/sci/ - Science & Math

Threadly reminder to work with engineers.

Occasional reminder not to work with people who aren't mathematicians or physicists.

Mathematicians should work with everyone. Easiest way to obtain nobel prize by bullshiting brainlets with basic toy models by telling them they can model the market, or social interactions lmao.

>only took through algebra 2 in high school
>taught myself precalculus and trig over the winter break
>took the placement exam again
>tested into Calculus
how do I make sure I don't fuck myself over?

>>11323573
By studying and working hard. Calculus isn't hard.
>>11323561
What exactly distinguishes a toy model from a "real" model?

>>11323583
That a toy model has limited to no applications to whatever phenomena you are studying. Are you autistic?

>>11323583
whenever people talk about calculus, they speak of it like a boogeyman. is it just because I talk to a bunch of brainlets?

>>11323590
Yes. You will be fine.

>>11323598
Awesome, thanks. The response I got from my coworkers when I told them my plan:
>teach myself over winter break
>skip two classes and get into calculus
was "why would you want to do that?" . I usually just told them it would save me time/money (which is true), and not that I wanted to take further math courses.

>>11323641
How is this useful for someone who want to do research in discrete math?

>>11323486

How am I meant to interpret this question? Does v form a row vector of a 1x4 matrix? I have done these calculations before using numbers in a matrix but I have never done it before with variables like this. Does this mean that v_1, v_2 etc are just components of the vector v?

>>11323864
Not sure if this is what your confused about or if this is new to you, but in linear alegebra you have to be very careful about the representation of a linear map as a matrix and the linear map itself. The linear map is defined in [math]\mathbb{R}^4[/math] so as an abstract function it takes 4-tupples and outputs a real number. The distinction between row and column vectors is a matter of convention and the question is setting that you are taking the 4-tupples as column vectors. Question a) doesn't depend on this convention as it's just asking for the set of 4-tupples such that their sum is 0 and then just the range of the function. For question b) you will find the matrix representation of the linear map, by simply substituting the canonical basis into the function and representing the result as a row vector.

>>11323623
make sure you know the unit circle like the back of your hand (just memorize it) and you'll be fine. You don't really need to know a lot for baby's first calculus class

>>11323486
What kind of faggots don't post links in the old thread?

>>11324132
>What kind of faggots don't post links in the old thread?
We don't hand-hold brainlets in this neck of the woods.

>>11324132
>faggots
Why the homophobia?

/mg/pill me on black holes

Does the infinity in the extended real numbers have any relation to aleph numbers? Or are they two entirely different kinds of infinities?

>>11322691
Note that [math]T\mathbb{R}^n[/math] is spanned by the differentials [math]\partial_i[/math], so as the Lie group of translations [math]\mathbb{R}^n[/math], the operators [math]\partial_i[/math] forms a basis for its Lie algebra. This is why [math]\exp\left(-ia^i \partial_i\right)f(x) = T_af(x) = f(x-a)[/math].
Or you can just assume [math]f\in L^2(\mathbb{T}^n,\mathbb{C})[/math] and do a Fourier transform, then compute from there.
>>11323513
Based and Connespilled.

>>11324293
Stones theorem on one parameter unitary groups, while similar to the lie algebra lie group correspndance, it has fundamental differences in meaning and actual statement and it's a bad analogy to make.

>>11324331
Good point, but Stone's gives us necessary and sufficient condition for the existence of an ESA generator [math]A[/math] for the one-parameter unitary, while the anon who asked the question [math]started[/math] from the generator [math]\partial[/math].

>>11323648
It's not. It's not useful to just about anyone. I suppose it is sort of useful if you're interested in doing geometry?

>>11324255
Different notions of infinity. Extended reals infinity is really just a symbolic infinity which exists for topological purposes, all it is there to do is to "compactify" the reals, i.e. to cap off an infinite tail.
The aleph infinities talk about the sizes of sets.

>>11324416

Seriously, what’s wrong with Took’s disproof of the Riemann hypothesis

>>11324445
The riemann hypothesis is a statement about the zeros of the Riemann zeta function which is a metamorphic function on the complex plane. Tooker just rambles about how the conjecture should be about some function in the extended complex which is not the Riemann zeta function. Therefore it's wrong because the conjecture clearly states the objects it talks about, and Tooker just says that the "actual" conjecture should be the one he presents. Not only this is extremely retarded, it shows how pointless his article actually is.

>>11324255
>extended real numbers
>aleph numbers
Neither bear any relation to infinity.
>different kinds of infinities
This is nonsensical to even suggest. Infinity is one.

Is there a way to check if a sudoku puzzle is solvable without actually solving it?

>>11324904
Less than 9^3 possibilities, less than 27 checks for each of them.
Just tell your computer to exhaust it, bro.

>>11324909
But that's the same as solving it.

>>11324914
Wait is that the same as solving it?
Idk

Coalgebras and homology.

Can someone recommend a good book on Hilbert's 12th problem?

>>11323431
I still don't understand the proof of Taylor's theorem

>>11324445
Stop posting this. We already explained it to you. The zeros he finds are not in C, they are in an extended version of C (and they are trivial). The riemann hypothesis asks for zeros in C.

>>11325220
Literally just "do mean value theorem n times"

How can I prove that some probability space with events A, B, C, D exists such that B is the complement of A, D is the complement of C, P(A|D)=0.99, P(B|C)=0.98 and P(I)=0.001?

https://drive.google.com/file/d/1TQS1V1R8cbWLKR2aXplbZ1-3c6fj-Rfv/view

numberphile man's math film

>>11325321
that's just a mediocre softcore erotica guised under some bad narrative

>>11325265
Okay so I take omega={1,2,3,4}, the sigma-algebra 2^omega, A={1,2}, B={3,4}, C={1,3} and D={2,4}. Then I found p1, p2 , p3 and p4 the probability of {1}, {2}, {3} and {4} respectively using the constraints and the fact that p1+p2+p3+p4=1 and this completely define a probability space. This also prove the unicity of such p1,p2,p3,p4. It works but it seems a little bit stupid to do that, is there any other method to prove the existence of such probability space?

