Since the ternary Goldbach is true by Helfgott: arxiv.org/abs/1312.7748. Then it immediately follows that every sufficiently large even integer is the sum of 4 primes. Is that correct? I ask here because it's kind of simplistic.

Where the primes are not necc. distinct.

Anybody familiar with autoregressive models and could help me find the expected value of one?

@RyanUnger Rourke-Sanderson

Thanks for any up votes :)

I don't see $\partial_3$ being defined anywhere in your question

@AlessandroCodenotti it's a chain map, standard notation

See: people.kth.se/~jakobj/doc/homology/homology.pdf

Simplicial homology chain maps all have the same formula, in this case I'm not working witho topological simplices but instead integer / prime sums

You definte it on a basic simplex, then extend it homomorphically (linearly)

It's pretty neat in general, but I'm not sure yet whether it will produce something worth while here. Perhaps I need to use coefficients in $\Bbb{Z}/(2)$ instead.

Is there a name for this shape?

@Ultradark yeah, it’s a stellated octahedron

@Semiclassical thanks

If you smoothed out the corners a bit could you do differential geometry and topology on this shape?

Couldn’t tell you. I stay away from nonconvex polyhedra

oh

@Ted Remember how a few years ago you gave an exercise asking to prove that a matrix satisfies its own characteristic polynomial? I learned a nice generalization today: let $p\in\Bbb C[x]$ and $a\in A$ where $A$ a is unital $\Bbb C$-algebra, such that the spectrum $\sigma(a)$ is nonempty. Then $\sigma(p(a))=p(\sigma(a))$.

(If $A$ is a Banach algebra then $\sigma(a)$ is nonempty for every $a\in A$)

Don't stop, thinkin about tomorrow, don't stop, livin todeeey! It'll be... better than before. Yester day's gone, yeeasterday's gone!

There is not a name for that shape, it has a symmetry group though that has a name :)

My mood is so good, to bad I know it will tank later and I'll start hating everybody

Hello

@Mr.President hello!

:D

:D

I need help about learning Mathematics...

What was your highest course in school?

I want to learn Calculus, following this book

I hate calculus, good luck!

Calculus Basic Concepts for High Schools : L. V. Tarasov

Learn the basics, then refer to a table of integrals, lol

:P

YOu are 10.5 K

very intelligent person, tell me if I should follow any other

My problem - I do not visualize limits

Remember that evertying in trig (all things you'll use in calc) is derivable easily from $e^{i\theta} = $ Euler's formula

Ok, thanks

Some things are hard to visualize, but google "limit of a function" for vis

You said you do not like calculus, do you like Probability(I do not understand tgis either)

googling "limit of a function" right now

I do like measure theory, I wanted to learn Probability but it's very difficult for me

Probablistic analysis is used in physics, number theory, everything

Yes, and I do want to learn probability, but it goes way above my head

measure-theoretic probability theory is one of those subjects I find myself wanting to learn about more recently

But that'd require me to learn measure theory first :P

Very interested in math, but Probability makes me feel an idiot

Measure theory basics are easy, but it gets detailed with convergence theorems

I recommend probability.net tutorials

They take you through the proofs with step by step exercises

There's actually a category-theoretic development of probability theory using sheaves and stuff

Should be downloadly (legally) free

suggest me something too, like probability.net( This is beyond my understanding)

@Mr.President yeah you'd need calc first

of course, all areas of mathematics are substitutes for doing number theory

You don't truely though, because the integrals are not Reimannian

in measure theory

They're Lebesgue integrals which are more general

for most practical purposes, measure theoretic probability is overkill

So any book for calculus that would clear the concepts( not looking for problem solving)...that you studied in school/college and liked a lot

e.g. if you want to compute the expected value of a Poisson random variable then measure theory isn't going to be terribly relevant

or the probability of a gaussian r.v. to be within certain limits, etc

Yes, the rules are similar, they're both linear operators on function spaces

(both types of integrals)

Will follow Tarasov, If I get bad grades I'll come and haunt this room

@Mr.President don't spend more than 20mins to an 1hr on one problem. If you get stuck, there is something easier that will help you solve that particular problem. Find what it is

*another problem

That's called an algorithm for studying

@ShineOnYouCrazyDiamond - Thanks a lot!! Also, I just downloaded a book from the starred message(your link, Proofs_from_the_book)...thank youuuuu, very nice book

Quick question, is $\Bbb{Z}^3 / M \approx \Bbb{Z}$ where $M \approx \Bbb{Z}^2$?

