somewhat justified.

>>12496685
My friend, I'm doing a PhD thingy on groups and homotopy and stuff. No contact with Satan because of this stuff yet, and I haven't done any witch stuff for years either after I stopped eating meat and ran out of chicken bones.

if a<c and b<d then does ab / cd < 1 hold for all positive a,b,c,d?

>>12496746

It's not an insult! I'm an unmedicated schizo myself, we need to own up

>>12496746
>performed witchcraft
>thinks they haven't contacted Satan
Anon Satan is inside of you
Math is the way we do his work

>>12496758
yes, because a/c < 1 and b/d < 1, and the product of 2 numbers which are less than 1 is less than 1.

>>12496758
[math]u>1[/math]
[math]v\ge 1[/math]

[math]c=ua[/math]
[math]d=vb[/math] (making the second condition even looser)

[math]\dfrac{ab}{cd}=\dfrac{1}{uv}<1[/math]

>>12496608
I don't know where I got it from but I'm pretty sure I actually weakened it for convenience and indeed it can handle a few zeros. Might be that your extreme example can't even be handled.

>>12496758
If 0<a<c and 0<b<d, then 0<a/c, b/d<1, so 0<(a/c)(b/d) = (ab)/(cd) < 1.

>>12496761
Based. Medication is neurotoxins just like alcohol and drugs.

>>12496768
But would Satan be more interested in applications than in abstract nonsense? One of them is more likely to cause chaos than the other. I accept His guidance in that case, nevertheless.
>I study hard into the midwinter night
>to these black arts I dedicate my life
>and no reward could ever be so sweet
>oh my Dark Lord, when will we meet?

Engineering Maths nigger here. Should we stop defining the derivative of a function as its tangent line to the curve at a point? That doesn't really tell us anything. Rate of change of a function over time is more practical in terms of understanding what it is.

>>12496808
>defining the derivative of a function as its tangent line to the curve at a point
That's a bit of sloppy language and a soon as you make it precise, you'll probably end up with the latter anyway.
Firstly, if you just say "of a function", you're permitting a much to big class of functions (even continuous functions often don't do the job of having a well define tangent line at all points.)
Let's consider polynomials (or maybe certain series, if you can characterize niceness properties succinctly). You say "tangent line" but I don't think you mean the synthetic object or the linear function. Let's say you mean the slope the linear function at a point that coincides with the function in question only once, in the interval where the function is convex or concave.
That slope is already a "rate of change" of the linear function. Although rate of change kinda has a temporal component to it, imho.

Anyway, I'm pretty sure your Prof defines the derivative of a function at a point by the limit, and the dervative of a function in an interval as a function taking you to the pointwise limits.

>>12496808
just call it whatever
as long as it works it works

opinions on this christmas cake?

>>12496925
Knot bad. I hope the black stuff is made of liquorice, as that would go well with the author's name.

>>12496925
Based

>>12496939
Licorice is disgusting

>>12496925
this is so nerdy that it would definitely make the front page of reddit
but you do you anon

>>12496950
It was probably taken from reddit too.

>>12496946
Yes, all sweets are. Full of excess energy. They make their consumer gain weight. However, some of them may have a pleasant taste, and liquorice is one of those. Try eat the actual plant some day.

>>12496955
actually i took it from twitter :^)

>>12497026
Basically the same thing

>>12495518
you know what they say about big wangs

Worst thread ever.

>>12495927
I know some analytic stuff but just the basics. Like you usually learn if for calculus so you don't reallly learn conics and the like in depth, I barely saw them in algebra
DESU I don't even know how deep shit goes
>>12496099
Wiki has nothing on analytic I think

>>12494557
You don't.
The Set Theory definition doesn't include codomains as part of the function. Hence, surjectivity is always relative to the codomain you're looking at, you should always make it clear the choice of codomain being discussed.

The advantage of this is that you don't need to keep changing function notation when you restrict or extend the codomain.

Another thing is that the Set category don't have functions as morphisms, you have to pair them with codomains.

>>12493809
>>12493907
>>12493928
That anon is joking, use another textbook for parts you don't understand or switch to a simpler textbook and try again afterwards. If you're not understanding it the textbook is either too dense for you and you should seek a lighter exposition or you're missing an important prerequisite.

>>12497626
>Another thing is that the Set category don't have functions as morphisms, you have to pair them with codomains.
Although I think you can well define a category without having functional source and target assignments - just make the composition a dependent partial (class) function?

What is the general relation between vector spaces, affine spaces and projective spaces?

>>12496925
Neat
>>12496950
Reddit strikes me as more of a consoomer type of nerd

>>12497692
you can use vector spaces to deffine affine and projective spaces.

Why is geometry so cool bros?

>>12491864
Anyone here study tensors? They're fun little things aren't they.

>>12496608
He said positive integers.

By the way, about the first problem you quoted, you can generalize it. Like, compute the sum of coefficients indexed by integers multple of 3. Them try indexes with remainder 1 on division by 3.

>>12497691
Hm... I guess so. But the damage has been done at this point.

>>12497809
as much as most geometers suck, unfortunately

>>12497691
No you can't, because you'll get more than just categories if you only insist on a partial unital associative composition. Any way you add in which morphisms must be compsible amounts to specifying domains and codomains of morphisms.