>>11324686
>>11325242
But that still means hes smart right?

>>11325484
No, any undergrad could do what he did.

>>11325484
That's another person lad.

>>11325484
>hes smart right?
He's not that smart if he won't even text me back. Who visits Anaheim and isn't down to go to Disneyland?
>>11325321
I hate the french so goddamned much

Could we uniquely determine the class of similar triangles by taking the ratio of the radius of the inscribed circle to the radius of the circumscribed one?

If I have a set of random variables [math]X_1, X_2, X_3, ... X_n[/math], and I pick a set of conditional independencies of the form [math]X_i \land X_j \land ... \land X_k \perp X_a \land X_b \land ... \land X_c | X_p \land X_q \land ... \land X_r[/math] and then apply the rules of conditional independence (https://en.wikipedia.org/wiki/Conditional_independence#Rules_of_conditional_independence)) recursively on this set to get a closure, can I always come up with a distribution that has exactly these conditional independencies (in the closure) and no more?

>>11325578
What's the domain?
Why don't you use proper grammar/sentences?

>>11325599
Just probability theory. What I'm asking is that can I always come up with a probability distribution which follows exactly a closure of a given set of conditional independencies, where the closure is calculated using the rules of conditional independence. Sorry if I wasn't clear.

>>11324143
Then why link the old thread? Have you ever seen single linked lists linked backwards?? It is retarded. Should be a double-linked list.

Opinion on Strang's Calculus? Is it better than Stewart's for a noob in calculus? I tried my hand at Spivak because I heard it was better at building intuition but I was taking way too long with fundamentals(probably because I had never had any contact with proofs) and was recommended to do something more practical for now. I'm currently watching Strang's Calculus Highlights on MIT OCW, I expect to be finished by tomorrow and then decide if I'll do his book or Strang's. Self studying, by the way.

>>11323648
That list is an acient meme that pre dates Christ. Ignore it.

>>11325760
>Have you ever seen single linked lists linked backwards?
What the fuck is a linked list? Is it math or science?

>>11325783
>he hasn't read up on algorithms and data structures just to flex on cslets that struggle with the most basic of constructive proofs

>>11325783
>math or science?
it is both. It is computer science which is based on a great deal of math.

>>11323486
Any hints on how to solve this? I can't find a way to make both fractions equal.
[eqn]
\log_{1,25}0,64 = x \\
\frac{125}{100}^x = \frac{64}{100} \\
\frac{5^3}{10^2}^x = \left(\frac{8}{10}\right)^2
[/eqn]

How do they get from the second to the third line? I looked and they don't use the variable "a" anywhere else

How do you choose what upper division math classes you want to take? I'm in my 2nd year of a math degree and I'll start taking big boy classes next year. Besides the required 2 analysis and 1 geometry class, how do I decide what to take?

>>11325988
what are you trying to solve? you already have x...

>>11325988
if you really want to rigorously find x then just factorize each number into its prime factors. you will notice that you have to take the reciprocal of the left side and square it in order to get the right. hence x = -2.

>>11326131
However many dildos you can stick up your ass. That's how many classes you can add to your third year.

What's a good book on operational calculus? I've been bitten by operational autism and I need my fix

>>11325988
oh anon
if I were a lesser man I'd be furious with you
how lucky for us both that I am a god

>>11325988
Did you try SIMPLIFYING THE FUCKING FRACTIONS TO GET
[eqn] \frac{4}{3} ^x = \frac{16}{25}[/eqn]
YOU ABSOLUTE UNBELIEVABLE RETARD

>>11326199
5/4 on the left, actually.
Weird typo.

did the unabomber letter disencourage you? When a random schizo on 4chan says mathematicians are a couple decades away of being replaced by automation is one thing, but this guy actually knows what he's talking about ...

>>11326215
>ignores random schizos on 4chan
>listens to random schizos from prison
sending a couple mailbombs does not make you an authority on automated theorem provers

>>11326199
Actually I did, here is what happens:
[eqn]
\left(\frac{5}{4}\right)^x = \frac{16}{25} \\
\left(\frac{5}{4}\right)^x = \frac{4^2}{5^2} \\
\left(\frac{5}{4}\right)^x = \left(\frac{4}{5}\right)^2
[/eqn]
Unless it is allowed to do:
[eqn]
\left(\frac{5}{4}\right)^x = \left(\frac{4}{5}\right)^{-2}
[/eqn]
Then x = -2

>>11326252
I mean:
[eqn]
\left(\frac{5}{4}\right)^x = \left(\frac{5}{4}\right)^{-2}
[/eqn]

>>11326097
Wait I figured out what was done. The LHS of the third line is contrived in such a way as to get the geometric series

>>11323486
>Random variable
>Is a function
fucking hate nomenclature

>>11323486
btw here is the update. 25 dead by coronavirus. Is not there any cure.

why are e and pi what they are?

are these specific values artifacts of how our number system works? as in, the speed of light is constant, and the value it has is dependent on the units you're measuring it with.

pi is not so interesting because i can understand it in terms of a circle's circumference, like a constant needed to massage the equation properly.

i don't really understand e though. i understand how to derive it, (1+1/n)^n as n -> inf
but what's the point? what is significant about that, and the interrelation between that and the natural log? it seems sort of arbitrary.

