and you can convince yourself that the values where y>0 is -3<x<2 and x>2

that was just an example question i don;t have the exact equation but it wasn't factorized

@MATHASKER then factorize it

ya i guess i could have done the root theorem but i didn't have enough time

ight thanks for helping

then that's another problem (which I cannot solve)

you are welcome

@zhk welcome back

@zhk ?

how is g(-x) = conjugate of f(x)

@zhk we are just defining g that way

OK

then how is conjugate of f(-x) = g(x)?

got it

thx

@zhk substitute "x → -x" into "g(-x) = conjugate of f(x)"

the problem is the book say putting how the fuck I gonna know that it is a supposition

Anyways thx alot man

@zhk because of the word "putting"

I think this book is not for stupid people like me

stop saying that

ok

@Daminark you know where it's from?

Yeah, Perelman just sorta walked in and proved stuff

oh that one

Oh and side note: Euler characteristic is crazy

graph theory?

Apparently degrees of zeroes in vector fields add up to it, and some sense of integrating curvature gets that as well

The idea is that you define these funky things called CW complexes

And then you define Euler characteristic to be sums of alienating signs on dimensions of cells for a finite such complex

Damin: agreed, the Euler characteristic is the coolest shit

And then you can extend to topological spaces by defining these Betti numbers, which are the rank of the nth singular homology group, whatever that means

Yeah honestly in analysis I really haven't had moments of pure shock as I have in geometry/topology

This was a wonderful lecture series I watched as a first year grad student: thegreatcourses.com/courses/shape-of-nature.html

Euler characteristic was one of the lectures

OMG Devadoss

you're a fan?

such fan

haha, well he was great in that series

@ForeverMozart I didn't know you were a grad student

That's awesome!

yup, in general topology (never took a serious course in the algebraic stuff)

so I'm not interested in manifolds, for instance

well, I'm interested, but I don't work with them

sanity check: $\Bbb Z^\infty$ is countable, $\Bbb Z^\omega$ is not, right? (former can only have finitely many nonzero entries; no restriction on the latter)

yes

Usually the first one is denoted $\mathbb Z ^{<\omega}$

Oh huh, I haven't met anyone doing research in general topology, what kind of thing in particular do you do?

Also I've got a bad memory so sorry if you already mentioned this @EricS but what's your shtick?

grad student, second-year. Came to UMN because of the good combinatorics program, but at UMN, combinatorics = algebraic combinatorics. So, I've had to learn some algebra, turns out I like algebra.

no advisor yet but hopefully by the end of the summer after reading with the CommAlg prof.

Ah, nice

I work with connectedness properties, constructing examples, proving theorems

in the meantime I run a blog, which if you read for any length of time you'll discover that I am interested in pretty much any math I've ever seen, and I see a lot of it :P

(but Imma shut up a sec because FM's work is pretty great)

Oh wait @Forever you've told me this before, now I remember

But yeah that's pretty fantastic!

Here is a book (2007) with many of the big open problems that keep us up at night carma.newcastle.edu.au/jon/Preprints/Books/…

OK I just saw topological games and now I'm excited

I'm interested in several of the categories there

We did a bit in analysis and those are fun

Dimension theory, continuum theory, a little set theoretic

and I've solved 2 of the problems there ;)

Nice

wait, maybe only one

yeah just one, but I've got some nice results toward answering another

I mean that's still pretty dank

one that's not mentioned there is called the Toronto space problem en.wikipedia.org/wiki/Toronto_space

so simple yet we don't know the answer

Reals don't count because they have a copy of irrationals

Irrationals don't count cause they have a copy of the cantor set

etc

Cantor set also has a copy of the irrationals

Whenever you have those problems which are really easy to state and yet still open i confuses me

so that's an interesting duality

Wait really?