>>12494688
you can do anything. but will you want to?

.

Is there a point in Math where the science it just seems made up?

>>12498278
The zigzag line is always outside of the circle, so what is actually proven here is that pi < 4.

>>12498287
yeah pretty much all math beyond multivariable calc is made up play-pretend

>>12498317
Is pi a half circle, thus pi=2?

>>12498576
Galois theory isn't pretend, though. Possibly the highest math can get and still relate to IRL situations.

Is there going to be a point where math is completely "solved"? ie. there will be no more research papers because it's all been solved.

>>12498715
No. You'll never run out of halting problems to solve.

>>12498715
There's something called Incompleteness Theorem. Go wiki.

>>12498715
sometimes shit gets solved and settled, but new fields of math appear at a faster pace
people flock to the new thing, it's also much easier to get to the border of new research and get papers published if you're studying new shit instead of algebraic geometry

you should also be aware that research papers of the type "we solved the problem X which Y asked in his paper Z years ago" make up 10% of all papers
the rest is "we made up a problem for ourselves and then solved it" or "we made up some definitions and derived some consequences"
the second type is especially good for getting many citations

>>12498151
>Any way you add in which morphisms must be compsible amounts to specifying domains and codomains of morphisms.
Sure but you don't have to go from the arrows to the objects this way, so you don't have to judge sets of pairs for what their codomain is

>>12498287
>>12498609
The made up question seems to be quite a different target one than "relate to IRL situations".
For the former, there's of course whole philosophies where basically everything is of the mind, so to answer that in your likely intended way, we'd first have to agree on a materialist ontology.
Regarding the second point, it depends on what "IRL situations" are. I think non-math and CS people probably don't ever apply Galois theory (even if it's relevant to things such as stoage backup strategies), but at the same time, supergeometries are a nice way to speak about fields with spins, so it's also kinda "out there" and "practical" (I mean just as practical as the exotic IRL Galois theory applications)

How unreal is the idea of me getting into a PhD program in the US for the next year as a yuropoor with not excellent grades getting a BS next semester?
Any school. Think I missed plenty deadlines on that.

>>12498715
No. There are in fact undecidable propositions in ZFC. Generalised collatz conjecture for example. Also by the incompleteness theorems no formal system with a recursively ennumerable set of axioms (the only sets of axioms we would be interested in) can prove itself consistent. And if it is consistent then it is incomplete. So assuming that ZFC, or any foundation of maths we come up with is consistent maths will be incomplete.

>>12499031
At least talking about First order logic. Dont know how the fuck higher order logics work.

>>12493909

you obviously not understand the question brainlet

>>12499027
some deadlines are late as Jan-15th if you're ok with a meh tier school

>>12499106
how do you even plot an arbitrary set A in a useful manner? will you also feed in topological info?
if you're just talking subsets of [math]\mathbb{R}^n[/math] with [math]n\le3[/math] this is just graphing software you're asking for

I think there's a mistake here, on the statement about the integrals along the circular arc.
If we had [math]j'(\tau) = j'(-\tau^{-1})[/math], then that would be true, but [math]j(\tau) = j(-\tau^{-1})[/math] implies [math]j'(\tau) = \tau^{-2} j'(-\tau^{-1})[/math]. Am I right?

>>12499031
>Generalised collatz conjecture
How do you generalize Collatz conjecture?

>>12499298
https://en.wikipedia.org/wiki/Collatz_conjecture#Undecidable_generalizations

>>12499239
How meh are we talking? Anyone have an idea of the quality of American postgrad?

>>12499483
Group 3, some group 2
Also if you're willing to send in applications to programs past their main deadline but before the final deadline (i.e. waive any hope of a TA position or research funding) then you can apply nearly anywhere. Honestly not a terrible idea right now, several programs I've seen have been pretty upfront about the fact that that shit's getting slashed hard right now because of Covid anyway.

>>12499483
Depending on your field there are plenty of fine schools with later deadlines.

Please give me an example of a ring homomorphism from a ring with 1 to another ring with 1 that does not preserve 1.

>>12499728
the inclusion [math]\{ [0]_8, [4]_8 \} \to \mathbb{Z}/{8\mathbb{Z}}[/math]

>>12499728
The zero homomorphism from any nonzero unital ring (for example the ring of integers Z)

>>12499752
nontrivial

>>12499762
ZxZ -> ZxZ
(a,b)->(a,0)
sends (1,1) to (1,0) which is not a unit.

>>12492140

if you you tie two different noodles is same as creating one noodle out of two. So if you have N noodles you can only do either (N-1) noodles and no extra loops or (N-1) noodles and loop. Making loop is less probable because you have to catch 1 out of total 2*N-1 ends to tie with.

Rest is trivial.

>>12492140
In every step the number of noodles goes down by 1. I.e. you have 50 turns. If you have n noodles, there's probability 1/n that you form a loop and end up with n-1 noodles and 1 more loop and probability n-1/n that you form no new loops and end up with n-1 noodles. So the expected value of loops is
1 + 1/2 + 1/3 + .... + 1/n

>>12499881
probability is 1/(2*n-1) for every step

Just read a nice book by Herman Hesse, practiced the violin for an hour and played a videogame for a little bit. Now gonna study some maths, what should I study today my fellow mg-chads, algebraic topology or functional analysis?

