@DanielFischer I don't know. There are several approaches in that thread. But that's not one of them. math.stackexchange.com/questions/805893/…

Well, maybe if I'm bored this evening, I'll take a look.

@G.T.R this game is completely insane ...

@chris'ssis

@Chris'ssis Every group of 3 elts is $\cong \Bbb Z_3$

@G.T.R hahaha

@chris'ssis damn

I'm glad to see they are doing these stuffs, @Chris'ssis. Heck our poor educational system in India.

Hey @Pranav

You are the Pranav in MHB, I suppose, @PranavArora?

Hi!

Yes, I am the same person

Hello professor @TedShifrin

@PranavArora Glad to have you here.

:)

Hi @Balarka. Salut @Gabriel

And hi @DanielF and @Chris'ssis

@TedShifrin hi

Hi @RandomVariable! :)

Did you look at this problem: math.stackexchange.com/questions/818494/… , looks very interesting to me.

@PranavArora Hello.

I tried it, but things got very messy and I gave up.

Its very difficult for me, I have tried a number of approaches but none seems to work. :(

So, what're you upto these days, @Pranav?

Me, meh, just trying to kill time, got nothing to do these days :P

=D

All exams got over recently, going to join a college in August :)

Good luck.

What kind of notation is this

M^n N^m

@nablablah Direct product of M n times and direct product of N m times.

No, dimension of manifold

@TedShifrin Huh?

hello @Ted

$M$ is an $n$-dimensional manifold

I am not familiar with that notation.

I helloed you above, @GTR

That's why I told you, @Balarka

OK. I wonder where seaturtles is. I need some help on galois theory.

Maybe he's changing identity again ?

Maybe. Why does he do that?

Dunno. To be truly anon, I suppose.

@TedShifrin I have been introduced to topological galois theory recently. The idea seems fun.

You mean covering spaces and fundamental groups?

@TedShifrin Yeah.

Hello professor @TedShifrin Your book about differential geometry is very beautiful and amazing for an undergraduate math student. I like your book very much.

A friend of mine is given the following exercise: Let $$f: \mathbb{R} \to \mathbb{R}, \; f(x) = \begin{cases} \lambda - 1 + x & x \leq 0\\ \frac{\sin(\lambda x)}{x} & x > 0 \end{cases}.$$ Find $\lambda \in \mathbb{R}$ such that $f$ is continuous in $x_0 = 0$. Now $f(0)$ by definition is $\lambda -1$ and $$\lim_{x \to 0} \frac{\sin(\lambda x)}{x} = \lambda,$$ which yields $\lambda - 1 = \lambda$ which has no solution. Did I make a mistake or is there a mistake in the exercise?

@Huy I agree with your conclusion

@MikeM You fancy a bit galois theory?

Nevermind, I think I got it.

Hello guys

hello nando

@Mike: it seems that after all there is a natural iso between $V^*\otimes W$ and $\text{Hom}(V,W)$

in the finite dimensional case

I wasn't sure if what I wrote is nonsense or not

but then I found the exact same thing as an exercise in some book

riemann surfaces are unique upto fundamental groups, right?

problem 1.49

i know, i am being extremely stupid.

@G.T.R Of course, I would have liked if Simona Halep won, but on the other hand, I don't like to be a winner by luck if you know what I mean. When you are the best, then no one can compare with you because you're simply godlike good. This is what I understand by being the best one. It wasn't the case for Simona today.

@BalarkaSen not even a little bit

there are uncountably many inequivalent complex structures on the torus

but even more basic than that, the riemann sphere and plane have the same fundamental group...

sigh. You're right.

so i was being stupid.

But. But but but.

How about compact riemann surfaces, @MikeM?

tori are compact

OK.

@MikeM what i want to prove is that if $Gal(L/\Bbb C(X)) \cong Gal(L'/\Bbb C(X))$ then $L \cong L'$. (not sure if it's even true though)

So I can freely jump from $\Bbb C(X)$ to $\Bbb CP^1$ and ask about coverings with isomorphic monodromy, can't I?

off the top of my head, i can;t find any counterexamples, but lots of examples sitting right before me.

even nontrivial ones.

I don't understand your notation but I also don't know much about that probably

@MikeMiller what notation?

what is $L$? what is $\mathbb C(X)$?