>>11325321
Would let Ed raw me desu.
>>11326279
That's correct, [math]a[/math] is an integration constant.
>>11326186
You mean operator calculus? The first volume of Simon & Reed covers this quite well. Specifically they prove the existence of an algebra homomorphism [math]\phi_A: B(\mathbb{R})\rightarrow \mathcal{B})(\mathcal{H})[/math] for every bounded operator [math]A[/math] such that [math]\phi_A(f) = f(A)[/math].

>>11323401
I'll do it. I'll report back in a year or so's time. My guess is what's going to happen is that I contribute but he doesn't put me down as a coauthor because fuck me

spent a couple of hours the other night thinking about ways to most efficiently solve problems (specifically finding the "most efficient" (quickest) algorithm that maps one set of numbers, like the natural numbers, to another), then basically realized what it came down to was I was trying to prove P=!NP and realize it was an unsolved problem at its core and gave up. Anyone else know this feel?

>>11325760
>>11325783
>>11325802
>>11325854
>algorithms
>data structures
>computer science
>constructive proofs
Use >>>/g/.

>>11326230
You do know he's not a random schizo, right? You do know what got him into Harvard, right?

>>11326787
>he went to harvard so he's worth listening to, r-right?

>>11324904
In theory, if there is less than 17 clues then the solution is nonunique

>>11326787
Well, if the majority of harvard admits are any indication, some combination of nepotism, financial corruption, and varsity sports.

>>11323486
Young tableaux

It is well-known that any Boolean function, i.e. a function [math]\{0,1\}^n \to \{0,1\}[/math], can be constructed using any set of universal logic gates, e.g. AND and XOR.

What is the generalization of this idea to [math]\{0, 1, \ldots, k\}^n \to \{0, 1, \ldots, k\}[/math]? What is the simplest set of universal gates in such a case?

>>11326745
>gigachadgigabrain.webp
>why yes I use both /g/ and /sci/, as I have the capacity to both be pragmatic and idealistic, how could you tell?

Are there any other solutions to this differential equation or have I covered them all?

>>11327642
Actually I think I might need to include every periodic function scaled just like I did with sin and cos

>>11323486
I'm about to start learning calculus from this
>Calculus and Analytic Geometry : Thomas and Finney.
I need a linear algebra book to complement this.
>Redpill me.

>>11327663
Calculus holy trinity is Apostol, Slovak, or Courant never heard of your book before

>>11327668
The calculus book I'm using is essentially a starting point for me. Those books you've recommended start at a level that's way beyond my skill or knowledge at this point.

>>11325321
Astounding!

How do I geometrically express integration on the unit circle from 0 to PI/2
in terms of the area under the curve for [math]\int_{0}^{\pi/2}e^{ix}dx[/math] ? Should the yellow area be equal the sum of the blue and green? It is not.
Both integrals for sin and cos = 1, so the result is 1+i which has the magnitude of sqrt(2). But the area of 1/4 of the unit circle is PI/4. What gives?

>>11327902
Convert to polar ya dunce

post yfw IUT finally clicks

http://www.kurims.kyoto-u.ac.jp/~motizuki/news-english.html
>2020-01-24
>(Past and Current Research) Posted the second IUTeich animation
>"Computation of the log-volume of the q-pilot via the multiradial representation".
http://www.kurims.kyoto-u.ac.jp/~motizuki/2020-01%20Computation%20of%20q-pilot%20(animation).mp4

>>11327284
I believe this extension is still universal:

NOT x <=> (k - x - 1)
x OR y <=> max(x, y)
x AND y <=> min(x, y)
etc.

>>11326316
e has tons of equivalent definitions, the most important one is that the solution to y' = y with y(0) = 1 is y(t) = e^t.
no particular reason that it is the number it is, that's just the number that makes that work.
because of that it shows up in dozens and dozens of places.

>>11327688
No those books I mentioned are perfectly suitable for a fresh high school graduate heading to university and a great introduction into proof based math. As for good linear alg textbooks, two good options are Matrices and Linear Algebra by Schneider and Matrices and Linear Transformations by Cullen

>>11327656
That's what you've got, bucko! Fourier series.

>>11328749
What do you mean?

threadly reminder to not work with anyone. the only giant whose shoulders you should be standing on is you

I know most of y'all dont even study maths but this a remainder that a lot of REU applications close in three weeks, so remind your prof about your recommendation letter you faggots

>>11328804
based

What's the consensus on Real Analysis and Complex Analysis around here ?

>>11328842
complex > real of fucking course

Why does my sinc look so gay? This is continuous Fourier series of a square pulse, not FFT, just brute force integrating. What are these cusps? Why are they split in the middle so it looks like a giant pussy? They appear to be bending wrong way, lol. Both the cosines and the magnitudes look wrong.
(I only used desmos to visualize generated datapoints).

>>11328835
I've already accepted my own failure, and anyhow I'd have to go out of state for any

Am I a brainlet if I run any sequences I come across through OEIS?

OMG look at this, this is so beautiful, a perfect sinc. I fucked up, I used a simple mid-point rule, so I coded 1/3 simpson, and now it is perfect. So smooth, so beautiful, I want to touch and stroke every little curve of it. I wanna start from the side then keep going deeper and deeper and would finally slide under the central lobe. It is so symmetric so deep so sexy. Coding and tweaking is the only way to truly learn this stuff. Gotta feel it. Screw matlab. I know mathematicians don't waste their time coding shit so they use matlab for that. while code monkeys could code it but they don't care don't know anything about math. The two extremes. No middle ground. This is sad!

>>11328759
what you have written captures every differentiable periodic function

How do I trick myself into accepting the reality of [math]\mathbb{R}[/math]? I have the philosophical stance that is it not a legitimate object, but this has been hindering my opportunities in maths.

>>11323486

Literally studying pre algebra cause I didn't go to school as a kid, and my gf who is studying Aeronautical engineering is motivating and helping me study math so I can get a good job one day too.