>>12500035
Functional analysis, and stay grounded.

Why do we require that the additive group of a ring is abelian? Is there something natural about this being commutative or what?

>>12499293
I don't see anything wrong with Diamond and Shurman here. I don't understand your reasoning, so if you can explain why you think there's an issue in some more detail I can explain what's up. The basic idea is that these parts will cancel because they're equivalent up to a transformation in the modular group so the modular function is the same over both parts.

Why is division by 0 not allowed?

>>12500278
what would you meaningfully define it as?

So did fermat really have a proof? It can't be the same one that Wiles found right? Or is he just a giant troll?

>>12500278
how can you divide something among nothing

>>12500397
he almost certainly thought he had proof but didn't
there were many, many incorrect proof attempts before wiles. he likely had one of those

>>12500202
Think about why the distributive law for rings implies that the additive group will be abelian.

>>12500397
Fermat had a different proof and a better one than Wiles
Fermat invented algebraic geometry in his head but didn't bother to write it down

>>12500416
He just didn't have space in the margin. Too bad. Maybe we don't even need algebraic geometry? Maybe it was something else? Spooky

>>12500422
Fermat most likely anticipated Wiles proof and just didn't bother because he knew it would be done later down the line.
Wanted to save some fun for future mathematicians.

>>12500408
Even wiles came up with an unsound proof at first. Did fermat have other proofs that were found to be false?

>>12500412
(1+1)(a+b)=2(a+b)=2a + 2b =
= (a+b) + (a+b) = a+ b + a + b
Add -a to both sides on the left and -b to both sides on the right to get
a+b = b+a.
Is this the simplest way of doing it?

>>12500431
That just sounds trollish and uncharacteristic of him... Very possible though.

>>>/g/79338923

>>12500447
Yeah that is the idea, more or less. Good job anon-kun.

>>12500467
Nice. Why can't /sci/ be as fun as /g/?

>>12500467
why did they do this?

>>12500397
Allegedly there's a proof that given then-contemporary knowledge Fermat wouldn't find a correct proof.

>>12499307
Speaking of Collatz, are there any solved generalised cases? (Like 999999999n+1?)

shit guys, ran out of space
maybe another time

>>12500590
forgot pic

>>12500594
How did you find Fermat's last page?

>>12500599
its at the back of Fermat's last notebook

>>12500278
Look up wheels.

>>12500547
yes the case in which the function is of the type f(n) = n+1 if n is odd and f(n) = n/2 if n is even. This is strictly decreasing after 2 steps therefore jt always loops around (1,2)

For [math]f:V\to W[/math] between normed spaces, what's a weak condition for
[math]||f(x+t\cdot d)-f(x)||[/math]
to be monotone?

Basically, I try to find a condtion on [math]f[/math] to be guaranteed, in a discretization of the derivative, that choosing smaller [math]\Delta t [/math] actually makes the linearization not worse.
That seems always to be taken for granted

(monotone in t in reals, d being in V)

>>12500216
The idea would work if the integrand only depended on the j invariant, but it depends on its derivative. As I argued, the derivative is not invariant under the relevant transformation.
I tried to do the calculations explicitly, it works if I assume that the derivative is invariant, but doesn't with the proper factor - we end up with an integrand having that new factor which I find hard to believe that still lands on the intended result.

>>12501054
Continuity.

>>12501159
Well no, f(x):=sin(x) at x=0, d=1 gives
||f(x+t·d)-f(x)|| = |sin(t)|
which is far from monotone.

I chosing dt in a convex interval does the job, but that's not super weak

>>12501195
>monotone near x = 0
?????

>>12495815
>YTM 2021
Tempting...

>>12501231
WAIT ITS THE REAL ONE I THINK!

We've missed you Yukari, welcome back, I unironically look forward to seeing completely excessive Ph.D. level explanations to junior undergrad questions again

>>12499293
>>12500216
>>12501117
Ok, I've found my mistake. Too many years not using complex analysis made me rusty...

Can someone redpill me on determinants? I'm bored to death with this dry ass matrix arithmetic. What do they represent? Some kind of multiplicative relation between the row and column vectors?

I'm only halfway through the first chapter and I understand maybe 1/4 of the proofs so far. Is this what it feels like to re learn a subject from the ground up

>>12501626
the product of the eigenvalues. The eigenvalues determine how much each vector in the basis changes size by, and the product in some ways gives you the change in size of the whole space.

>>12501231
Välkommen till Stockholm.

>>12501727 Thanks senpai!! Then it makes sense why for example the Jacobian determinant is equal to the radial distance when going from normal to polar coordinates

>>12501853
yes as the space "gets larger" the further away from the origin you go

>>12500540
How would such a proof work? That seems tantamount to saying "the set of theorems within some reasonable N implication steps does not include wiles' theorem". But how would one find that set, how would one exhaust the set of immediate implications of any given set of assumptions? Is it a mechanical brute force somehow, or is it impossible due to the unknown nature of how creativity generates new knowledge from givens, the unknown ways parts can fit together that we might not notice until we get blessed

>>12501941
Probably in a similar way that you can prove that you cant square the circle or trisect and angle or double a cube using just a compass and straightedge with no markings. You find the amount of things you can construct with certain techniques and then see if the theorem falls into the set of things you can prove.

