/mg/ maths general: dropout edition

[Anonymous No.11626387]

talk maths, formerly >>11614130

[Anonymous No.11626394]

he's strong

[Anonymous No.11626398]

>>11626387
>>11626394
Do you think he can build muscle? I wish I could

[Anonymous No.11626404]

>>11626398
>Do you think he can build muscle? I wish I could
Mathematicians use "we", not "I".

[Anonymous No.11626423]

>I was 10 years old at the carnival when I saw an old black man playing a large drum and singing strange african songs
>his skill banging the drum fascinated me, and I watched him for a long time
>the old man stopped and called me over
>"Hey sonny, can you hear the shape of a drum from the beat alone?", he asked me
>from up close, I could now tell he was blind
>I answered that I didn't know
>he told me that it's simple to realize that's not the case if you just consider two 16-dimensional tori with different Riemannian metrics that have different eigenvalues
And that man's name was John Milnor.

[Anonymous No.11626427]

>>11626387
Less than 1 isn't the same as 1.

[Anonymous No.11626444]

Consider a Banach space [math]X[/math] and some continuous functional [math]f \in X'[/math] which defines a hyperplane [math]H = \{ x \in X : f(x) = 0 \} [/math].

If a set S is nowhere dense as a subset of H, is the linear span of S nowhere dense in X?

[Anonymous No.11626470]

>>11626387
I want to kms this semester i cant take classes and the retard that teachs me stats is a programmer. This is the way she defined "random variables". She NEVER defined B btw... Literal retard tier. Do you have any easy abstratc or guide from your unis??

[Anonymous No.11626473]

>>11626444
no ass. the only good thing asians hae is white skin

[Anonymous No.11626475]

>>11626444
Gay video, but checked

[Anonymous No.11626477]

>>11626444
>If a set S is nowhere dense as a subset of H, is the linear span of S nowhere dense in X?
What have you tried?

[Anonymous No.11626771]

what are the pre-reqs for motives

[Anonymous No.11626776]

Is there actually a difference between degrees and radians, or are they just different ways of representing the same values? For example, 2pi is the same thing as 360 degrees.

[Anonymous No.11626810]

I posted this in sqg a few days ago and still can't solve it. I've tried using pairs of lines at right angles but I can't even prove it for kites.
>Each point on the exterior of the mandelbrot set has a finite number of iterations under the mandelbrot function before the magnitude of the iterated term is equal to or greater than 2. If you associate each of these points with a non-negative integer x, where x is the number of iterations for the specified point under the mandelbrot function before the magnitude of the iterated term is equal to or greater than 2 it becomes apparent that for any quadruplet of non-negative integers a,b,c,d you can find at least one set of four points forming the vertices of a rectangle whose x values are a,b,c and d respectively, with the basic proof measuring pairs of opposite vertices of the rectangle.
>Prove at least one square with non-zero area exists that satisfies this property for all non-negative integers a,b,c,d.
>Fuck guys I've tried this for over a day now and I can't do it. After parsing this garbage the non-zero area requirement is preventing me from picking squares arbitrarily close to -2+0i for very large integers and I can't think of any counterexamples in case it's bait. Have I been given a barely known open question as homework as a joke?
Any help?

[Anonymous No.11626851]

Am I setting this up wrong or something? I'm trying to show
[eqn]
\sum_{k=0}^{n} {n \choose k}=\sum_{k=0}^{\left \lfloor \frac{n}{2} \right \rfloor} {n \choose 2k} \sum_{k=0}^{\left \lfloor \frac{n}{2} \right \rfloor} {n \choose 2k+1}
[/eqn]

[eqn]\sum_{k=0}^{\left \lfloor \frac{n}{2} \right \rfloor} {n \choose 2k} =\sum_{k=0}^{\left \lfloor \frac{n}{2} \right \rfloor} {n \choose 2k+1}
[/eqn]

In order to prove that the number of subsets of odd cardinality equals the number of subsets of even cardinality on any power set. Could I adjust this to make it easier/work? Also posted in /sqt/, feel free to reply there if it's not worthy of discussion here. >>11626654

[Anonymous No.11626852]

>>11626851
oopsie, the sums in the first eqn are supposed to be added together

[Anonymous No.11626853]

>>11626776
First, you should take the brown trig bootcamp
http://www.math.brown.edu/~dkatz/trigbootcamp/

Second, radians are kind of bullshit because you could just instead declare 'doublepi' to be 6.283... then you can easily to trig like 1/2 dblpi is the diameter, 1/4 dblpi is 90deg etc.

Third is there really a difference? There is, mainly because rads require an understanding of calculus https://youtu.be/CnQXRdgN_7Ibut for us plebs just doing trig it's just a different symbol for the same thing, if that's what you're asking

[Anonymous No.11627460]

>>11626387
Is applied mathematics a good major? I also like computation and math.

[Anonymous No.11627479]

>>11626851
(1-1)^n = 0

[Anonymous No.11627481]

Did anyone understand the Real Numbers more profoundly than pic related?

[Anonymous No.11627837]

>>11626444
the set probably needs to be convex at least, no?

[Anonymous No.11627849]

>>11627481
what? empoleon?

[Anonymous No.11627852]

>>11626404
Mathematicians may use "we", a mathematician still uses "I".
English is really easy mode when it comes to personal pronouns.
Why make it artificially more difficult?

[Anonymous No.11627867]

Where can I read up on the rules of multidimensional calculus, mostly differentiation is what I am using.
I am talking about how the chain rule and product rule ...etc behave.
From what I can see it is almost identical to the 1 dimensional case.
But it's nice to have a reference just to check.

Lots of books only treat the 3 dimensional case. I am working with n>3 dimensions.

[Anonymous No.11627875]

>>11627867
Never mind. Apparently Calculus on Manifolds by Spivak has all I need.

[Anonymous No.11627962]

Suppose I have some metric d on the plane R^2. If all Euclidean circles in R^2 are also circles wrt. d, does that imply that d is constant times euclidean metric?

[Anonymous No.11627990]

>>11627962
Fells like the this comes down to checking the triangle inequality for [math] \vert\vert x-y \vert\vert^{m( \vert\vert x-y \vert\vert )} [/math] for monotone [math] m [/math]

[Anonymous No.11628005]

>>11627990
This does not work for general m. Obvoiusly doesn't work for m(t)=2, but even if we require m to be strictly monotone, e.g. m(t)=t^2 +1 this doesn't work.
If we take x=(0,1), y=(1,0), then applying the triangle inequality to 0,x,y we get
1^2 + 1^2 >= sqrt(2)^3, which is false.

[Anonymous No.11628018]

>>11626771
EGA?

[Anonymous No.11628021]

>>11628005
>This does not work for general m
Yeah, it was not a proposition, the task is to rule out those to-be-metrics

[Anonymous No.11628031]

>>11628005
>This does not work for general m
Yeah, it was not a proposition saying that it "works".
It was a guess that one can reduc the task of ruling out such metirc by rejecting those of this form f(d)^g(d), wher d=|x-y|

[Anonymous No.11628195]

>>11627962
no, try d(x, y) = ||x - y||^0.5

[Anonymous No.11628448]

any of you speak latin?

http://eulerarchive.maa.org/docs/originals/E033p1-79.pdf

[Anonymous No.11628462]

>>11628448
http://www.tonalsoft.com/monzo/euler/euler-en.aspx

[Anonymous No.11628483]

>>11628462

thanks anon, I'm in awe a human being like this existed

[Anonymous No.11628509]

Hello, based department?

[Anonymous No.11628519]

>>11628509

well-based? well-based on what?