Oh hmm

usually I think there must be a counterexample in those cases, we just aren't clever enough to construct it yet

I would be shocked if there is some super deep proof

I think there's either an example, or it is undecidable

OK so I usually think of the Cantor set as $2^{\omega}$, and in that way I can sorta see it...?

well the irrationals are homeomorphic to $\omega^\omega$

(Also @EricS I can relate to that, everything I've thus seen aside from epsilonics excite me)

so you can see one way

now if you take the middle thirds cantor set

then the non-endpoints are homeomorphic to the irrationals

(so take the numbers in $2^\omega$ which are not eventually all $0$)

in other words^

Ah, that makes sense

actually, the Cantor set is equal to a copy of rationals plus a copy of irrationals

^ that fact has always fucked me up

yeah kind of wild

one way produces a nice connected space

the other way produces a zero-dimensional space

Lol maybe during the 4 weeks off in the summer I should read Kechris

just find some interesting research papers

lots of stuff in this field is accessible + interesting

Well, see I'm still a second year undergrad, I don't even know the very basics of topology.

Like, we did metric spaces in analysis and I've picked up a bit for use in difftop but that's it

oh, well that's a problem

Now in third quarter analysis we're doing non-metric topology stuff

Cylinder sets, Denjoy sets, etc

But only a little bit, next year is when I'll actually do a proper class (heh) in the subject

groans

What is it?

It was good! :P

right, of course :P

lol why do you have a picture of a sloth flying through space?

So we had a facebook group for admitted students at my school, and I was in an earlier round. I got a lot of people to pull a prank by changing our profile pictures to sloth photos and/or putting a lot on the page

It was huge, so I sorta kept that sloth persona

As a kind of meme

Oh wait I dropped details

This prank was on the people who were coming in March, at the normal time

H

?

Hey @Balarka!

heya

How's it going?

fine

i guess

Still working on geometry?

I spent the morning working on chemistry. Time to do math now, though, yeah

Also @EricS checked out your blog, a lot of things I'd probably need more background but I definitely see that you're interested in a variety of subjects

Nice @Balarka

>.–

As Balarka can confirm I make quite a lot of high quality puns

yeah you came in in the middle of a long-ass sequence that I haven't done a very good job of maintaining

we'll be back to the one-shot posts next week, at least for a while

I see

Hi

Hey @Astyx!

What's up ?

Not too much, how about you?

Same

Anything fun you're gonna do today?

Got to go to Poitiers and vote

Yay

You ?

Well, first I'm gonna go to sleep soon :P

Then today I'll probably try to get some work done

Oh yeah, not everyone is on the same time zone :p

For sure, it's 2:30 here

(Being partially nocturnal is very inconvenient. On 3 days of the week I have class at 10:30, the other 2 at 9:00, which isn't friendly to my sleep schedule)

I have to wake up at 6:30 for exams tomorrow

Ugh

I may just go to bed now because I'm not getting work done in this state of being :P

See you!

jeje arrighty

Bye, sleep well !

The topology of my dream are starting to get weird. For example, there's a penrose stair like topology last night

where a false awaking actually does not get you to dream layers closer to reality

(NB the fact I realise that is because I am awake now. But one can imagine if the number of false awaking goes to infinity, then I will be essentially trapped in my dreams and cannot be woken up again)

Anybody moderator here;; quick

Moderator anyone

quick please

there is a mod office room @satyatech

also you may ping Daniel Sir.

Is that about your trigonometry question ? @satyatech

@Astyx ya ,kcuf(jumbled) that textbook many wrong questions there

Anybody delete that question

Why is it urgent though ?

More negative votes may get piled on it

And I would lose my rep

That's not dramatic

@Secret That sounds so weird that I think I will have these dreams tonight myself.

@satyatech Rep is not important at all. It is not money and can't buy you bread or love.

Hello

Hello

how do you find the minimum or maximum of an expression containing two unknowns

unrelated to each other

@SBM You need to give an example question.

Hello @mats! How is progress on Riemann Hypothesis? =)

@JamesBond I am up against a brick wall for the moment.

@MatsGranvik I miss your old handsome picture. =)

I was waiting for Demailly to publish his 'Complex analytic and differential geometry' but it seems it will forever remain as a PDF.

@JamesBond Are you actually Jasper Loy?

I also want to take a look at Zheng's 'Complex differential geometry' but can't find a copy anywhere online.

@MatsGranvik Yes. Currently there is an account with that name on MSE, but that is not me.

ok

Also, it appears that the three volumes of Gunning's 'Introduction to holomorphic functions in several variables' is out of print.

It is very sad that good books often go out of print.

I think the first two volumes though are still sold in some places for hundreds of dollars each, which is absurd.