>>12497692
A (proper) subspace of a vector space is a lower dimensional (hyper)plane through the origin (the terminology is slightly weird here because hyper normally strictly means dimension one lower, but the only other way to explain this is by the formal definition which I assume you've seen).
An affine subspace of a vector space is just some lower dimensional plane that might not go through the origin.
Projective space is the space of lines in a vector space, which can be thought of as taking a vector space and forgetting about scaling.

>>12501951
>cannot do given thing
>find amount of things you can do with given techniques
These statements are different. What if we started talking about 3D synthetic geometry, asking how to cube a line let's say. How do we know there's not some game-changer space like popping out extra dimensions or other unknown routes that fermat saw? What if his proof was truly marvelous?

>>12501951
FLT is probably provable in a fairly "weak" theory of arithmetic...

>>12499728
That's normally a requirement of the definition of ring homomorphism.
What you're talking about sounds more like a ring-module homomorphism, for example the map from Z to Z given by multiplication by 2.

>>12500500
they're autistic, quite simply

>>12501962
The statements are not different if something doesnt fall into the set of shit you can do with a set of techniques then it by definition cant be done with those techniques.

If you are saying "what happens if he discovered some [insert maths developed hundreds of years in the future] and wrote a proof thinking of that" then you could be right, but its extremely unlikely. Maths is typically built on other maths, typically using real life problems as an inspiration. As such you dont get guys from the middle ages writing proofs using riemannian geometry. So assuming that fermat didnt in his head invent modular forms or whatever the fuck proves FLT is a pretty educated guess, though it is just a guess.

>>12501964
I have no knowledge as to whether it is possible with tools from his time to prove the theorem, all I am saying is it it cant be done this is probably how they would prove it.

>>12501985
if it cant be done*

>>12501981
>As such you dont get guys from the middle ages writing proofs using riemannian geometry.

Are we certain that Euler didn't do that? Or some ancient indian or middle eastern mathematician? Those dudes apparently discovered lots of shit long before other parts of the world did. And Euler... He discovered so much fundamental and new maths it's insane

Do you guys think of plan B from time to time? If mathematics really goes south for you, what will be your back up journey?

I imagine myself trying to get into data science. It looks interesting and rewarding enough to be an alternative.
I'm just not sure about having to torture myself with endless debugging sessions, sometimes caused by bad language designs etc, not a mystake from the coder part. Also the fact that, unlike math, the tools you learn can become useless quite fast. Plus with age comes less energy and clarity to learn so much from a whole new field.

>>12502069
Thats not how history is done, because you cant ever guarantee anything. History is just a lot of educated guesses, there is no certainty. But making the fair assumption that dudes in the past werent packing the same mathematical tools modern mathematicians do we will probably find that fermat didnt actually have a proof. Thats how history is done.

>>12502075
The same is true for data science. But a good programmer learns knowledge which is language agnostic so he can easily adapt. If you learn K you can get a job in HFT pretty easy, and K is not some meme shit that's constantly changing. Good fucking luck learning K though.

DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU
DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU DESU

>>12491873
is that wildberger?

>>12502082
>Good fucking luck learning K though.
This is /mg/ not /dpt/; /sci/ not /g/.

>>12502091
All of that is irrelevant in J. Probably K as well. Who needs to know computational complexity when you don't have loops? Have a look here my dear anon. https://www.jsoftware.com/papers/algebra.htm

>>12502101
Anon dear. Terse notation, matrix algebra, building complex functions by composing simpler ones etc. are nothing out of the ordinary for a mathematician. Don't take the meme I posted TOO literally, it was the most suitable I had for the situation. (And of course computational complexity matters, idiot.)

>>12502106
True, but it's not just terse notation. Well it is, but operators have rank and valence, and modifier constructs. That makes things a little tougher. Point free style, which is more performant and flexible, becomes even more complex. Computational complexity matters somewhat, but not as much when the language is at an appropriate level of abstraction. The compiler can make those decisions for you if you write your code in a general enough way.

>>12500823
Nobody cares

>>12500416
>Fermat invented algebraic geometry in his head
that's not true though
fermat invented interuniversal teichmuller theory in his head and proved his last theorem via abc conjecture, but later he realized it's all wrong

>>12495352
Depends. What are you interested in? Several variables? Conformal mapping? Value distribution theory?

good youtube channel
https://youtu.be/grzFM5XciAY

I fucking hate how physicians sometimes decide to break already flimsy math notation because they are lazy pieces of shit. Is it that hard to write x/(kT) instead of x/kT?

>>12501207
Yeah but there's no criterion when we are "near".
Consider maybe instead
[math]f(x)=\sin(9001\cdot x)[/math].

You choose a [math]\Delta t\approx 0.01[/math] in your differential equation solver and think you're good, then you choose a smaller [math]\Delta t[/math] and it gets actually worse.
:/

>>12502556
I think you mean physicists. And while I agree that experimental physicists are not well mathed, both statements are equivalent. You apply operations from right to left. The parentheses are unnecessary.