I feel stupid

>>11328851
>>11328890
This bears no ontological relation to maths.

>>11323486
rna mods to make you immortal. got this.

>>11325617

Bump. Please help

>>11329665
[math] \mathbb{R}[/math] simply isn't real. Will you fight? Or will you perish like a dog?

If a number is not a divisors of 5040 I don't even believe in it's existence

>>11325617
>Just probability theory.
see >>11329751

>>11328842
Functional>Harmonic>Complex>>>>>Real>Numerical. It is the decrepit forerunner and nothing more. Run away from it like you would the cursed crypt of your ancestors

>>11329917
OK, but how do I convince the rest of the world of its unreality? It seems like infiltrating the body of mathematicians is the way to go here. But it's hard to do when you do not believe in [math]\mathbb{R}[/math] and have to constantly preface everything with "assuming it exists". It creates a lot of social tension and I do not want to be seen as another Wildberger-tier crank.

>>11329665
what exactly is your problem with it ?

>>11328661
i think he's becoming a schizo

>>11329665
stop reading autistic set theoretic bullshit
finish your first semester at uni and you'll be okay

>>11328661

just love the fact that this samurai speaks native english

>>11329665
You deluded foolhardy fool. You'll lose.

>>11323513
physicists are retarded, you only spam this shit because you are a physicist

I understand that, roughly, an operator on a bounded space has a countable spectrum.
How can this be made more precise? That is, under which general conditions are the eigenvalues of an operator either finite or countable?

>>11329665
Adopt a formalist stance, nothing is "real"

>>11330167
>an operator on a bounded space
You mean a bounded operator on a separable Hilbert Space?

>>11330138

Most math literate retards who work hard have undeniably helped ground mathematics in various forms of intuition (geometric, physical, computational, game theoretic...) and have furthered mathematics as a whole. Let's admit it, we have shitty ape brains, and the mathematicians who best go beyond these limits are autistic geniuses incapable of communicating the content of their mind with normal humans. Math literate retards help translate.

Physicist are gay though, especially when they think math is just some abstract nonsense tool for their bullshit. Yet you do get Feynman diagrams or such things from time to time.

I'll never solve the twin prime conjecture. I've been working on it since I was 17 and now I'm 32.

Presentations of non abelian groups. Although it won’t be in the final for sure

>>11330138
I'm not a physicist, I'm a shitposter.
I also don't spam it, the "Threadly reminder to work with physicists" poster is another person.

>>11329711
Don't give up anon, as long as you try your best to understand the material you will be fine. The first few math topics you will learn will be fairly straightforward, I would say that if you get a good background in topics such as inequalities, trigonometry and linear equations you will be able to tackle more complex mathematics.

>>11325763
I would unironically do spivak, his problems are really interested and he has a clear and concise way of explaining things. If you have trouble with the proof part there are resources online and books you can get that teach you some proof methods. But generally if you slowly work on the proofs in the first chapter you get the hang of it.

>>11330367
Well yes, that's a good framework to ask the question in, let's say.

>>11329751
What is this then? Fourier transforms is not math?

>>11330016
Probability theory is not math?

>>11330517
Only deep thinkers like >>11329665 understand what real math is. You are not supposed to do anything dangerously practical. You just need to stay philosophical.

>>11323561
why won't you do it tho? I'll pay you $10

>>11329665
Please reveal to us the concerns you have with any of the well-known constructions of the real numbers. We can hopefully remedy them.
It doesn't seem that you do have specific concerns, which makes me wonder whether you know how they are constructed?

I'm a math hobbyist. Been learning a lot of geometry recently, so I've been trying to learn a bit of physics even tho I don't know much about it.

I get the LHS of the EFE because it's all geometry, and I've found definitions which link it up with things I'm familiar with, which is mostly the geometric "coordinate free" approach using tensor fields, differential forms, etc.

Problem is I don't even know how to begin understanding the energy stress tensor outside of basic intuition from HS physics about momentum and stuff. And it's been basically impossible to find abstract information about it (like, does it have to meet certain axioms? is there a good coordinate-free description of it? is there a general definition for it on lorentzian manifolds of any dimension?)

any links appreciated

>>11330799
The EFEs are the strong-EL equations of the Einstein Hilbert action [math]\frac{1}{4g^2}\int_M d\operatorname{vol}_g R[/math] with [math]R[/math] the Ricci curvature.
>the energy stress tensor
Generally [math]T[/math] is defined to be the functional derivative [math]\frac{\delta S}{\delta g}[/math], or [math](d\otimes d^*)Z[/math] where [math]Z = Z[g][/math] is the partition function as a section of a [math]V[/math]-bundle on the moduli space.

>>11330875
>Ricci curvature
*Scalar curvature.

>all of these yous
>real questions: crickets
the absolute state of this "math" thread

>>11330167
If [math]A\in\mathcal{B}(\mathcal{H})[/math] is bounded and compact, we may apply the analytic Fredholm alternative on the resolvent map [math]R_A:D\rightarrow \mathcal{B}(\mathcal{H}),~ z\mapsto (A-z I)^{-1}[/math] to gain information on the spectrum [math]\sigma(A)[/math], where [math]D\subset \mathbb{C}[/math] is an open set. Specifically, the analytic Fredholm alternative states that, given a bounded holomorphic Banach algebra-valued function [math]f:D\rightarrow \mathcal{B}[/math], either [math](1-f(z))^{-1}[/math] does not exist for all [math]z\in D[/math] or there exists a [math]discrete[/math] set [math]S\subset D[/math] such that [math](1-f(z))^{-1}[/math] is analytic on [math]D\setminus S[/math] and meromorphic on [math]S[/math] with [math]\operatorname{dim}\operatorname{ker}(1-f(z))^{-1} <\infty[/math] for all [math]z\in S[/math].
By using [math]f(z) = \frac{1}{z}A[/math] and noting that [math]1-\frac{1}{z}A = \frac{1}{z}(z-A) = (zR_A(z))^{-1}[/math], if you can find an open set [math]D[/math] (not containing 0!) such that [math]R_A(z)[/math] is invertible at [math]any[/math] point [math]z\in D[/math] then you're guaranteed to have a discrete spectrum for [math]A[/math].