[Anonymous No.11628525]

>>11628519
I would assume it means that the space has a good base point.

[Anonymous No.11628531]

>but what's this "based department" you talk about? do you work there?

[Anonymous No.11628743]

>>11626398
glad to see this again

[Anonymous No.11628752]

>>11626851
if [math]f(x)=(x+1)^n[/math], then [math]f(x)=\sum^n_{k=0}\binom{n}{k}x^k[/math], and [math]f(1)[/math] is your first sum. How can you split [math]f(x)[/math] to achieve a similar result on the right hand side?

[Anonymous No.11629031]

>>11627849
I thought it was Dedede

[Anonymous No.11629032]

>>11628509
profound quote

[Anonymous No.11629036]

>>11628519
Listen kid, I don't have a lot of time. It's well based on-

[Anonymous No.11629039]

>Almost all real numbers are normal
wow gee you really need a degree in maths to figure this out?

[Anonymous No.11629052]

>>11629039
I'm not sure if I had even heard of normal numbers before this post.
t. postgrad

[Anonymous No.11629225]

>TL;DR Can one prove the CLT using Banach's fixed point theorem?

Let [math]\langle \mathbb X, L^2\rangle[/math] be the Hilbert space of probability densities with zero mean and unit variance. If one were to find a contraction mapping [math]\phi: \mathbb X \to \mathbb X[/math] such that for any density [math]f_X[/math], it would hold that [math]\phi \circ \dots \circ \phi (f_X)[/math] ([math]n[/math]-fold composition) gives the density of [math]\frac{1}{\sqrt{n}} \sum_{i=1}^{n} X_i[/math] (where the [math]X_i[/math]s are iid with density [math]f_X[/math]) - then the standard Gaussian would have to constitute a fixed point of this contraction; one might then invoke Banach's fixed point theorem, giving a really cool proof of the CLT.

I couldn't find anything meaningful on this on google, only a few breadcrumbs. Does anyone know of a proof along these lines? Does it even sound feasible or am I missing something trivial here?

[Anonymous No.11629230]

is math uniquely difficult or just very vast?

i believe the primarily reason for my own struggles in elementary school was my lack of a theoretical framework to help me make narrative sense of the material. i remember feeling very frustrated with how it felt like i was given a bunch of vaguely related puzzles to solve, and that made it difficult to recall.

by contrast learning other topics was more like being told a story about how the world works. it felt less like memorizing raw information and more like expanding my worldview, and it took no effort to recall.

am i right in thinking that this is the main reason why students complain about math being hard? is there a point where you can comfortably absorb new math?

[Anonymous No.11629304]

>>11629225
Here is something similar: consider the operator [math] \phi(f_X)=f_{(X+X')/\sqrt{2})[\math], where X' is an independent copy of X. In particular, [math] \phi^n(f_X)[/math] is the density of the random variable [math] \sum_{i=1}^{2^n} X_i/\sqrt{2^n}[/math]. (this is not exactly what you want, because it only works for powers of 2).
It is easy to see that [math] \phi [/math] preserves the variance of the distribution, and does not decrease the entropy.


On the other hand, the standard gaussian is a fixed point of this operator and has maximal entropy among all distribution with unit variance. With a little extra work you can show that everything works out as you would hope. You can find the details in the book by Koralov and Sinai.

[Anonymous No.11629311]

>>11629304
latex fix:
[math] \phi(f_X)=f_{(X+X')/\sqrt{2})[/math]

[Anonymous No.11629316]

>>11629304
latex fix:
[math] \phi(f_X)=f_{(X+X')/\sqrt{2}}[/math]

[Anonymous No.11629379]

Working through Pinter during the lockdown. I need to prove that C is a subgroup of some group G with [math]C = \{a \in G: (ax)^2 = (xa)^2\ \forall x \in G\}[/math]. Is it enough to invert the relation [math](ax)^{-2} = (xa)^{-2}[/math] and claim that, as every element is the inverse of some element in G, the inverse element exists in C? Is there a name (like the center) for a group like this?

[Anonymous No.11629439]

>>11629379
Yea, you can do it like [math]a^{-1}x = a^{-1}(x^{-1})^{-1} = (x^{-1}a)^{-1} = (ax^{-1})^{-1} = (x^{-1})^{-1}a^{-1} = xa^{-1}[/math].

[Anonymous No.11629461]

>>11628195
>>11628031
>>11627962
What about the following question: is d(x,y) forced to be a function of ||x-y||?

[Anonymous No.11629503]

>>11629461
Choose your d to be the discrete metric. Then every circle is a circle, but the metric has nothing to do with the Euclidean one.

[Anonymous No.11629510]

>>11629503
No, none of the circles are circles in the discrete metric.

[Anonymous No.11629513]

>>11629503
in your example d(x,y) is function of ||x-y||

[Anonymous No.11629523]

Is Xiaoqu Yuan based or cringe?

[Anonymous No.11629537]

>>11629304
Neat! I'll look it up.
I still think though that [math]\mathbb X[/math] being a complete metric space and [math]\mathcal N(0,1)[/math] being both the limit of a sequence of autoconvolutions (with proper scaling) of an *arbitrary* element of [math]\mathbb X[/math] and a fixed point of the convolution operator on its own -- well this setting just BEGS for Banach's theorem to be invoked IMO. I'll look into that entropy idea you mentioned, but I'd still love to hear if anyone has thoughts regarding this particular direction

[Anonymous No.11629546]

>>11629523
Why don't you read him and find out ?

https://www.wikihow.com/Be-a-Mentalist

[Anonymous No.11629653]

Why can the rules of logarithms only be applied when the logarithmic coefficient is 1?

[Anonymous No.11629899]

>>11629439
So this is essentially the center group again then? Why even bother with the square?

[Anonymous No.11629927]

>>11629537
i just looked up the argument in the sinai book, and they do explicitly show that the autoconvolution operator is a contraction, at least in a sufficiently small neighborhood of the fixed point. the main idea is to linearize the operator around the fixed point and compute its eigenvalues

[Anonymous No.11629932]

>>11629899
Oops I missed the square. I don't know.

[Anonymous No.11629957]

>>11627569
Hey im not dead, busy with schoolwork and going to algebra later

[Anonymous No.11629963]

Is there a better way to write [math]\not \mathcal{R}[/math]? I used \not\mathcal{R}.

[Anonymous No.11629970]

>>11629963
\mathbb{R}

[Anonymous No.11630096]

>>11629957
stop giving "her" attention

[Anonymous No.11630112]

>>11629963
kek

[Anonymous No.11630150]

>>11626387
Is it somewhere scientifically publishable if I cracked RSA?

[Anonymous No.11630171]

>>11629461
What about identifying R^2 with the unit sphere (minus a point) via stereographic projection?
Then pull back the natural metric on the sphere, and circles are still circles.
Only problem is your space is then not complete.

[Anonymous No.11630183]

>>11629379
You need to prove that products and inverses of things in C stay in C. Literally just write it out lmao. For a, b in C and x in G:
(abx)^2=(a*bx)^2=(bx*a)^2=(b*xa)^2=(xab)^2
so ab is in C. Same for inverses by saying "any element x of G is y^(-1) for some y" and swapping things around with a^(-1) and x and substituting y^(-1) into the x
Try asking this kind of shit in sqt next time
>>11629461
The answer is yes.
Geometric lemma: given any two distinct points in the plane and d>0, you can find a finite number of (Euclidean) circles of radius d such that the center of each circle lies on the previous one and the two given points are both centers of some circles
i.e. you can go anywhere in the plane in a finite number of jumps of size d
Proof of geometric lemma: trivial
Solution of original problem: just apply the lemma
>>11629957
Kill yourself

[Anonymous No.11630219]

>>11629970
But I want to use \mathcal{R}.