Do you have in mind $(a,b,c) \sim (a,b',c')$?

point being, it's not exactly obvious which Z^2 subgroup of Z^3 you have in mind. There's at least three.

I have a $0$'d out component I think, so should be easy in this case

@Semiclassical There's infinitely many. nZ x mZ x 0 is one such family.

The quotients are interestingly different from Z in those cases

@BalarkaSen ew

interesting

@Semiclassical oh $m=n = 1$ I believe for me

but ew

Free R-modules man, very different beasts than vector spaces in general.

Here's related: math.stackexchange.com/questions/3325488/…

looking at your question, I think it'd just be the isomorphism (a,b,c) -> b

Yeah, but you'd probably still have to solve the same system to find the kernel

actually, what I'm saying is a bit bad. What should say: the equivalence class containing (a,b,c) gets mapped to b.

It's part of an attempt proof at Goldbach's using Helfgott's result. But probably won't work. Worst case, it's a learning experience

it can be interesting to understand -why- a given method doesn't work, yeah

Perhaps I need coefficients in $\Bbb{Z}/(2)$ but that goes into group rings, which I'm studying at the moment

@Semiclassical any ideas on the question?

Feel free to post an answer

$A c = (x, 0, z)^t$: $3$ equations in $n$ unknowns, all done in $\Bbb{Z}$.

$A$ is allowed to be anything (primes or 0 as entries), and $n \geq 1$ can be chosen to also be anything.

open.spotify.com/playlist/…

xo

may i post an unanswered question here, or is that generally no considered kosher?

i don't really know what to make of the sequence presented therein

@Semiclassical solved it using Gauss-Jordan elination and reasoning about choice of coefficients.

see answer

I have a question about the Collatz Conjecture.

If a counterexample was found, does that mean that there must be infinite amount of counterexamples?

a priori it may be possible that a counter example gives a cyclic sequence, which does not imply that there are infinitely many counter examples

oh ok

Thank you @s.harp

@s.harp you're a student in Heidelberg right?

@ÍgjøgnumMeg yes, that is right

@s.harp do you live in a WG?

No I live in a little town next to heidelberg with my girlfriend

are you looking for a flat?

Oh fair

yeah :(

I gotta move in a little over a month and I haven't found a place yet lol

the usual websites like WG-gesucht etc are almost useless in my experience

Ah that's what I've been using

did you try the studentenwerk?

ie the student dormitories

Yeah I'm on a waiting list but I don't know when they will get back to me

and it's making me nervous hahaha

it might be worth giving them a call

they sent me an email a couple of days ago saying I was on the waiting list

ah

but idk if that means I'll definitely get smth before the 1st of October

Oh well! At least I got to pick my modules already

I'll be homeless if that's what it takes

lol

what are you taking?

errr

ANT 1, Modulformen, Höhere Analysis und ein Proseminar in der Topologie

you have to take höehre analysis?

I don't know if I have to, but I think I should

I already signed up for my talk in the seminar

a late one, so I can pretend I knew what was going on all along

are you doing master or bachelor?

Master

im pretty sure you cannot count proseminars in the master

you need to take the real seminars

Yeah probably not, but I don't have the background to take any of the proper seminars

so it's just for ergänzung

ok^

:)

I think there was going to be one on Quadratic forms and then it was cancelled or smth

a tip: this professors lectures are easy going, about interesting high level stuff and with a verbal examination at the end - mathi.uni-heidelberg.de/~freitag

looks like he isnt doing a lecture next semester

Ok, I have one more question: given f(x)= (7x/4)+(1/2)+((-1)^(x+1))((5x/4)+(1/2)) is there a way to write f(f(f(..n times..f(f(x)))) as f(n,x)?

but in the fututre probably

@s.harp oh nice, I'd like to do riemann surfaces

@QuoteDave its usually written $f^n(x)$ but be careful that you dont confuse it with $f^{(n)}(x)$ or $f(x)^n$.

Milne has notes on Modular Forms with emphasis on Riemann surfaces

Well I meant given n and x f(n,x) will be the same as f^n(x)

But without doing all that multiplying (is that's what it's called?)

prof freitag does lots of modular forms stuff

Hello, everyone. Looking for help, question, thanks