>>11331118
>[math]\operatorname{dim}\operatorname{ker}(1-f(z))^{-1}<\infty[/math]
Of course I meant [math]\operatorname{dim}\operatorname{ker}(1-f(z))<\infty[/math]

>>11330799
Look up classical field theory and in particular the covariant formulation of EM. The actual mathematical shit the tensor needs to obey is pretty weak. Adapt your question to something like mass density in classical gravitation, it has a pretty clear physical interpretation, but for the equations to make sense, the funciont needs to satisfy pretty weak hypothesis. I believe with these objects is were physics really starts to take a hold of the theory, as these objects make the equation into a consittuitve relation. What this means is that the stress energy tensor is data that one needs to get from observations or intuition based on the system you are studying. You can make arguments as to why certain SET are not physically plausible, but it's bad to make the theory too narrow.

i cant solve a single equation here
i should just kill myself right

>been working on paper for 1.5 years
>looked bad initially, then looked promising, now starts driving me mad
>could have published other stuff during that time, but cannot stop working on it
help

>>11331196
yeah.

>>11331041
You seem to be mistaken.
This is a thread for discussion of mathematics.
The thread for your questions is >>>/sci/sqt

Holy shit is maths physical. I had exhausted myself so badly I needed to binge like 5000-6000 kcal in two days to regain my ability to do anything.

Hello mathematical friends, I'm trying to solve linear equations in [0,1] and I can't seem to find any ressource on the matter.
I'm using the fact that if a row meets say its upper bound its positive coefficient are all 1s and negative are all 0s and made some significant progress, but Gauss-Jordan doesn't seem very efficient, see pic related. Any advice?

how to deal with lazy collaborators

>>11331308
don't assume they will start working by themselves, give em a hard kick in the arse, never collab with them again after your project is finished

>>11331259
I'm always fucking starving after a couple hours of focused research. I'm doubtful intense brain activity is actually burning significant calories, though. I know chess players consume ridiculous amounts of energy during tournaments but I think that has more to do with prolonged very high stress levels than thinking a lot.
I would buy that hard thinking drains your glucose levels or something like that, which would make you exhausted and craving food.

>>11331321
>>11331259
https://en.m.wikipedia.org/wiki/Ego_depletion leave it to psychologists to fuck up such a basic experimental set up.

>>11331321
>>11331407
For me it was probably due to exercising too much and not eating enough to compensate for that. But yeah, that was still an interesting article to read.

>>11330443
What have you tried?

I'm asked to show that the transformation [math]T(z)=e^{2\pi i\theta}z[/math] on the unit circle is ergodic if and only if [math]\theta[/math] is irracional. I'm a bit stuck with the return implication but what tried was to suppose I have a measurable function which are invariant unde [math]T[/math] start with an arbitrary [math]z\in S^1[/math] and take the set of [math]\{z, T(z), T^2(z),...\}[/math]. Because [math]\theta[/math] is irrational this set is infinite and because it is bounded we can take a subsequence which has a limit and I think it is clear this limit is not in this set. Now I take this limiting value and take the same ser as before but starting with this value and I add another countably infinite set of distinct values. What I think will happen if is I continue this process I will get all the elements of [math]S^1[/math], but I don't know transfinite induction or shit that may allow to inspect this more rigorously. Any ideas?

for the love of god somebody please tell me why I'm wrong.

>>11331918
>>>/sqt/

What does it mean to evaluate a polynomial in a matrix? [math] p(A) = B[/math]
If I know A and p, how do I calculate B?

>>11331918
factor the numerator?

>>11331938
Take [math] p(x)=x^2+2x+5 [/math]. You know what [math] A^2 [/math] and [math] 2A [/math] are, and 5 represents [math] 5I [/math]. Done

>>11331918
no gods or kings, only math

>>11331970
Thanks

>>11331885
I'm confused, doesn't this follow very simply by construction? theta = a/b -> T^b(z) = z, and a similar proof by contradiction to show no such b can exist for irrational theta?

>>11330168
>Adopt a formalist stance, nothing is "real"
But formalism has been BTFO and refuted countless times already.

>>11332155
brainlet response

>>11331885
Use Koopman's lemma. The map [math]T[/math] pulls back to a unitary [math]T^*\in \mathcal{U}(L^2(\mathbb{C},dz))[/math] such that [math](T^*f)(z) = f(Tz)[/math] such that it is ergodic iff 1 is a simple eigenvalue. It then suffices to examine the equation [math]T^*f(z) = f(z) = f(e^{i2\pi\theta}z)[/math] which implies [math]f\in L^2(\mathbb{C},dz)[/math] defines a branched cover of [math]\mathbb{C}[/math] with each branch being "twisted" by [math]\theta[/math]; more specifically, the preimage of [math]z=1[/math], say, under [math]f[/math] contains all points [math]e^{in\theta}[/math] for [math]n\in\mathbb{Z}[/math] labeling the branches, if you will. Since [math]\{e^{in\theta}\mid n\in\mathbb{Z}\}[/math] is dense in [math]S^1\subset\mathbb{C}[/math] for irrational [math]\theta[/math] you are done.
>>11332154
That's not a good idea; contradiction forces you to begin with the non-ergodicity of [math]T[/math] for [math]\theta\in\mathbb{Q}[/math] which is in general not really a tractable condition. Points [math]z[/math] returning infinitely many times under [math]T[/math] is [math]not[/math] equivalent to non-ergodicity.