[Anonymous No.11630225]

>>11630183
My bad, I assumed the Euclidean and metric circles must have the same center. My proof is only valid with this assumption.
In general this anon is correct >>11630171
Although
>only problem is your space is then not complete
is a dumb remark to make since completeness is irrelevant to the question

[Anonymous No.11630254]

>>11630183
All that stuff is straightforward, it's almost identical to proving that the center of the group is a subgroup, which was the previous exercise. I'm just having trouble convincing myself that [math](ax)^2 = a * x * a * x = x * a * x *a[/math] implies [math][a, x] = 0[/math] for an arbitrary non-Abelian group which would just reduce it to the previous problem with a square thrown in.

[Anonymous No.11630267]

>>11630254
I don't think it does.
Have you tried checking it for the quaternions?
Specifically, [mathij \neq ji[/math], but [math](ij)^2=(-ij)^2[/math] seems to make me thing it gives an example of that not happening.

[Anonymous No.11630514]

>>11629963
maybe \mathfrak{R}? it requires the amsfonts package iirc. it looks kind of dumb and dated for the real numbers since most sane people just use \mathbb{R} nowadays.

[Anonymous No.11630528]

>>11630514
I'm not using [math]\mathcal{R}[/math] to denote the real numbers, I'm using it to denote a relation.

[Anonymous No.11630622]

I'm having problems seeing

[math] y^{j+1}\sum_{i=j}^\infty \binom{i}{j} \frac{1}{(1+y)^{i+1}}=1 [/math]

Anybody got a view on it?

[Anonymous No.11630712]

>>11630622
[eqn]\sum_{i=j}^\infty {i \choose j}x^i = \frac{x^j}{(1-x)^{j+1}}[/eqn]

[Anonymous No.11630875]

>>11626387
I'm trying to prove a version of Clairault's theorem where only one of the partials is continuous at (x_0, y_0). If you do the normal trick, you can show using the MVT that [math] \frac{\partial ^2f}{\partial x \partial y} (\xi _1, \eta_1)[/math] and [math] \frac{\partial ^2f}{\partial y \partial x}(\xi, \eta)[/math] exist at points [math](\xi_1,\eta_1), (\xi,\eta)[/math]. I assumed in this case that [math]f_{12}[/math] is continuous but [math]f_{21}[/math] is not at [math](x_0,y_0)[/math]. Supposedly I am supposed to use a form of the IVP to show that the partial [math]f_{21}[/math] is equal to the partial [math]f_{12}[/math] at the point [math](x_0,y_0)[/math]. However, I absolutely cannot see how this works since I feel like I am proving the continuity of [math]f_{21}[/math] which obviously cannot be true by assumption. Any help?

[Anonymous No.11630954]

>>11626387
Why did he drop out? And why is his twitter so cringy.

[Anonymous No.11631094]

>>11630954

[Anonymous No.11631313]

Good morning, /mg/!

>>11629957
Hiya! You mentioned on the video that [math]m<n \implies S_m \subset S_n[/math]. Can you think about a natural way to extend an m-permutation to an n-permutation?

>>11629963
Bait or not, this is pretty creative.

[Anonymous No.11631324]

>>11630183
I dont see how your lemma helps at all. Can you spell it out for me?

[Anonymous No.11631559]

>>11630254
Nigga how stupid are you? I literally told you how to solve the problem and you reply with
>all that stuff is straightforward
but then you still have absolutely no idea what you're talking about.
Forget about commutators
Forget about centers
Literally just read the shit l wrote, it shows you exactly how to do the problem.
>>11631324
As I mentioned before, my proof only works if the circles have the same centers in the Euclidean and the given metrics.
The proof is that given two points x, y and some r>0, look at the (metric) circle of radius r around x. It's also a Euclidean circle of some radius r' around x. Then pick a point x1 on the circle and look at its metric circle of radius r. It's also a Euclidean circle, and it passes through x since d(z, x)=d(x, z)=r, so it's in fact a Euclidean circle of the same radius r' as the first one.
Pick a new point on this circle and iterate until you reach y.
What you get is that the metric circles of radius r around x and y have the same Euclidean radius r'
Hence d(a, b) does not depend on who a and b are, but just on their Euclidean distance so d(a, b) is a function of ||a-b||.
>>11631313
Shame you didn't die in your sleep last night, tranny

[Anonymous No.11631609]

>>11631559
>Hence d(a, b) does not depend on who a and b are, but just on their Euclidean distance so d(a, b) is a function of ||a-b||.
How does that follow?

[Anonymous No.11631644]

>>11630954
I can't speak for him, but I began my PhD in math around the same time at Cal.

You don't have to be smart to finish a PhD, just lucky or determined or desperate. An idiot I know pulled an all nighter the night before the thesis was due. No doubt QC could have finished, but as he says, better things out there.

A friend once said, you don't have to be smart to be a professor, you just have to be crazy. Judging from my postdoc advisor, who is not at all motivated by uncovering deep mathematical truths, and more motivated by playing the game and LARPing as someone powerful who hobnobs with the head of the Uni, this seems correct for the 70-95% of math professors who aren't literal geniuses.

[Anonymous No.11631831]

>This theorem [Stark-Heegner's theorem] was first proved by Heegner [52] in 1952, but his proof
was not accepted at first, partly because of his heavy reliance on Weber.
In 1966 complete proofs were found independently by Baker [3] and Stark
[96], which led people to look back at Heegner's work and realize that he
did have a complete proof after all (see Birch [6] and Stark [98]).
Does this happen often?

[Anonymous No.11631837]

>>11631831
no

[Anonymous No.11632042]

>>11630712
thx

[Anonymous No.11632066]

>>11631313
die faggot

[Anonymous No.11632273]

>>11626387
>dropout edition
I remember some more or less bitter and esoteric tweets by Yuan, but just came across this list of hot takes

https://twitter.com/QiaochuYuan/status/1140701214943793152

>mathematics lost its soul somewhere between 1900 and 1960

Do you agree?

[Anonymous No.11632288]

>>11632273
>people used to do math because they cared about something and wanted to understand it (gambling, the motion of the planets, w/e), and at some point in the 20th century math lost contact with any notion of caring or mattering; most math being done today doesn't matter at all

i used to be in a math grad program and left partly because of this; main reason i think it's worth talking about is there are lots of really smart people in math and IMO their talents are being almost entirely wasted

Related
>https://blog.jpolak.org/?p=1891
>By Jason Polak
John Baez says:
Tuesday January 9, 2018 at 06:23
I think this is wise advice. I suspect that the Langlands program attracts very competitive mathematicians.
It's good that you submitted that your paper to multiple journals. I find that a lot of my students are crushed by their first rejection – I have to prod them to resubmit. Almost every half-decent paper gets accepted eventually. But it's possible that some of the same referees got your paper multiple times, if you were writing about a sub-speciality with a few recognized experts. (Often journals lazily grab the first name off your list of references – I know this, since my name comes early in the alphabet.)
Good luck in your new field!

[Anonymous No.11632293]

>>11632273
I agree absolutely

[Anonymous No.11632333]

>>11632273
>>11632288
>>11632293
>math should always be applied and you can't pursue a quest for mathematical truth if you can't apply it to a real word problem

[Anonymous No.11632341]

>>11632273
woah there Qiaochu

[Anonymous No.11632348]

>>11632333
I doubt he was aiming at forbidding people their joy.