>>12502556
sometimes i write up shit in latex and i don't want to write a fraction like this [math]\frac{x}{kt}[/math] because it looks fucking ugly in the middle of the text
so i change it to x/kt and i know I should write x/(kt) but the parentheses are also ugly so i throw them out
i don't think that's a terrible move, because everyone understands that i would write tx/k if i wanted to multiply by t

>>12502631
x/kT is the same as x/k*T=(x/k)*T I never seen anyone stating otherwise.

>>12502532
Remings me of vihart.
The guy looks a bit creepy but indeed that modular form video is good.

>>12502556
That's barely particular to "physicians"

And it's also a spectrum. If you read blogs in the type theory community, they get equally triggered that no paper coming out of a math department is rigorous. E.g. when they take the quotient ring R/{0} (that's naturally isomorphic to R) and keep working as if R/{0}=R, which doesn't make sense in standard foundations, since you end up with inconsistent statements (in the light of Regularity) like {x=x}.

>>12502631
I agree with you that () should be there, but "x/k*T" will not be well typed, at least in SI units. So it's natural that this sort of thing happens.
In the context at hand, something like Exp(E/kT) can only mean Exp(E/(kT)) because k has units of energy over temperature. Just like if you say F is force, F=m/a can't be mistaken to be meaningful, since the units of F are that of m·a from the getgo.
Again, this isn't particular to math.

>>12502532
Reminds me of vihart.
The guy looks a bit creepy but indeed that modular form video is good.

>>12502556
That's barely particular to "physicians"

And it's also a spectrum. If you read blogs in the type theory community, they get equally triggered that no paper coming out of a math department is rigorous.
(E.g. when they take the quotient ring R/{0} (that's naturally isomorphic to R) and keep working as if R/{0}=R, which doesn't make sense in standard foundations, since you end up with inconsistent statements (in the light of Regularity) like {x}=x.)

>>12502631
I agree with you that () should be there, but "x/k*T" will not be well typed, at least in SI units. So it's natural that this sort of thing happens.
In the context at hand, something like Exp(E/kT) can only mean Exp(E/(kT)) because k has units of energy over temperature. Just like if you say F is force, F=m/a can't be mistaken to be meaningful, since the units of F are that of m·a from the get go.
Again, this isn't particular to math.

>>12502532
Reminds me of vihart.
The guy looks a bit creepy but indeed that modular form video is good.

>>12502556
That's barely particular to "physicians"

And it's also a spectrum. If you read blogs in the type theory community, they get equally triggered that no paper coming out of a math department is rigorous.
(E.g. when they take the quotient ring R/{0} (that's naturally isomorphic to R) and keep working as if R/{0}=R, which doesn't make sense in standard foundations, since you end up with inconsistent statements (in the light of Regularity) like {x}=x.)

>>12502631
I agree with you that () should be there, but "x/k*T" will not be well typed, at least in SI units. So it's natural that this sort of thing happens.
In the context at hand, something like Exp(E/kT) can only mean Exp(E/(kT)) because k has units of energy over temperature. Just like if you say F is force, F=m/a can't be mistaken to be meaningful, since the units of F are that of m·a from the get go.

>>12502803
>The guy looks a bit creepy
Where does he show his face?

>>12502859
If you hover your mouse over the how to learn video

https://youtu.be/fo-alw2q-BU

And this isn't supposed to be a petty insult either, he just has unfortunate eye structure (and an off jar)
On that note, this channel is quite good
https://youtu.be/ZbTJHCTQArQ

I also don't like the "childlike enthusiasm" if it comes from a math major, as in
>I was overwhelmed when I learned this absolutely amazing formula
but that's jus my personal taste of content - I like the things speak for themselves.

>>12501631
you should really be spending time with each proof until you understand it. and yes, that's what it feels like. it will get easier with time.

>>12502871
i generally agree with you and yet geometry is a field of gorgeous and elegant formulas.

>>12499251

It only needs to be an approximation as in this picture. I only care about simple shapes like squares, circles, maybe a convex hull or a union of convex hulls. Basically stuff like this picture.

> if you're just talking subsets of Rn with n≤3 this is just graphing software you're asking for

A conformal map is always R^2 -> R^2. And yes, of course it is just graphing software. But if you've actually tried you'd realize that this isn't easy to do in something like Matplotlib. There are a million tutorials on how to do a domain coloring, but not one on how to plot (an approximation of) the image of a set under a conformal map.

>>12503065

the picture

>>12503065
take a set of points
apply function to each point
plot the new points

>>12491864
Does Affirmative Action exist in the maths community? In other words,if a highly qualified white male candidate was the most qualified among a pool of candidates, but there was a diversity need at the Uni and there was a marginally qualified black female candidate, would black female candidate be selected? If this is the case, isn't this going to limit significant research advances in maths? Won't the field be bombarded with race-obsessed analysis?

>>12503074

that would be a pretty ghetto solution. The important feature is that it allows you to visualize the map as a deformation of a grid.

The key features are:

1. a way to input a line segment and calculate the image of that line segment
2. a way to take the intersection of a grid of line segments and a shape such as a circle

Plotting individual points and their images under the map would not be acceptable level of quality. I know this must be possible in some program.

Maybe matlab can do it, but I only have octave.

>>12503076
it's becoming the norm, but the math GRE is still a big barrier that prevents awfully poorly qualified but 'diverse' candidates from getting positions thanks to the color of their skin. Fields very close to math like Ivy economics PhDs are neck deep into anti-white anti-male admissions procedures, and it's showing. Research is currently garbage.