>>11332157
but he is right. formalism was indeed refuted since before it even existed.

>>11331885
Assume [math] \theta[/math] is rational.
Then, for some [math]n[/math] we have [math]T^n=Id[/math], as you well know.
So for any set [math]U \subset S^1[/math] with [math]\frac{1}{n} > \mu (U) > 0[/math], we have that [math]E= \cup _{i=1} ^n T^i (U)[/math] satisfies [math]T(E) = E[/math] and [math]\mu (E) < 1[/math].
If [math]\theta [/math] is irrational, we consider some [math]U[/math] with [math]\mu (U) > 0[/math]. Then, unless I'm going clinically insane, [math]\overline{U}[/math], the closure of U, has nonempty interior, and [math]\mu (\overline{U} - U) = 0[/math].
Finally, [math]\cup _i T^i ( \overline{U} ) = S^1[/math] because it's dense, and thus [math]\mu ( \cup _i T^i ( \overline{U} ))= \mu (S^1)[/math], and since [math]\cup _i T^i ( \overline{U} ) = \cup _i T^i (U) \cup \cup _i T^i (\overline{U} - U)[/math], which gives [math] \mu (S^1) \leq \mu ( \cup _i T^i (U)) +\mu ( \cup _i T^i (\overline{U} - U) )= \mu (\cup T^i (U) [/math]

I'm sorry if there are any mistakes, it's two in the morning.

>>11331918
>Type your answer in factored form.

>>11323648
It's a meme list. Just read this instead https://web.evanchen.cc/napkin.html

I have a general question. I am currently teaching myself Linear Algebra and Analysis through Axler's and Pughs books respectively.
A major problem I am having is figuring out which problems to work out at the end. And how many to do. How do you math bros go about doing this? If I did every problem on Pughs book it would take me years -- time I don't have.

>>11332633
>Axler
cringe

>>11330461

Thanks Anon, I won't give up

>>11332436
Took me a moment to see the tricky part...
14

>>11332721
nvm it was even trickier than I thought. is it 7?

>>11332633
ebin

>>11328661
IUT's canned. this retard cant even be assed to explain his work properly

>>11323590
It's because of Communist Core if you're an American. Such a misunderstanding of how arithmetic works (pushed by Democrats) can only result in not learning anything. I happen to take a common core class called College Algebra, ask me anything.

>>11332633
Try to do as many problems as you can at the end of a section but you don't need to do all of them (like you said; and this would probably be a waste of time).

I have OCD and I tend to want to be a "completionist" and do every problem. You're better off trying the first 5 or so problems and really asking yourself if you understand the material. If you feel that you have at least a decent grasp on it (you could explain the basics of it to a 5 year old) then you're in the clear.

>>11332171
Hey Yukari poster, what is your background in math? Are you a PhD student or...?

>>11332899
>You're better off trying the first 5 or so problems and really asking yourself if you understand the material.
This is a horrendous idea. Most books I've ever read have their exercise sets roughly graded by difficulty. You're doing the warmup freebies and then telling yourself you understood everything.

>>11332984
He did mathematical physics for masters, and then maths for phd.

>>11333003
this
if the problems look easy, I just do the last 2-3 in the list, if I can do them then I ignore the remaining ones

>>11332723
try 10

>>11332723
try 11

>>11332154
Fucking moron. Why reply to a post about ergodicity when you don't even know what ergodicity is?

>>11333019
>He
I'm not a "he."

>>11333457
Nor are you mr. Chen.

>>11331885
Prove that (1/n)* sum from 0 to (n-1) of f o T^j converges in L^2 to the average of f (integrate, divide by 2pi) for f in L^2(S^1). i.e. that the time average of a function is the space average. Do this by converting to the fourier series for f and seeing it for complex exponentials. Remember parseval!
Now, depending on how you defined ergodicity you may need to find some characteristic functions to plug into this result.

>>11323486
Why there is not any ocw or ivy league topology video course online?

>>11325783
why are u in this board brainlet?

>>11332984
Close but not quite.

>normal high iq
>why yes i do understand the necessities of adapting one’s analytical and empirical toolkit to the dynamics of a technologically dependent society in order to further facilitate abstract conceptual understanding even in the face of the obvious pettiness and inferiority of the most common of these novel tools and can reserve disdain for such barbarity while utilizing the full power of these hideous implements because the ends do indeed justify the means, how could you tell?

>>11333630
Meant to quote >>11333019

>>11333532
Why would you need that when you can watch wildberger's series?

What am I reading

>>11333019
>He

Yo I need your help mathfags. So my statistics prof introduced to us factorial numbers for the first time, and I wrote a) in my notes.
So from it I deducted b), is it correct?
Just want to make sure since math isn't my thing at all.

>>11333784
looks fine

>>11333749
Yes. A gym going fat Chinese guy living in Canada.

>>11332984
https://www.perimeterinstitute.ca/people/Miroslav-Rapcak

Do you think Girard has read CTMU?
https://pdfs.semanticscholar.org/8548/a157279b27de84d1effd772b683c7b9d7701.pdf

Trigger warning: this is a homework question

I'm trying to parametrize the conic C:(XY+YZ+XZ=0) in the real projective plane by a change of coordinates which takes points from the real projective line (φ:P1(R)->C⊂P2(R)). I found projectivities for Y^2=XZ, and X^2+Y^2=Z^2, some of the other standard forms for nondegen conics, but I cant find a map for this one.

WELCOME
TO
THE MACHINE

>>11333742
Take your zoloft

>>11334081
It's from the transratiometer guy lmao

Any good boolean algebra books?