His complained is probably superficial, though, as the math that's applied feels probably too messy and too baby-steps-like, for his likings.

But I'm not even sure if the premise is right, that before 1900, math was perceived fundamentally different.
I think by then, math was already long divorced from phsyics in a strong sense.

>>11632341
Not a novel idea.
Although yeah, I'm almost surprised he dares to say this in left-twitter. (I'd think the broad majority of mathematicans, or academics in general, really, are hard on the progressie side)

[Anonymous No.11632358]

>>11632273
I think the sentiment is true but I don't really agree with the dates. Math was definitely still thriving in 1960. If he had said 1980 or 1990 maybe I'd have agreed.

[Anonymous No.11632378]

>>11632358
what are those events or non-events you have in mind?
what was thriving in the 1960? (And how did this thriving relate to the topic at hand, not being devoice from something soul-ful? I think for him he means topics of human interest, he's a sex tantra kind of guy)

[Anonymous No.11632392]

>>11632341
dangerously based

[Anonymous No.11632424]

>>11632348
>I'm almost surprised he dares to say this in left-twitter.
the fact that he would even consider posting something like that publicly after living 6 years in Berkeley, CA is a pretty clear indication he was starting to crack badly by that point

[Anonymous No.11632438]

>>11632424
I saw he got into a discussion with a black twitter lady on that post anyway

[Anonymous No.11632527]

anyone read laws of form? it seems pretty interesting.

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

[Anonymous No.11632558]

>>11632527
Does it solve any problems?
Otherwise I'd not get into a book full of entirely idiosyncratic notation. I know that historically grown notation can be awful, but a refactor always requires a good reason, since you need a violent progressive to radically set new standards (Atatürk, Napoleon, etc.).

[Anonymous No.11633087]

Threadly reminder to have loving platonic relationships with physicists.

[Anonymous No.11633092]

>>11633087
why only Platonic?

[Anonymous No.11633160]

>>11630954
He need money for sex therapist, Machine Learning Money.

[Anonymous No.11633167]

>>11632273
The amount of navelgazing going on in this dude's twitter is honestly disturbing. This kind of hyper-self-awareness is not mentally normal at all.

[Anonymous No.11633175]

How is it disturbing and mentally abnormal?

[Anonymous No.11633181]

>>11633167
>navelgazing
What's that?

[Anonymous No.11633185]

>>11633167
He is a high functional Incel

[Anonymous No.11633186]

>>11633181
1.double click
2. right mouse button
3. Search Google for "navelgazing"

[Anonymous No.11633202]

>>11633175
Normal people aren't constantly examining every minute detail of their psychological state under a microscope. He's obsessed with his own emotions.

[Anonymous No.11633288]

>>11633186
>Google
yikes

[Anonymous No.11633294]

>>11633087
Any tips or advice?

[Anonymous No.11633338]

>>11633288
Don't you have some fungus in your toes to eat?

[Anonymous No.11633418]

>>11633338
If you weren't a doofus you'd use bing

[Anonymous No.11633424]

>>11633418
Why?

[Anonymous No.11633436]

>>11633424
Bing number 1

[Anonymous No.11633575]

>>11633294
Write a blog and invite people to participate on a github project.

[Anonymous No.11633676]

>>11633418
>not using duckduckgo
nigger

[Anonymous No.11633681]

>50% of my year's math grade is CA
>Final exam in two days is worth 50%
>Get 27/50 in CA

What do I need to get in the final exam to get over 65% overall? I'd like to at least get a C for the year in math

[Anonymous No.11633784]

>>11633575
>github project
You mean one of those where a bunch of autists gather up to make a program that computes something something cohomology or are you talking about something else?

[Anonymous No.11633806]

>>11633784
I was mostly thinking of a collaborative TeX file.
Also because I'd like to do something like that, given I'm on vacation now.

[Anonymous No.11633892]

>>11633806
I see, I see.
Best of luck finding some project to engage in.

[Anonymous No.11633927]

>>11633892

[Anonymous No.11633951]

did the tranny 41% himself

[Anonymous No.11633956]

>>11633951
we can hope
unfortunately half the traffic in this thread is anime trannies so it really doesn't matter much

[Anonymous No.11634000]

>>11633956
>half the traffic in this thread is anime trannies
Sir do you know what website you're on? Should we run the concussion protocol?

[Anonymous No.11634016]

>>11633956
>half the traffic in this thread is anime trannies
https://www.strawpoll.me/19940909

[Anonymous No.11634075]

>>11633951
Nope. Just busy working on stuff. Sorry for worrying you.

[Anonymous No.11634113]

>>11633294
Advice for what? Being friends with physicists?
Fuck, I don't know... Be friendly to them and invite them to do fun stuff together :>

Unrelated, anyone here that still follows the abc blog posting on Woits blog? Scholze completely btfo'd the doubters imo.

[Anonymous No.11634121]

>>11634113
Are they still going? I thought that had petered out weeks ago

[Anonymous No.11634142]

>>11633951
He'll join his brethren soon

[Anonymous No.11634148]

>>11634142
There was an informative thread on /tv/ today about how the Wachovkis (The Matrix) had a dominatrix made them transition for humiliation and a sex kink

>>11634113
That's literally just drama shit.
If only people would discuss and explain his work here, instead of fapping to a 30++year old married German who just sympathetic because he looks like a 20yo cute sperg.

[Anonymous No.11634167]

>>11634148
>There was an informative thread on /tv/ today about how the Wachovkis (The Matrix) had a dominatrix made them transition for humiliation and a sex kink
Link? Sounds hot

[Anonymous No.11634210]

>>11634167
Can't find the thread in particular Karin Winslow. Larry W. left his wife in the early 2000's for to be a sub and live out his crossdress and public humiliation fetish that his then wife didn't like.

[Anonymous No.11634431]

>>11632288
good guy baez

[Anonymous No.11634440]

>>11632273
>mathematics lost its soul somewhere between 1900 and 1960
This is as good as saying that math lost its soul with the fall of ancient Greece. The philosophy behind it changes, but it's arbitrary to say that it lost its soul.

[Anonymous No.11634530]

bros.... i dont feel so good....

[Anonymous No.11634562]

>>11634530
Why?

[Anonymous No.11634638]

How's this meme list I made for myself? I've read some undergrad lvl material for analysis and algebra (and absorbed a lot of it without reading a book fully), did Hoffman and Kunze and really liked the rigor and problems

>rudin PMA
>herstein topics (these 2 just for the problems, mostly)

then
>Arnold ODE
>Ahlfors Complex analysis
>[some kind of number theory book]

then
>lang algebra
>folland analysis

then
>lee manifolds
>evans pde
>some more books on algebraic topics

What number theory book should I use? Apostol, Hardy & Wright (but no problems), and Niven/Zucker/Montgomery all look pretty good. Thanks.

[Anonymous No.11635293]

I have an online test on about 2 days, I know nothing of the material so I know it's beginner stuff but help me out please, I don't think I can eaaily cheat due to the way questions are structured so I translated some and will probably translate all asking for help on how to pass this test, I can't fail anons

[Anonymous No.11635297]

>>11635293

[Anonymous No.11635429]

Weekly reminder:
Today OATS ft. Constanze Roitzheim and equivariant homotopy https://sites.google.com/view/nialltaggartmath/oats
Tomorrow Regensburg ft. Peter Kronheimer and genus versus double-points for immersed surfaces https://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/index.php/Regensburg_low-dimensional_geometry_and_topology_seminar

[Anonymous No.11635593]

Can someone explain this in a way that a literal retard will understand? I barely know algebra so I'm struggling to make sense of how the RSA algorithm works.