>>12503211
What will be the end result to this idiocy? Chinese Unis producing better research? The Mother of Invention moving East? Forced reparations/redistribution of wealth?

>>12503076
i would posit that this is an extraordinarily small problem for research compared to the drain of good mathematicians toward high-paying industry positions, such as in ML. if you actually care about research output, think about how to enlarge the space in academia and to make it properly lucrative instead of pretending there should be some limited number of spots which are being stolen from you. Mathematics doesn't need less people doing research.

>>12503253
yes, Chinese unis will soon outpace almost all Western universities. Once the 'old guards' are all gone and replaced with a sufficient critical mass of 'diverse' people obsessed with only race and gender based research (throw in climate research too), it will be over for Western academia. It's not a matter of 'if' but 'when', because at this point it's inevitable. A handful of universtities will retain prestige thanks to Asians forming the faculty guard: MIT for example. Everything else will go down in rubbles, this is the end result.

>>12503253
>idiocy
you're clearly just angry because you weren't good enough to get into some program. if you're truly of the caliber to contribute meaningfully to mathematical knowledge, there should be no question in your mind as to whether or not this will have an impact. it's the hard, simple truth that the admissions practices which you discuss are just substituting fodder for fodder.

>>12503275
>implying climate research is bad
>implying mathematics has slowed down at all
>muh doomsday
get out of our thread, there are so many other containment threads on /sci/ for you.

>>12503272
Then try to a better job at marketing your research to those in charge of the budget. You need to convince them that adding another $100k+ deficit to the budget for an extra mathematician in the ranks is satisfying both a fundamental research need, but also a fundamental business need.

>>12503291
I do now, of course. In an ideal world the value would be inherent (as the pursuit of knowledge is invaluable) and I wouldn't need to do any such thing. As the practical becomes more and more efficient and automation reaches further and further into the sphere of thoughtless labor, we will have more prosperity to throw at those doing scientific research. So in a way the best way to make academia more lucrative in the long term is funnily enough to go work in industry.

>>12503099
If you plot enough points, the straight lines between them will approximate curves under the conformal map.
maybe plot everything at [math]f(n,m)[/math] for [math]n,m\in\mathbb{Z}[/math] then plot, say, 200 sampling points of the form [math]f(n,m+\frac{k}{100})[/math] and [math]f(n+\frac{k}{100},m)[/math] for every pair [math](n,m)[/math] then draw straight lines between sequential sampling points. As we increase the sampling count it gets arbitrarily close to any curve. This was almost certainly how the image you posted was actually made. see curve-stitching.
You can definitely do this in Octave or something equivalent, if not with some built in function then with 20 minutes of programming.

>>12503277
Actually, I did get into a good program. It just took a very long time, particularly when compared to my less successful and less gifted non-white peers.

>>12503282
Math faculties in the US are still guarded by the math GRE, I said it. But it won't be for long. Also climate research currently is all bogus because it's funded by special interests which survive on government funding, so p-hacking and data cooking is rampant. You'd be completely blind to not see this.

>>12503315
The GRE can be waived though. It was for me, because I was doing maths research in my undergrad. I don't see why it wouldn't be waived because some liberal Dean thought the GRE was racist.

>>12503314
>Less successful and less gifted
I just highly doubt this is true. Maybe on the fucking GRE or something (says absolutely nothing about aptitude for mathematical research). It's notoriously difficult to judge your own mathematical abilities.
>>12503315
The Math GRE doesn't guard shit. Also, it's been cancelled this year so I suppose you'll have the chance to find out how meaningful it is. The Math GRE says not a single word about someone's capacity for research. Only research experience and publications do.
You can make up whatever you want to try to delegitimize climate research because for some reason you have a fucked up fantasy where your grandchildren fucking starve. I have no idea what leads you people to this. Are you Exxon Valdez shills? I'm going to be perfectly honest: you are never going to contribute anything of worth to human knowledge. To what ends do you exert your voice on others?

>>12503321
Yes, the general GRE is being waived in droves because 'diverse' demographics do less well on average than Asians and, to a lesser extent, whites. The subject GRE can be waived discretionally so it probably will be waived for minority applicants only, if it's not already happening unofficially.

>>12503336
You're pulling so much fucking nonsense out of your ass, it's pathetic to think you're allowed in this community. We need our own /mg/ GRE to filter out the rightoid undergrads.

Just imagine, in 20 years, there will be fields in maths such as "Algebraic Geometry from the Afro-American perspective".

>>12503332
Why are you angry bro? P-hacking is real and empirical climate research is so deep into special interest funding that you can't really take it as honest unless you do meta analysis for every fucking paper you see.

>>12503337
I'm not even close to a 'rightoid', I'm stating literal facts. You can take the general GRE stats from ETS and see for yourself that mean differences in demographics are tangible and unis have responded by waiving.

>>12503337
>Thinking that you can gate-keep an anonymous image board
>Literally being unable to process/argue against opposing points of view

>>12503355
There's no argument to be had, I'm talking with someone who unironically believes that a 3 hour test about double integrals is the savior of the mathematics community. I'm not arguing, I just think the premise is flawed. I'd rather everyone get the chance to do math research if they can. Why should I give a shit which group of hacks gets filtered out along the way? The people who make it will always be the ones who contribute noticeably and meaningfully to research.