I'm leaving in like 5 minutes though anyway

$\Bbb C(X)$ is the field $\Bbb C$ adjoined with the transcendental $X$. $L$ and $L'$ are galois extensions of $\Bbb C(X)$

@N3buchadnezzar @G.T.R above you have a very nice integral I'm going to propose for a contest (don't use Maple, Mma) :-)

opens wolfram

@N3buchadnezzar :-)

i dont see it

@N3buchadnezzar $$\int \frac{1}{(e^x-1)(e^{x+y}-1)} \ dx$$

Limits?

@N3buchadnezzar It's indefinite ...

@Chris'ssis Is there a better method then partial fractions?

I think there is.

@Chris'ssis Let me do it.

I tried with some functional equations, but it gets complicated.

Partial fraction does the trick though.

No one voted for $\wp_\text{buckwheats}$

@BalarkaSen I found a nice integral as well

More of "hah that's clever" than a real challenge though=)

@N3buchadnezzar That's too hard for @Balarka ;)

@PedroTamaroff Should be $\sin \sin x$ and $\cos \cos x$. Does not make it any harder though

Ah you sillyman.

I am so silly

I'd love to get some help (linear algebra) math.stackexchange.com/questions/824173/linear-spaces-bases-r2

I misread.

OK.

Consider $f(x,y)=x-y$ and $f(x,y)=y-x$.

Well, that's $\to\Bbb R$.

Yup.

Can someone recommend a book about representation theory of associative algebras ?

@IlanAizelmanWS Is that good for you?

@PedroTamaroff Need $R^2$, isnt my example good enough?

@IlanAizelmanWS Your idea is fine, but what you wrote is wrong.

The kernel of $T(x,y)=(x,y)$ is $\{0\}$.

@PedroTamaroff Why?

@IlanAizelmanWS Tell me the definition of kernel.

Heya mr @Pedro and @Ilan !

vielen Dank @Deutschland :)

@RandomVariable: Did you see my PM at MHB? :)

@PranavArora No I didn't. Let me go check.

Ok, thanks! :D

mr @seaturtles!

@BalarkaSen no, e.g. $\Bbb C(\sqrt{X})$ and $\Bbb C(\sqrt{X+1})$ are both $C_2$ extensions of $\Bbb C(X)$

hello ted

Why aren't those isomorphic, @seaturtles?

oh, not covering the identity automorphism

they are isomorphic, but distinct

It seemed to me that @Balarka's question was iso ?

it's possible, but he said "unique extensions," and two extensions can be isomorphic but distinct

I'll think about nonisomorphic extensions

@TedShifrin Prof. Teeddddd! :) Oi!

heya @Ilan ...

@IlanAizelmanWS You should re-read your definition of kernel.

@PedroTamaroff Just got it sir.!

@PedroTamaroff For every V in KerT, T(v) = 0

@IlanAizelmanWS $\ker T=\{x\in V:Tx=0\}$

@PedroTamaroff Which means T(v) = T(v) = 0

@PedroTamaroff For every u in R^2 and v in R^2 T(u) = v, and S(u) = v. thus T(u) = S(u)

The kernel is the things that get mapped to zero.

@PedroTamaroff Did I get it right now? ;)

Heya, @Pedro. Good evening, @Ted. Hi @all the rest.

@IlanAizelmanWS No.

Good evening, @DanielF

@PedroTamaroff Now, if we pick$ x=y=1$, we get the $S(1,1) \ne T(1,1)$ because $(1,1) \ne (2,2)$

@PedroTamaroff I did for sure.

I just found a $579 bill on my credit card that doesn't belong there. I will be distracted for a while :P

@IlanAizelmanWS consider ker=0 to see the answer is "no."

o:

@PedroTamaroff Much too hard.

identity theft, sneaky family members? drama!

Wasn't me.

@BalarkaSen I integral, but then I can't.

It probably was @seaturtles with one of his many identities

@PedroTamaroff haha, that's math110-talk

@PranavArora I'd need more time to think about that one.

But is it a correct way to approach the problem?

I have never applied this kind of approach to any other problem so I am little doubtful about it

@BalarkaSen don't forget math110, and their annoying "How Prove 1+1=2"

@seaturtles isomorphic.

@BalarkaSen I've seen that used by other accounts a lot too. I don't know if I should suspect multiple accounts or some kind of ugly sociolect.

Math 110 is linear algebra at Berkeley :D

not a counterexample.

@seaturtles unique upto iso, i meant to say.

@DanielFischer I suspect multiple account.

What was he suspended for not so long ago?

@PranavArora With initial conditions, it seems OK.

@BalarkaSen do you want the putative isomorphism to preserve their internal copies of C(X)?