[math]x[/math] is the modular multiplicative inverse of [math]a[/math] under modulus [math]m[/math] if [math]x = (1 / a) \mod m[/math].

e.g. [math]\text{let } a = 3, m = 11[/math]

[math]x = (1 / 3) \mod 11[/math]
[math]\implies 3x = 1 \mod 11[/math]

The solution is [math]x = 4[/math], since
[math]12 = 1 \mod 11[/math]
[math]\implies 12 \mod 11 = 1[/math]

To find a solution you could search numbers from 1 to [math]m[/math], and check if [math]ax \mod m = 11[/math]. However if [math]a[/math] and [math]m[/math] are coprime, there's a shortcut.

e.g. [math]text={let } a = 5, m = 7, gcd(5, 7) = 1[/math]

Okay now what's the shortcut and why does it work?

[Anonymous No.11635597]

>>11634638
>>lee manifolds
I would replace by Tu's Introduction to Manifolds
>>evans pde
if you've never seen PDEs, this book will be dry and unmotivated as fuck

[Anonymous No.11635601]

>>11635593
https://en.wikipedia.org/wiki/Euler%27s_theorem apply this with the assumption that a and m are coprime. If at least p is prime, then you have [math]a^{p-1} \equiv 1 \text{mod }p[/math], and now you have an inverse. Then you get rid of the largest multiple of p that fits into your inverse.

[Anonymous No.11635605]

>>11635597
>>11634638
>lee manifolds
>TU's manifolds
Lee is too long and verbose, Tu is imprecise and skips over important details ( for example, he doesn't prove that d/dx_i form a basis of the tangent space of R^n at a point).
I would suggest you read Shigeyuki Morita's book "Geometry of differential forms". It's great! It even has answers to exercises at the end. Surprised how few people know about this book.

[Anonymous No.11635606]

>>11635605
>for example, he doesn't prove that d/dx_i form a basis of the tangent space of R^n at a point
what ? I've just looked into the book, it's there

[Anonymous No.11635613]

>>11635606
Care to point out the pages?

[Anonymous No.11635618]

>>11635613
in the second edition it's page 13

[Anonymous No.11635624]

>>11635618
You're right, I was mistaken.Thanks for correcting me.

[Anonymous No.11635633]

>>11635624
>Tu is imprecise and skips over important details
I remember this book being quite the opposite, but it's been some time. do you have other concrete objections ?

[Anonymous No.11635638]

>>11635633
>do you have other concrete objections ?
Not really. I take back my criticism of Tu. It's a good book.

[Anonymous No.11635646]

>>11635601
Hmm, not seeing how it all fits together but apparently you can use the extended Euclidean algorithm to solve that... but how exactly do I get the [math]ax = 1 mod m[/math] into [math]ax + by = d[/math] given that m and x are coprime and x is prime?

[Anonymous No.11635651]

>>11635646
idk

[Anonymous No.11635658]

>>11635646
you use this algorithm to find inverses modulo m
IF ax + my = 1
THEN ax = 1 mod m

[Anonymous No.11635659]

>>11635646
If m,x are coprime, then by bezout's theorem there are integers a,b such that
am + bx = 1
so m| bx - 1
so bx = 1 mod m

[Anonymous No.11635664]

>>11635658
>>11635659
Thanks I understand now.

[Anonymous No.11635675]

>>11633956
>>11634016
>half the traffic in this thread is anime trannies

[Anonymous No.11635706]

>>11635675
>half the traffic in this thread is an anime trannie

[Anonymous No.11635715]

>>11635675
that one Tranny vote was me and I was just voting for it becaus I thought everybody would. Seems the natural thing to do but oh well

[Anonymous No.11635717]

>>11635715
lol

[Anonymous No.11635771]

>>11634562
my ability to concentrate and will to do anything is at all time low

[Anonymous No.11635823]

>>11635715
Tbqh the idea scenario was everyone voting "No." so that I could produce pic related.
But everyone voting yes would have also been funny.

[Anonymous No.11635896]

>>11635771
What's disturbing you?

[Anonymous No.11635964]

>>11635429
Less than 15 minutes!

[Anonymous No.11635981]

>>11634016
>transgenda
no
>post anime
yes

[Anonymous No.11636166]

I'm so retarded I left my masters thesis until the last two weeks, and now I realize I can enjoy working on it after all. I think I'll make it, thank god I'm not really trying to get any original results, but this is getting ridiculous.

[Anonymous No.11636178]

where can I get a dedekind fade

[Anonymous No.11636199]

>>11636178
Come here if you want some Dedeking bruises.

[reggie No.11636204]

>>11636178
Come her and I'll give you some Dederwarchsener

[Anonymous No.11636311]

>>11636166
What were your advisor and your professor thinking?
I'd have given you hell.

[Anonymous No.11636327]

what is math even a study of

[Anonymous No.11636464]

>>11636311
I don't know, haven't communicated with them since january.

[Anonymous No.11636509]

Is it true that a commutative ring R is an UFD if R*/{units} is free?

[Anonymous No.11636516]

>>11636509
>Is it true that a commutative ring R is an UFD if R*/{units} is free?
What have you tried?

[Anonymous No.11636541]

>>11636516
Ive tried solving it and i solved it
Thanks for the help

[Anonymous No.11636558]

>>11636509
>commutative ring
Did you forget local?

[Anonymous No.11636564]

>>11636558
No? Local would be too strong of a condition.

[Anonymous No.11636565]

>>11636327
itself

[Anonymous No.11636568]

>>11636565
No that would be metamathematics.

[Anonymous No.11636572]

>>11636564
Don't you need local for [math]R - {units} [/math] to be a module tho?

[Anonymous No.11636588]

>>11636565
ok but what is it? i can't see past the symbols and blindly following instructions.

[Anonymous No.11636593]

>>11636588
Read Serre

[Anonymous No.11636634]

>>11636593
i appreciate being given a direction, but if i was capable of following "read x" advice at will then i would not be here and my english would be punctuated. is it really something that can't be explained in a few sentences

[Anonymous No.11636662]

Wouldn't the residue be
[math]{exp(-t)\over 2i}+{exp(-t) \over 4}[/math]?

[Anonymous No.11636676]

>>11636662
stupid questions go in /sqt/ >>11628445

[Anonymous No.11636692]

>>11636662
Why would it, it's the residue at a particular point.

>>11636676
I understand the sentiment, but if we redirect any math, we're left with just banter and Scholze drama.
I mean what would be the topic /mg/ is about? Hardly ever do people make an effort to discuss question, and each topic is hated by this or the other group.

[Anonymous No.11636716]

>>11636692
>but if we redirect any math, we're left with just banter and Scholze drama.
redirecting sophomore analysis homework =/= "redirecting any math"

[Anonymous No.11636730]

my invitation to explain what math is remains open :) it might even make for an interesting discussion for the resident experts

[Anonymous No.11636749]

>>11636692
>just banter and Scholze drama
The authentic /mg/ experience.
Also, a dude asked about Quillen functors yesterday on /sqt/. Someone go help him.

[Anonymous No.11636769]

>>11636749
redirect him to /mg/ lmao

[Anonymous No.11636787]

>>11636730
I doubt there can be insights about this centuries old topic that goes beyond what's one click away
https://en.wikipedia.org/wiki/Definitions_of_mathematics
https://plato.stanford.edu/entries/philosophy-mathematics
let alone the conflation of the subject matter, its ontology and the practice thereof.