>>12503099
>>12503309
Also if you're plotting conformal maps that can be represented as complex functions you can always decompose it into
[math]f(z)=\mathcal{R}(f(z))+i\mathcal{I}(f(z))=u(z)+iv(z)[/math] so that [math]f(z)=(u(z),v(z))[/math] and we can plot things simply in any graphing calculator
for example here is [math]z^z[/math] in desmos
https://www.desmos.com/calculator/yfrkt8qipv
and a simpler example with [math]z^2[/math] here
https://www.desmos.com/calculator/zno68nrdm6

>>12503343
I'm fucking fuming because I'm disgusted on an animal level by dishonest skeptic shitbags.

>>12503377
>skepticism towards the dogma is a sin that makes you physically and psychologically unwell, and also quite violent
Seek help

>>12503377
stay mad retard

>>12503377
literally seething lmao
suck my cock nerd

>>12503377
I kinda agree with you, it's just so common it doesn't even elicit a reaction anymore from me though.

>>12503426
Why should legitimate criticism and pointing out facts even elicit a visceral reaction? You people have mental problems I swear.

>>12492044
>Stein's proof of Cauchy's integral formula for higher derivatives looks fishy.
>The mathematician writing a book on a very basic subject must be wrong because I don't understand it.
You must be 18 years or older to post on this board

>>12491864
/sci/ bros this might be a stupid question, but:
why can't we just make a ZFC FOL AI? Give it the ZFC axioms, a then let it sequentially interpret the abstracts of all the literature that's publicly available, covert it all to theorems, and then give it a crack at whatever Millenium prize problem.

Text interpretation is de-facto a solved problem, the validity of each interpretation can be cross referenced by making the AI interpet the papers that cite said paper (checking around the footnote location). Then the AI has a cumulative theorem set of like, 100k, and can just buzz away using FOL.

>>12494570
Please compute a probability for me.
Can you even schizo?

>>12496925
God-damn I hate math fags so fucking much.
Literally the most pretentious shit.

>>12493809
Start from the easiest textbook you can find that contains references.
After you finish that you can read one of the references, and it will probably be manageable.

I am working through a book on naive lie theory which is basically lie theory for retards but I'm kind of confused on this proof about the lie bracket operator. I am supposed to show that if

[math]U,V \in \mathbb{R}i + \mathbb{R}j + \mathbb{R}k \implies \left[U,V \right] \in \mathbb{R}i + \mathbb{R}j + \mathbb{R}k[/math] where [math]\mathbb{R}i + \mathbb{R}j + \mathbb{R}k[/math] is the vector space of pure imaginary quaternions. Since it is a vector space I would assume it is closed under multiplication so that would imply [math]\forall U,V \in \mathbb{R}i + \mathbb{R}j + \mathbb{R}k, \, UV, \, VU \in \mathbb{R}i + \mathbb{R}j + \mathbb{R}k[/math] which would imply [math]UV - VU \in \mathbb{R}i + \mathbb{R}j + \mathbb{R}k[/math] which implies [math] \left[ U,V\right] \in \mathbb{R}i + \mathbb{R}j + \mathbb{R}k[/math].


However the question says "Using bilinearity or otherwise" but I don't know how bilinearity would play into this.

>>12502091
aocp would like to talk to you

>>12503448
authomatic theorem provers exist
converting meaningful mathematics into things automatic theorem provers understand is a huge pain. takes a year even for solved problems. and yes, one or two things have been proven using them.
math is a fuckhuge domain so random walks through it and spitting out random theorems is basically useless and you'll have trillions of proofs of 1=/=3 and similar shit for every jordan curve theorem it gives you.

>>12503371
Plenty of category tards around who can't take a simple integral let alone a double.

>>12503426
>the logical reaction to skeptism should be anger
>science has shown
>trust the experts
It's all so tiresome

>>12503512
>Since it is a vector space I would assume it is closed under multiplication
for example the set of all symmetric matrices is a vector space, but it's not closed under matrix multiplication.

This is a basic ass question but here I go:
Starting college soon after a gap year, doing community specifically to save money.

I think I'll be a far better student due to having time to mature which I desperately needed. Nonetheless I struggle with math because I hate memorizing.
I love math when I have everything explained, or figure it out myself -- I was the kind of kid who'd learn something during a test instead of studying it, trying to figure out the problems.
I just find it very deflating to be told something is true without a deeper logic to it, the kind of logic that would make it possible for me to logically discover said truth within a day or a week.

What are some good books for this? I'm planning to take calculus but I won't lie, I need a better fundamental understanding of geometry.

>>12503569
most math classes beyond the introductory ones should present proofs for almost everything they assert

>>12503569
Read something that is not quite analysis but goes into proofs. For Calculus people usually recommend Spivak or Apostol

>>12503561
I think a better way might just be to write out [math]U = ai + bj + ck, \, V = di + ej + fk[/math] then do the lie bracket most of which can be split up due to bilinearity

>>12503371
>>12503540
>3 hour test about double integrals
Oh fuck it's much worse than we thought

>>12503569
Sounds like you'll do better in college level math than in lower level stuff if you like proofs and logical construction
just make sure you have your foundations laid. especially trigonometry. so many lads get filtered by calculus courses, not because they fail to understand calculus, but rather because they do not understand basic trig on an intuitive level.