Good morning. I want to ask a simple question: how can I determine if a $2x2$ square matrix represents an hyperbolic plane?

Example: $\begin{pmatrix} 1 & -2 \\ -2 & -5 \end{pmatrix}$

This is a matrix of a scalar product on a certain basis. Let's call it ${v_1,v_2}$

It is said that $\text{Span}(v_1,v_2)$ is an hyperbolic plane. Why?

Hi chat

Hi @Alessandro

Hey all

Hi yall

Got a quick analysis question as to why $\widetilde{r}$ is chosen as $\min(r/2, 1/2M)$

It just seems a bit too much like magic how they pulled out such an $\widetilde{r}$

@blue Not off the top of my head but I can get pen and paper.

Hey @Balarka

It's been a while!

Hi @Kari. Yeah.

You been doing okay?

More or less, I guess.

hi @BalarkaSen

Getting enough sleep? :-b

h

sort of

@BalarkaSen I found those lectures in algebraic geometry youtube.com/…

seems nice

anyone know about network adjustment?

Hi, could someone solve a question about Taylor series for me, I've asked it four days ago and the only thing I got are some vague hints. The question is listed on my profile as my latest asked question, and I can provide a link if necessary.

@blue I think I have something. Note that $M$ and $N^2$ also commutes.

Then $(M - N^2)(M + N^2) = M^2 - N^4 = 0$

$MN = NM$, aka $NMN = N^2M$. But $NMN = (NM)N = (MN)N = MN^2$.

So $MN^2 = N^2M$.

So $\det(M - N^2) \cdot \det(M + N^2) = 0$. This does not mean $\det(M + N^2) = 0$ but it feels like it should hold.

Any ideas about my $\widetilde{r}$ question, @blue and @Balarka?

Once you understand $\det(M + N^2)$, you should be able to understand $\det(M^2 + MN^2) = \det(M) \det(M + N^2)$

I need help with the following question: math.stackexchange.com/questions/2262597/…

If you have time, have a look at it, please.

That's what I wrote, @blue.

That was a conclusion to this

@Kari I'm afraid I will have to look carefully to answer that question. Maybe someone else can help :)

@blue Er, can you? Can't you have nonzero matrices multiplying to the zero matrix?

Or am I just worrying too much.

Yeah, but so what? [1, 0; 0, 0]*[0, 0; 0, 1] = O

@blue would you be able to help me with my question. Not to pressure you or anything, it's just you seem active here. If you don't have time for it, that's fine.

@blue So I guess you have to show that M - N^2 is not only nonzero, but nonsingular also. I don't know how to do that off the top of my head.

@BalarkaSen It does, doesn't it?

$(M-N^2)(M+N^2) = 0$, so if $(M+N^2)$ has nonzero determinant, you could multiply both sides by its inverse to find $M - N^2 = 0$

Hai

ohi

Hei

Sup Amin

How would one determine the Taylor series of $f(x)=A/(x-B)^4$ at the point x=c, using the Geometric series?

How's it going?

network adjustment thats how ><

trying to figure that out wbu ?

@AdamWarlock what would you do if it was 1/(x-1) ^n

Gonna head over and get some breakfast soon, then do some mix of homework and a nerf war

@Kasmir

what is a nerf war?

Well, I'd say that I'd take the negative value of that and say that it is equal to the sum of $x^n$ @Kasmir Khaan

@AdamWarlock you can forget for the moment about the A because its a constant and the rest is just the formula for geometric series

I've also asked this one before on the forums, maybe you might be interested in that? What I got was the actual answer, but without any steps...

Nerf is a brand that makes toy guns and fake swords

Id assume they shown no steps because none are needed , only playing with constants and the fact that 1/ 1-x = x^n

@Daminark haha one would assume you are old for that but yeah :D

I'm not too old for anything :P

@KasmirKhaan the whole thing? I'm assuming I will have the Geometric Series, but multiplied by a factor $1/B^4$ And also, I kind of tend to get lost in too long arythmatic stuff so I kind of appreciate every in-between step haha

@Daminark just one advice , dont tell that fact on a first date :D let her find out when its the right time, (witch is never imo ) =p

Aight, I'll keep that in mind. My current girlfriend, insert math textbook here is not yet aware of this fact

@SteamyRoot Ah good idea.