[Anonymous No.11636802]

>>11636769
Fucking kek.

[Anonymous No.11636854]

>>11636692
>Why would it
My takeaway in this example was that we were plugging in z=i into the expression

[Anonymous No.11636877]

>>11636854
>we were plugging in z=i into the expression
the function isn't defined at z=i, so...

[Anonymous No.11636881]

>>11636787
yes, thank you for the sober answer. what was i even thinking trying to answer a centuries old question, that's way too complicated. i thought i already learned my painful lesson from all those years of fruitless semantic arguments, but i guess my delusions of having a human spirit must be returning. time to go back to work and leave this topic to my betters.

[Anonymous No.11636885]

>>11636877
I guess that's a good point, thank you

[Anonymous No.11636893]

>>11636877
Everything is defined if you are an engineer or a physicist.

[Anonymous No.11636907]

>>11634440
Not really arbitrary - it could simply be restated in the form of, "the philosophy behind mathematics changed to something that I consider less meaningful based on some metric(s)." As a working mathematician I feel that's justifiable on the grounds that you must accept that modern mathematics is just about making increasingly difficult puzzles and trying to solve them.

[Anonymous No.11636930]

What's the most autistic thing to study in math

Hard mode
>No set theory
>No formal logic

[Anonymous No.11636934]

>>11636930
topology

[Anonymous No.11636942]

>>11636934
I agree

[Anonymous No.11636944]

>>11636930
combinatorics

[Anonymous No.11636948]

>>11636934
which one ?

[Anonymous No.11636961]

>>11636934
general topology is basically set theory, but it would be very near the top if it wasn't 99% dead.
>>11636930
In my anecdotal experience the most autistic mathematicians tend to be the people doing pure algebra. Representation theorists in particular are overwhelmingly gigantic spergs.
>>11636944
Combinatorics is the polar opposite of autistic. Combinatorialists are the most normie people you'll ever find in a math department.

[Anonymous No.11636967]

20 year old college freshman here
if i got a C in diff eq, a B in my honors vector calc course (retake), a C in my proofs course (which is the same grade i got on the last retake), and a B in linalg, where do i go?
i kind of know i'm probably not good enough at math for a pure math degree but i still want to do math
i'm stuck between computer math and probability math, send help

[Anonymous No.11636973]

>>11636961
Geometric topology. Sure other fields might have a few more autists, but the ones in geo-topology more than compensate for their relative sparsity.

[Anonymous No.11637015]

>>11636961
>Representation theorists in particular are overwhelmingly gigantic spergs.
Yet their ranks also include the giga chad Jesper Grodal. One could perhaps say that representation theory leads to extreme cases.

>>11636930
Integration for the sake of winning an integration bee.

[Anonymous No.11637023]

>>11636930
reminder that autistic neq hard
for me, it's model theory

[Anonymous No.11637033]

>>11637023
>no formal logic

[Anonymous No.11637058]

>>11637033
:^)

[Anonymous No.11637142]

>>11637023
>writing down neq
Now this is autistic.

[Anonymous No.11637167]

I have an open book end of year maths exam tomorrow morning, kings. I'm scared tbqh.

[Anonymous No.11637187]

>>11637167
What topic? Anything but discrete math.

[Anonymous No.11637195]

>>11637167
What topic? Discrete math would be nice

[Anonymous No.11637216]

>>11637187
Various topics, broadly engineering maths. Differential equations, logarithms, sinusoidal functions and algebra II mostly.

[Anonymous No.11637381]

>>11637216
table of integrals
substitution
by parts
taylor series
sin(x) = x
cox(x) = pi/3 = e/2 = g/10
donezo

[Anonymous No.11637435]

>>11637381
Also every time you have an integral, just divide the dx by dy, invert the integrand to get the integral of something times dy/dx, move the dy/dx in front of the integral and by the fundamental theorem of calculus you have the derivative of an integral, equal to the integrand itself.

[Anonymous No.11637588]

Why are textbook written by French mathematicians so tsundere?

[Anonymous No.11637598]

What the FUCK did he mean by this

[Anonymous No.11637602]

>>11636930
symplectic geometry

[Anonymous No.11637822]

academia is a fool's gamble. I'm just going to live in a lot raising chickens and potatoes to survive and go to the town's library to use the internet when I'm stuck

[Anonymous No.11637850]

>>11637602
>not even the most autistic thing in differential geometry

[Anonymous No.11637885]

>clearly, trivial, obvious
>left as an exercise for the reader
>skips a lot of detail in proof
>doesn't say more than he needs to
>very hard exercises
>no q.e.d. or end-of-proof square

>but ultimately, the frustration makes you a better mathematician

[Anonymous No.11637897]

>>11626387
legit question: Why would you aspire to do anything that can be done by a website calculator? If there is more than that to aspire to these days being a mathematician, 1) what? 2) That should be like the first thing they tell kids.

[Anonymous No.11637915]

>>11626473
There's something very oafish about this objection.

[Anonymous No.11637945]

>>11637588
they're a bunch of anal fucks with no taste
>>11637822
okay grothendieck
>>11637897
1) creativity, intelligence and actual understanding of the concepts. you need to understand calculus before even using an "online calculator" to solve integrals, or a physics simulation program to study the structual stability of a bridge design, etc. 2) yes. read Lockhart's Lament

[Anonymous No.11637986]

>>11637602
the real answer could be fukaya categoies. combines the powerlevels of category theory, symplectic geometry, and homology into one.

[Anonymous No.11637990]

>>11637897
calculators cannot do a single thing beyond like freshman year math

[Anonymous No.11638105]

>>11631094
What a navel gazing idiot. Nothing you do will matter.

He most likely lacked originality and creativity. He seems to be those type of mathematicians that were very good at symbol pushing and doing well on exams, but that can only get you so far. His whole rationality less wrong worship was just a cope, and of course, he realized this, and that's why he goes on the opposite end of the spectrum by becoming an insufferable new age cunt. Still as shallow as ever.

[Anonymous No.11638559]

>>11638105
>haha just git gud, if he was better he would enjoy math
that's not a very smart argument, although i agree that the guy is cringy

[Anonymous No.11638742]

Let m be *any* positive integer larger than 2. Let k be *any* nonnegative integer.

Suppose we fix *some* value for k, say k=K.

K can be any number, but it's fixed. We have not fixed any value of m yet.

Can we then always write m = n + K, where n still enjoys the same property as m of being any positive integer larger than 2? Is this always valid for any nonnegative integer K we fix?

I feel like the answer is an obvious yes, since m can be any number and so if you suppose m =/= n + K for some K, m and n any integer larger than 2, then you can simply reassign m-> m + d, d being the difference m-(n+K). But this logic seems rather circular since I'm assuming the thing I'm trying to prove in the reassigning of m.

[Anonymous No.11638756]

>>11638742
yes my man
choose n to be 10
then m is 10 + K > 2

[Anonymous No.11638762]

>>11638742
>Can we then always write m = n + K, where n still enjoys the same property as m of being any positive integer larger than 2? Is this always valid for any nonnegative integer K we fix?
Fix K=2 and let m=3. Then n+K > 4>m.

[Anonymous No.11638780]

>>11638756
Nice, although this wasn't exactly what I was looking to show (I realize now that my post should have been written clearer).

Specifically, I am interested in the following:
For any *fixed* integer value of K, and m being any integer > 2, can I write m = n + K such that any m may be represented as this sum, and since m can be any integer larger than 2, does n inherit this property? i.e. n also becomes any integer larger than 2? Essentially I'm interested in what happens to n. Since m is assumed to be any integer, does n inherit this property of also being any integer, for any fixed nonnegative integer k=K?