>>12503523
Fair, though that seems solvable. Nat lang parsers exist, so I assume that can be automated with some dev? The random walks thing could be fixed by reinforcement learning on real math papers right? Then it’s not just gonna be permuting all combinations of FOL steps, it’ll pull the ones used in real papers. You might also assign weights by a combination of relevance score and number of citations. So you might plug in “P=NP” and it’ll parse papers and assign weights to their conclusions based on relevance to P=NP and number of citations, then run the reinforcement-learned stuff on a handful of most-relevant conclusions + intuitive steps (reinforcement learned) + FOL syntax. I assume some relevant conclusion would result that way.

>>12503342
Sure, but by then research is dominated by China where no such nonsense is tolerated. American and European universities and journals will be mere jokes.

>>12494670
>finnish
>algebra
>tranny

Sounds hot in my mind desu, like some dainty taftaj-type deal but european and w/ blue eyes, but in reality i know i'd be disappointed. Also, although im partial to algebra, which math subject produces the best trannies? I think an analysis tranny could be interesting, nice and tight and well-groomed like a fine [math]\epsilon[\math]-[math]\delta[\math] proof.

Mathematics layman and aspergers here.
I'm 19, is it too late to start? If not, is Khan Academy a good tool?

>>12503771
no
yes

>>12503776
Thanks.

>>12503448
There are some program, I think quantamagazine published some article on this topic (there's a sort of putnam but for robot)

>>12501981
>first paragraph
How do you go about finding the entire set of impossible actions with a given technique?

>>12503771
>19
lmao you're brian has already degenerated and your learning capabilities are now similar to that of a 60 yo since u stop maturing at 20 LOL go do a brainlet hobby like machine learning or organic chemistry old man

Merry Christmas /mg/!

>be me have a good friend J who is working on getting a PHD in math
>I made it clear to J I don’t believe in math, but I won’t let it get in the way of our friendship as long as he doesn’t bring it up too much
>just wanted to say merry Christmas to math on behalf of my good friend J

Merry Christmas /mg/, I got money to support my "underpaid, academic, mentally masturbative little number crunching hobby (get a real job son)". What meth related presents did you get?

>>12504066
I got a new pipe and some primo crystal

>>12503771
no. I know someone who started with calculus at 23 and is now doing PhD in math at a good school. They worked like fucking mad though. I think they completed almost all of a math major within a year and a half or two years while working part time, and then they did a masters at a good school.

>>12504028
False, neural connectivity decline starts at 26 and loss of fluid intelligence at 40.

>>12503771
Dude it's never too late.
I know a guy who started his PhD at around 50. He's a very distinguished intelligent mathematician now.

>>12504144
Damn, that's impressive.
>>12504254
Damn... he must've had plenty of knowledge prior, right?

>>12504271
He was a chemist beforehand working for some drug company and hated his life. So he got a divorce and went into math lol.

>>12503758
If you think that is a hot combo, I recommend you stop consuming p*rnography ASAP. I'm hideous and hate my outer meat shell.

>>12504043
>>12504066
You too!

merry christmas fellow mathe/mg/cians
>>12504388
>>12504066
>>12504043

I got a bit tipsy after my parents made me drink homemade Glühwein variant and somehow ended up discussing Erdős numbers with my uncle, and he then told me he had a classmate back in the days whose grandfather was a military attaché and met Hitler. Because my uncle met this guy, his Hitler number is 2 and mine is thus 3.

>>12504403
https://www.youtube.com/watch?v=nFMIPQxGLww töttöröö :DDDDDDDD t. angel

>HIGHER HOMOTOPICAL STRUCTURES
>Centre de Recerca Matemàtica (CRM) Barcelona
>January 11 to July 10, 2021
>This is a 6-month intensive research program devoted to homotopical and higher-categorical methods in many areas of Mathematics. Due to the current health situation worldwide, the initial events of the program will be held online or in hybrid form. Still the organizers hope that some of the activities can take place in the CRM Auditorium, and visitors will be welcome along the entire period.
http://www.crm.cat/en/Activities/Curs_2020-2021/Pages/IRP_Higher_Homotopical_Structures.aspx

>>12504440
Cringing at myself hahaha!

>>12504440
>>12504475
based
Also I wish I had other mathematicians in the family except myself. Easy on the Glühwein Brudi!

>On Projective Representations of Finitely Generated Groups
https://arxiv.org/pdf/2006.02832.pdf
Seems quite nice.

>>12504590
Same, but at least he's a well-learned guy and knows something about pretty much everything. No drinking today, and thus no night spam PROMISE! Have a nice Christmas day.

/mcmg/

>>12504388
You are ugly outside and even uglier inside. Please stop posting.

Collate infinity
Happy chrimballs y'all
Someone make the next thread with a non-mochizuki japanese mathematician

>>12505839
You got it, friend
New >>12505939

merry xmas
]
https://www.openbible.info/topics/math

Casual here. What's the status on the Riemann hypothesis?

>>12507313
riemannian

>>12506541
>[math]\pi=3[/math]
based engineer biblical writer