Given two finite groups [math]H, K[/math]. Are their semidirect products [math]H \rtimes_\varphi K[/math] and [math]H \rtimes_{\varphi^{-1}} K[/math] isomorphic?

>>11334441
>Given two finite groups H,K. Are their semidirect products H⋊φK and H⋊φ−1K isomorphic?
What have you tried?

>>11334441
[math]H\rtimes_\varphi K \cong K\rtimes_{\varphi^{-1}} H[/math]

>>11334446
Well, constructing isomorphism is obvious choice. [math]F: (h,k) \rightarrow (\varphi^{-1}_b(a), b)[/math] looked promising, but it isn't right.

>>11334213
wildberger

>>11334441
>open wikipedia
>[math]H \rtimes _{\phi} K[/math] is constructed with [math] \phi : H \rightarrow Aut(K)[/math]
Does [math]H \rtimes _{\phi ^{-1}} K[/math] even make sense?
How are you even defining this stuff?
Wasn't [math]\phi ^{\star}(x) = \phi (x)^{-1}[/math]an anti-automorphism?

>>11334485
It's wrong unless H=K. You are turning phi around.

>>11333951
kek is that actually him? LOL

>>11334511
Sorry, I wrote it like that because notation is easier. By [math]\varphi^{-1}_b(a)[/math] I meant [math](\varphi_b(a))^{-1}[/math]. It was too cumbersome to include it first, and second time I just forgot.

>>11334523
That's not a homomorphism, anon.
Remember [math]a^{-1}b^{-1}=(ba)} {-1}[/math]

>>11333951
https://www.youtube.com/watch?v=WsFlaUU-t1o

This is yukari?

>>11334531
Should've been [math](ab)^{-1} = b^{-1} a^{-1}[/math]

>>11333951
>resident PHD student
>checks out the other resident phd students

>>11334542
Why don't you ask him?
Just send a big fat email "Hey lad, do you post Yukari Yakumo from the Touhou franchise on an anonymous slovenian whale hunting forum?"

>>11334556
confirmed jacob barnett is yukari poster

>>11334531
Is it true at least for cyclic groups? I'm desperate

>>11334578
Read >>11334460 & >>11334513

>>11334578
>cyclic groups
We call the inversion map [math]I(x)=x^{-1}[/math]. For an abelian group [math]G[/math], [math]I(ab)=(ab)^{-1} = b^{-1} a^{-1} = I(b) I(a)=I(a) I(b)[/math] and thus [math]I \in Aut(G)[/math] , so at the absolute least, the definition makes sense.

>>11334556
why do literally all the white ones look like cock gobblers

>>11334616
neoteny induced by endocrine disruptors during development

>>11331857
Mostly sieve theory.

>>11334664
what is "sieve theory"

>>11334703
Various methods for approximating the size of sets of integers, usually using weighted functions and accounting for error terms. It gets monstrously difficult. One equation can have dozens of terms.

>>11327642
Where did you get this? Im actually interested in delay equations.

>>11334556
HOLY FUCKING SHITTTTT

>>11328872
Yes, and should be ashamed of yourself

where the fuck did "c" come from?

>>11334556

>>11333951
https://www.perimeterinstitute.ca/people/Sara-Bogojevic

my wife

>>11334515
This one is actually him. I've seen him a couple of times and we briefly discussed matters such as whom was our favorite 2hu, etc.
https://www.perimeterinstitute.ca/people/Jingxiang-Wu

>>11335491
c is the arbitrary x-value of point P. Did you even read what you posted?

>>11335514
the tangent can be any point on the curve? wtf?

>>11335506
>tfw no qt maths gf
>tfw the logician I went on a date with never messages me first

>>11335506
I wonder if her parents called her Amalia after Emmy Noether

>>11335491

>>11335509
Are you telling me yukari poster and jacob barnett work at the same institute?

>>11331294
Espèce de bouffon. Just one step: Row 1 <= Row 1 - Row 2

Look up Galois Field 2 (GF2) or equivalently Z/2Z and vector spaces over this field.
Look up "reduced row echelon form". Even Khan Academy did this shit

>>11335498
Hey hey people...

was he the greatest geometer of all time ?

>>11332398
Look up the fat canto set

Ive been working on long term unemployment

>>11323486
Just got my first paper accepted. reputable journal with only minor edits to formatting. very excited. current in 2nd year PhD

currently working on some perturbation theory techniques for a method of solving PDEs on compact rectangular subsets of R^n with a multilinear rank constraint.

Okay now WTF is a topos and why should I care?
Also none of that "it's a cartesian category which blablabla" or "it's a generalization of topological spaces" bullshit.

>>11331308
You have collobrative work in math courses?

>>11337458
the author of the post you replied to must be talking about research

i am not a math guy but working on linear algebra bullshit lately. planning on applying for patent for an implementation of my algorithm as well.

has /mg/ ever made any memes?

>>11332624
>Chen
Is this a 2hu meme?

Can anyone explain this concept to a brainlet, specifically why we can change f without changing the fourier coefficients?

>>11337810
The fourier coefficients of an integrable function are defined as [math]c_n(f)=\int_{-\pi}^{\pi}e^{-ixn}f(x)dx[/math]. You should know from calculus that the integral of two functions that are only different at a finite number of points is the same. Don't know what other concepts you are having trouble with. The general idea is that fourier series only approximates a function in an average sense.

>>11337854
Ah thank you, I misinterpreted as completely changing what f(x) is.

>>11337438
Topoi are a lot of different things, depending on what field you're coming from. What interest is it to you?

>>11336988
Cool! Good luck, hope it performs well

>>11336988
Congrats!! That's awesome!!