Essentially I'm trying to prove the following:

I have m = (some positive integer) + k, where m can be any integer larger than 2

and then I want to get rid of k on the RHS by saying that since m is any integer, and k is some fixed integer, I can write m = n + k to obtain

n = (some positive integer),
for any integer of n larger than 2.

Basically I want to show that n inherits the property of being any positive integer larger than 2 because m is any positive integer larger than 2, for any fixed nonnegative integer k.

apologize for the autism

[Anonymous No.11638785]

>>11638780
note: The (some positive integer) needs to remain the same, so if its equal to some positive integer s, it should remain equal to that same positive integer s after getting rid of k by the reassignment m = n + k, where hopefully n inherits the freedom to be any positive integer larger than 2 from m

[Anonymous No.11638790]

>>11638780
what ?
let K = 2
let m = 3
then m is an integer larger than 2, but n = m - K = 1 is not larger than 2.

[Anonymous No.11638793]

>>11638790
I should also have specified that m is at least 6 larger than K. I.e. m-K >= 6. Sorry I'm retarded

[Anonymous No.11638802]

>>11638793
okay

so we have m = n + K, hence n = m - K. this is what we get:

n > 2 if and only if m - K > 2.

what does this tell us ?

[Anonymous No.11638807]

>>11638802
nice, thanks!

[Anonymous No.11638816]

>>11638807
(have you noticed that the direct reasoning is far more instructive than searching for contradiction?)

[Anonymous No.11639038]

>>11635429
Regensburg in less than 3 hours!

[Anonymous No.11639100]

>>11639038
whore

[Anonymous No.11639329]

bros.... how do i get motivation and enthusiasm to study mathematics?

[Anonymous No.11639331]

>>11639329
cocaine

[Anonymous No.11639366]

I have a linear algebra doubt.
Suppose I have a 16x16 matrix given. I also have a set of a few other 16x16 matrices, some of which have elements with variable values.
Is there an efficient way to find the shortest sequence of matrix multiplications on the set of matrices so as to obtain the given matrix?

[Anonymous No.11639368]

>>11639329
Been there. You need to find something that really really really interests you. Then you get a motivation boost comparable to a billion (10^12) big bangs occurring at the same time and at the same place! Come and see if the topology seminar hits this nerve in roughly 10 minutes.

[Anonymous No.11639392]

>>11639366
I don't think there's a simple algorithm to do that, even if you would want to look for "any sequence of multiplications"
also look up mortal matrix problem

[Anonymous No.11639394]

>>11639366

do you know anything more about those other matrices? are they a specific set of parameterized transforms?

[Anonymous No.11639401]

This board makes me feel like a subhuman, it's like trying to understand another language

[Anonymous No.11639409]

>>11639394
they're matrix representations of basic quantum gates, u3 and Cnot. (https://qiskit-staging.mybluemix.net/documentation/terra/summary_of_quantum_operations.html))
I have to use them to make a unitary transformation, which is a 16x16 symmetric unitary matrix.

[Anonymous No.11639418]

>>11639409

i'm not familiar with those transforms. my first idea would be a greedy optimization. start with an identity matrix, and for each transform, find the parameters that get you closest to your target. apply best transformation, and repeat.

[Anonymous No.11639428]

>>11639418
ah ok that's probably the best way to go about it for now, i'll try that thanks

[Anonymous No.11639462]

>>11639428

you may want to read up on other graph search stuff too. for example, A* search. it's an incredibly well-researched area, and you can apply these ideas to a huge variety of problems.

it's a crime that most undergrads don't learn this stuff

[Anonymous No.11639623]

>>11638559
Not even a git gud argument. Research is very different from passing exams.

[Anonymous No.11639664]

>>11637897
First of all, all these computational tools were developed by mathematicians and extending the range of problems amenable to computation is still an active area of inquiry in math and CS.
Second of all, most of the problems that mathematicians think about have very little to do with what a calculator can do. Even though sometimes a computer can help work out some examples, you do not prove theorems with calculators. You do not get insight or ideas from computers.
You might get answers to specific questions, but not understanding, which is what math is about.

[Anonymous No.11639698]

>>11639664
You're really underestimating how useful "working out some examples" is. Being able to find out in an afternoon whether a conjecture fails for some slightly nonobvious small case is extremely helpful. Being able to look for patterns in a big folder of complicated examples without having to spend 20 minutes per example grinding out computations and hoping you never make a mistake is also extremely useful.

Unless you work in some ridiculously abstract area that's so masturbatory nothing you study is even computable pretty much everybody uses computers in their work nowadays.

[Anonymous No.11639716]

>>11639664
what are you understanding? or, what is the insight about?

[Anonymous No.11639801]

>>11637897
Problems of mathematical interest are those for which there is not yet a way to make sense of what are they and in what context do they even exist.
>>11639716
It is impossible to know the usefulness of mathematics that you do except in retrospect. Why did it turn out effective? Well, I would ask why would number theory and geometry be good leads towards ideas of fundamental importance instead, because those are the "god given" concepts in some sense.

[Anonymous No.11639815]

Rate.

[Anonymous No.11639841]

>>11629039
it is something that makes intuitive sense but proving things is hard

[God No.11639891]

>>11639801
hello my son. it is i, the father of mathematics. i command you to answer anon's questions to prove your love and appreciation of my creation!

[Anonymous No.11639919]

>>11639815
i personally hate when authors do the following:
>theorem says conditions from i to iv are equivalent
>there is an obvious and natural way to prove 1 equivalent to 2, 2 equivalent to 3, 3 equivalent to 4
>author goes 1=>2=>3=>4=>1 where the proof of 4=>1 is some retarded gay shit

[Anonymous No.11639933]

>>11639919
>1, 2 and 3 are equivalent
>1 implies 2 is theorem 5.24
>2 implies 3 is theorem 4.32
>3 implies 1 is theorem 1.6

[Anonymous No.11639937]

oh my goodness what just happened!? some strange force took possession of my body and made me type those weird words! i fear my mind is so pure that it attracts strange entities. i better practice some more algebra until they lose interest.

[Anonymous No.11639947]

>>11639937
*tips fedora*

[Anonymous No.11639992]

>>11639947
anon please! this is no joke! i think i might really be haunted. i knew i should have stayed away from those "centuries old" topics, but the allure of the abstract arts was just too much to resist...just imagine the POWER we could obtain! equipped with the power to dissolve and transmute all concepts, no math would ever stand in my way...i must obtain this stone even if it costs me my life.

[Anonymous No.11640098]

not bait but this genuinely bugs me. If math is all about logic and rationality, then why are irrational numbers allowed? what gives?

[Anonymous No.11640109]

>>11640098
There is nothing irrational about rational numbers. The name "irrational numbers" is just a remnant of our retarded ancestors who didn't understand what they were doing.

[Anonymous No.11640110]

I'm taking a course that heavily uses constructive logic and I'm having trouble telling what classical derivations also hold in intuitionistic logic.
It's not obvious to me which derivations use RAA or LEM.

Can you recommend any resources that would help me with this problem?

[Anonymous No.11640121]

is it possible to calculate the percentage probability of another percentage probability as a percentage of that probability?

[Anonymous No.11640134]

>>11640109
Not even that, it's just a quirk of language. Rational comes from ratio, and we just tacked on the prefix ir-

[Anonymous No.11640136]

>>11640098
irrational = not rational = not a ratio

[Anonymous No.11640153]

>As a consequence of Cantor's proof that the real numbers are uncountable and the rationals countable, it follows that almost all real numbers are irrational
>almost all
explain yourself, mathematician

[Anonymous No.11640160]

>>11640121
so far what I have is [math]\left(1-\frac{100-p}{x}\right)100[/math] where p is the percentage probability you want to scale and x is the percent you want to scale it by.