Yah so there you go, @blue.

JEE problems are convoluted man

2hard4me

I ned halp with my Taylor series pls math.stackexchange.com/questions/2262597/…

it's still hard4me

@Balarka Do they actually have convolution? :P

imma get back to either do my stuff or melt more minds

@Daminark Man. You need help. Seriously.

Get a pun 101 class.

:|

That was good tho

('-')/

Hi @Ted.

Howdy @Balarka, demonical Demonark

Hey @Ted!

I'm literally at the point of crying over math lol. Why is proving stuff with the Geometric series so difficult?

@Adam: How did $x-c$ just appear out of nowhere?

@Ted What do you mean?

Ohh, I see, that's a typo. Sorry

You had $\dfrac1{(1-\frac xB)^4}$ and then all of a sudden $x-c$ appeared in the next part.

I am trying to find stuff by Robert Nye but failing

@TedShifrin Hi Ted , Do you by any chance know about Network Adjustment? =p

@Ted I think I forgot to mention that it had to be evaluated at the point $x=c$

You need to write $x-B = (x-c)-(B-C) = -(B-C)\big(1-\frac{x-c}{B-C}\big)$, and then you're set to go. @Adam

Never heard of it, @Kasmir.

@Balarka: I gave our $\Bbb RP^2\subset\Bbb RP^3$ to an old student/friend of mine who did his thesis in complex algebraic geometry. He's "thinking." :P

lol oops

It's a pretty interesting intuition, how the boundary of the triangles - instead of cancelling - sum up to a nontrivial element of $H_1$.

@TedShifrin hmm =p well what is the best way to minimize errors in a big collection of data? thats basiclly what I have to do , trying to help someone who works as engineer =p

Hi @Ted

I am glad I understood this point.

Well, they pretty much have to, @Balarka.

@Ted I actually did that on paper a while ago (Or something close to it), but I couldn't figure out how to get that in the form of what the answer's supposed to look like.

Hi @Alessandro :)

@Adam: I just showed you how :P

@Ted Yeah, but the rewriting part is what's bothering me :P

For the 4th power, it's probably better to differentiate the geometric series 3 times.

What do you mean? What's bothering you?

Ooh, so if you differentiate it four times, then terms like that 1+n and stuff will appear?

Three times, excuse me.

Well, I dunno. I haven't written it out. But notice that everything will be powers of $\dfrac{x-C}{B-C}$!!

(Which is good, because somewhere you need to be using the fact that $B\ne C$.)

Oh, if you want the coefficient of $x^n$ after differentiating three times, you have to start with $x^{n+3}$, and then you have a coefficient of $(n+3)(n+2)(n+1)$, yeah.

@TedShifrin Ted ! I have a very important question in geo that I know for a fact you are the only person I know who can help me with it :D or at least gives me a good hint =p

I am not the only person, @Kasmir. Your university is full of math people.

Hey @Eric!

@TedShifrin lets say that i locate couple of points in a region, then i got this machine that once i input those values ( coordinates of points in ) it can tell me with good accuracy the coordinates of any point i want near it , now If i want to move that machine a bit from its position , how can i determine the error the machine spits out ? =P

@Ted that makes a lot of sense, I think I'll be able to do a large part of the exercise by myself now. But would you like to submit a solution in which you write everything step-by-step, just for future reference? It would be very helpful for a beginning mathematician. And if you don't want to, that's fine, you've dropped some good hints.

hi chat

yo @Daminark

@Kasmir: What coordinate system is the machine using? Is it the same before and after?

Heya @Eric

@Adam, OK, I'll write down what I told you.

@Ted Thank you very much, I'll let you know if I've solved it.

when even

@TedShifrin the coordinates are unique, but the machine once moved , it does not work as good as first postion, first i have to input in it couple of points ( so it knows where it is ) then it can give me any point i need , but once i moved it , it wont give results with good accuracy because thats how it works =p

@TedShifrin the whole idea , is that its time consuming to do the first prosses each time i move it , so i want to know the error caused by that move

So the machine gives coordinates in the $xy$-coordinate system both times? You just don't know how much you've moved it (i.e., $\Delta x$, $\Delta y$)?