>>11337923
>What interest is it to you?
I'd like to understand it from the algebraic geometric viewpoint

>>11337438
>Also none of that "it's a cartesian category which blablabla" or "it's a generalization of topological spaces" bullshit.
so you don't want to actually understand what it is intuitively? fuck off to >>>/lit/ then.

>>11338645
Neither of those are intuitive retard, one is too abstract, the other too broad

>>11337438
wassamatta wit'chu dawg? chiquita'chu better bleev ah-muhnuh letchu tra'gain. I can 'ardly figrout what wud'ja's sayin' nigga. Tsbest'chu reread what I done writ ferya sluntbucket b'fo'ya reweave yo' query, and then lay down the rumpus mandinga naw whatchu wanna know?

>>11338668
>Neither of those are intuitive retard
>one is too abstract, the other too broad
Sounds like you're an intuitionlet with shit-tier intuitions. I suggest developing them first before jumping into AG.

>>11338517
The category of sheaves on a Grothendieck Site. In case you don't know what a Grothendieck site is, just think of a topological space.

I can intuit the truth of this by looking at it visually, but I'm unsure if this technically counts as a rigorous proof. In what sense are these kinds of visual "proofs" appreciated or taken seriously by mathematicians?

>>11338807
The diagram basically encodes the "formal" proof. Since everything is labelled and you can reason about the various angles it is pretty easy to see that the proof is valid and if necessary could be expanded (tediously) to a proof from geometric axioms.
The beauty of the diagram is that it conveys the key idea of the proof in a simple manner which would be hard to do with words alone. In essence it abstracts away the boring details. Mathematicians love stuff like this because it makes their work much easier and more fun. For example commutative diagrams are used everywhere.
The downside to proof by picture is that by abstracting details it becomes easier to hide/miss something and give a false proof. For this reason it is important to maintain a healthy scepticism and the ability to translate into symbolic maths if need be.

>>11323486
Brainlet here. Been trying to solve this all day >.<

>>11338869
Realistically, it should oscillate between 1 and 1.5. But 1.5. Also not math retard.

>>11338843
to be fair, comparing commutative diagrams to visual proofs such as >>11338807 is misleading

I'm trying to learn on my own and I'm currently banging my head on the wall reading through a college algebra book for the bare minimum shit I don't already know. Would jumping straight to a Calculus book be advisable after I'm done or should I go through a Pre-Calc book before jumping into calculus?

mathfags who didn't head into academia, what do you do and do you find it interesting?

>>11334556
>most of the girls are cute or somewhat attractive
>most of the guys look like mongoloids

huh

Are there any good videos/apps where I can practice and relearn basic elementary math?I've been a math brainlet my whole life and I want to make a change.

>>11339272
Khan Academy exists.

>>11336687
Sseth here

>>11334578
yes

>>11339351
And today, we're going to be talking about one of the most niche, most AUTISTIC generals to ever grace the 4chan board.

>>11339320
Thanks.

>>11339366
Do you LOVE dabbing on low iq gaijin.
Do you HATE rounding decimals.

>why yes, i'm the weak-* topology. how could you tell?

>huh? oh, you're talking.

Now if a bitch sucks yo' dick, for five dollars per square inch
and gets forty dollars, includin a five dollar tip
How big was the dick she just sucked? (Say what?)
Say how big was the dick she just sucked? (What?)......

If you remove every living animal out of the sea
then wouldn't the world's ocean water level decrease?
This means the planet wasn't three-quarters water (that was deep)
This means the planet wasn't three-quarters water (that shit was deep)
It's nigganometry.

>>11339839
>not even hausdorff
pig disgusting

Good afternoon.
I am the discrete topology.
There is none as strong as me.

Salutations friend. I am the trivial topology. How may I help you?

Is it just me or is his explanation hot garbage?

>>11340307
No one understands algebra, its just useful.

>>11340307
Where is this quoted from? I'm just triggered that Tao is memed so much.
The statement says "roughly speaking", so I'm not going to get into a debate about it. That cohomology measures "obstruction" is a general saying.

>>11323486
studying tropical geometry because the name sounded fun

>>11340355
this

>>11340360
Wikipedia.
>roughly speaking
Roughly speaking isn't an excuse for nonsense.

>>11340307
The explanation is correct.
>>11340368
What are you on about? Do you even know what de Rham cohomology is? By "fundamental theorem of calculus failing" he obviously means how the exact forms sit in the closed forms.

>>11340231
Dafuq is the trivial topology? Is it the indiscrete topology?

>>11340672
>By "fundamental theorem of calculus failing" he obviously means how the exact forms sit in the closed forms.
That's literal nonsense.
The fundamental theorem of calculus says that the integral along the line is equal to the difference between the antidifferentials at the edges.
It literally only makes sense when the antiderivative exists, which is exactly the issue that occurs in de Rham cohomology. The fundamental theorem doesn't fail, it literally just doesn't make sense, i.e. there is no antiderivative.
Besides, the fundamental theorem of calculus in higher dimensions is just Stokes, which always holds.

>>11340676
[math]\tau = \{ \emptyset, X\}[/math]

hbd mordell:)

>>11340714
What the fuck are you on about? That's not what he means, obviously.
"Fundamental theorem of calculus" is a heuristic statement which says "when you go around a loop, you accumulate 0." you'd have to be a complete idiot to take this seriously and act like it's some kind of rigorous statement. it's about your intuition for how original fundamental theorem, green's theorem, stokes theorem, divergence theorem, cauchy's theorem for holomorphic functions, etc. are related.
"it literally doesn't make sense." it only doesn't if you associate fundamental theorem with an antiderivative, which you obviously should not.

>>11341546
>it only doesn't make sense if you associate the fundamental theorem to what it actually says
>what Tao actually meant was this loop thing which he never fucking said