It correctly identifies 75% as 200% of 50% e.g. 1/2 -> 1/4
110% * 90% = 90.909% 1/10 -> 1/11 etc. etc.

but it produces some garbage when the numbers are too low.

[Anonymous No.11640161]

>>11639815
absolute kino

[Anonymous No.11640170]

>>11640153
the infinity of irrational numbers is bigger than the infinity or rational numbers

[Anonymous No.11640173]

>>11640170
nevermind forget i even asked

[Anonymous No.11640174]

>>11640153
cantor was a retard who fucked up maths forever

[Anonymous No.11640184]

>>11640153
>explain yourself
Mathematicians should put more effort into explaining themselves, than to explain all that bloody mathematics to idiots.

[Anonymous No.11640187]

>>11640134
>>11640136
And where does the word "irrational" derive its meaning of "stupid, not logical"?

[Anonymous No.11640198]

>>11640174
As far as trolls on /sci/ goes you are pretty weak. How about insulting anyone who knows math by calling them a pedo, faggot, cuck, kike, nigger, or the worst of all, liberal? Please try again when you got it.

[Anonymous No.11640202]

>>11640184
on what grounds do you call me an idiot my friend. i may not know math but i still have feelings

[Anonymous No.11640207]

>>11640187
Look bro, if you'd rather we call them the quotionals and the unquotionals or some shit, that's fine, but you sound like the retard who thinks [math]i[/math] not real because it's imaginary, when it's just a naming convention and lateral or complex would also suffice

[Anonymous No.11640273]

Something about this doesn't belong

[Anonymous No.11640277]

>>11640273
No that looks about right

[Anonymous No.11640308]

>>11640273
That's me. I did that.

[Anonymous No.11640310]

>>11640110
Intuitionistic logic is decidable, so there should be something analogous to truth tables for it.

[Anonymous No.11640357]

>>11639401
Just Learn and join Godhood with us.

[Anonymous No.11640361]

https://s.wayne.edu/isaksen/eCHT/
>12, 14, 19, and 21 May 2020
>4-hour online mini-course, offered on consecutive Tuesdays and Thursdays at 11:30am in Detroit (Eastern Time).
>Speaker: Gijs Heuts, Utrecht University Title: Unstable homotopy groups
>Abstract: This will be a four lecture crash course on calculational methods in unstable homotopy theory, containing a mixture of classical and some more modern material. There is a wide range of tools available with which to study the structure of the homotopy groups of spheres (and other spaces). In this course I will focus on the following: rational homotopy theory, the EHP sequence, the Goodwillie tower, and v_n-periodicity in unstable homotopy groups. I hope to explain how each of these informs our understanding of unstable homotopy theory and how they can be applied to calculations. These lectures are intended to be accessible to graduate students.

[Anonymous No.11640383]

>>11640174
t. actual retard

[Anonymous No.11640500]

>>11640361
Nobody cares

[Anonymous No.11640505]

Don't know if this is the right place to ask. So bear with me math chads.

I am re-learning math/stats but mostly in hope that it would would make me better at business/finance/econ in the future.

But I am wondering if I should learn physics too since I see so many physics grads in banking(investment banking and shit) and finance? Is it useful or are those people hired for their sheer intelligence and not specifically because of their domain knowledge?

[Anonymous No.11640512]

Requesting your pictures of anime girls with advance math texts.

[Anonymous No.11640521]

>>11640505
they are hired for their intelligence and general math-related knowledge
NOT for knowing physics

[Anonymous No.11640531]

>>11640110
Learn lambda calculus and Curry Howard.
It's actually very clear/intuitive when a proposition is true constructively and when not.

[Anonymous No.11640555]

>>11640521
Thanks. I am 28 and wouldn't really have the time to re-do both at this age. Though feel insecure about the people who learnt hard physics chem and math at HS itself.

[Anonymous No.11640560]

>>11640555
>Though feel insecure about the people who learnt hard physics chem and math at HS itself.
cheating bastards
nobody told be about this metagame when i was a kid

[Anonymous No.11640612]

Is there a succesful mathematical construction of the Feynman path integral in the context of ordinary non-relativistic quantum mechanics?

[Anonymous No.11640744]

>>11640512
>no replies
Oof.
Have a fresh one.

[Anonymous No.11640770]

>>11640744
Also this one.

[Anonymous No.11640798]

>>11640612
afaik i know, no. the measure doesnt exist

[Anonymous No.11640821]

>>11640744
Lang is a meme.

[Anonymous No.11640839]

>>11640512

[Anonymous No.11640844]

>>11640839

[Anonymous No.11640849]

>>11640798
yea I understand the measure theoretc approach doesn't work, but there are many other ways to construct an object like the path integral. But from what I understand all these approaches cannot cover all example of interest in physics. Well at least the approach that I'm looking at, doesn't cover singular potentials like the coulomb potential.

[Anonymous No.11640873]

>>11640844
I've seen you (or whoever) post the Associative Algebras book before.
Please make a pitch.
I can't even find a table of content online (looking at springer, google, amazon)

[Anonymous No.11640889]

>>11640844
>>11640839
>poorly cropped, blurry book covers
learn to MSpaint

[Anonymous No.11640938]

>>11640873
Okay, so I basically just use it for reference, but it does cover a lot of things quite nicely. For learning purposes, I don't know if it's the best in any of the included things, but it does cover a lot of stuff relevant for my purposes very nicely, and for that purpose I would at least recommend it. I don't know if I can give a pitch for the book without knowing what you are actually after, so I'll give you the table of contents.

1 The Associative Algebra
2 Modules
3 The Structure of Semisimple Algebras
4 The Radical
5 Indecomposable modules
6 Projective Modules over Artinian Algebras
7 Finite Representation Type
8 Representation of Quivers
9 Tensor Products
10 Separable Algebras
11 The Cohomology of Algebras
12 Simple Algebras
13 Subfields of Simple Algebras
14 Galois Cohomology
15 Cyclic Division Algebras
16 Norms
17 Division Algebras over Local Fields
18 Division Algebras over Number Fields
19 Division Algebras over Transcendental Fields
20 Varieties of Algebras

[Anonymous No.11640944]

>>11640844

[Anonymous No.11640976]

>>11640938
Thx. If you're a "he", cut your nails. You have a role to perform.

[Anonymous No.11641006]

>>11640976
No problem. I think the book is probably good for learning stuff, too, so why not download it and give it a try? Naturally, you will first check your uni's digital library, assuming you are in one, just so that you will not be guilty of piracy!

Anyway, good night /mg/.

[Anonymous No.11641030]

>>11641006
Gn

[Anonymous No.11641263]

>>11640174
based and poincarepilled

[Anonymous No.11641304]

>>11626387
guys I'm really just looking for advice
due to a combination of my apathy plus what I think was IBS and apnea, I've been doing basically nothing in Multivariable Calculus. I've got an exam tomorrow and I'm just wondering if you guys have any suggestions for things I should focus on. My plan is to just go through the book and do at least one of each of the tested concepts so that I can do some reverse-engineering.

I'll relearn this stuff when I need to in a few years, I promise. Not an engineer, btw.

[Anonymous No.11641708]

nothing more rewarding after a hard day at the conjecture mines than jerking off drunk and smoking after

[Anonymous No.11642161]

>>11640938
nice nails tranny