Cool @MeowMix

I just received my convocations for the written exams of X and ENS, the adrenaline suddenly went up

Ohhhkay (deep sigh:p), I finally truly get my mistake. I interpreted $e_1\mapsto e_3$ as we pick the first columns of the identity matrix and place it in the third row of the new matrix. But what it really meant was that the position of the first columns $e_1$ is replaced by $e_3$

Hm, permutation matrices are also orthogonal

which means their inverses are their transposes, right?

Correct, @ShaV. The $j$th column is $T(e_j)$.

@Ted Well, I haven't achieved anything yet :p but I just got stressed since it shows that the exams are really really soon

Yes, thank you:)

true, @Akiva

@Astyx: Fais de ton mieux.

Je vais essayer

Salut, @Sophie.

Is Sophie french ?

Hey @Arctic

hey

Hi @Sophie @Arctic

@TedShifrin I found some alternative representations to that weird limit $\displaystyle\sum_{h=1}^\infty \frac{(-1)^{h+1}}{hh!}=\int_{-1}^0\frac{e^x-1}xdx$

@AkivaWeinberger change of basis matrices between orthonormal basis are orthogonal

Why is this the same, @Sophie? Oh, you substitute $u=t\log x$? But, no, I don't see it.

Ugh exams @Astyx

Heya tern.

Competitive exams, even worse @Daminark

I prove that with generating functions

$\displaystyle\sum_{h=1}^\infty \frac{x^h}{hh!}=\int_0^x\frac{e^t-1}tdt$

Oh god

OK, I'll believe that, @Sophie. And this relates to the original how?

Is this like, entrance exams if I remember right?

@Astyx, Demonark will have sympathetic nightmares for you.

Kind of @Daminark

In the worst of scenarios I'll have another year to prepare them so it's not that big a deal :p

OK, that's something at least, but still, like I'm not too fond of exams just in the context of like, midterms and finals

I have the proof written down here somewhere. You can see it checks numerically

Because there's your level of expertise, and then there's that chance that you get flustered. Which is annoying since exams are like, worth the vast majority of the grade

So there's so much at stake

OK, @Sophie. Interesting.

Like yesterday when I looked through the test and saw that nothing felt too impenetrable, the worry disappeared and everything was fine, it was even fun. But if that doesn't happen, it starts to get to you more than it should

So I still don't know if that infinite series is something we should recognize?

But it's good that you're not fretting too much, anxiety is not helpful

I guess I was always a confident test-taker. I spent 40 years telling my students that getting all worried just makes things worse.

It's Ei(-1)+gamma according to mathematica

I think I should be more stressed

Or something like that

Ugh. Ei is some elliptic integral?

Exponential integral

Oh, the thing you wrote down?

So far this year, the test I was most productive in studying for was my worst one

No causation ofc, it just happened to be the case

Gamma the constant, I assume?

That's why I never study

Euler-Mascheroni, yes

Well, never studying is not the right answer, either.

(Fun fact, $\Gamma'(1)=-\gamma$, IIRC)

I know, I'm kidding, of course :P

I'll go now, good day/night to all of you

This midterm, I tried to study a bit, but there was that Klein bottle talk and I wasted so much time. It ended up being easy, and luckily the question on ODEs (the topic that just didn't click for me) was the one that involved integrating factors, which most of us didn't think of since they only came up briefly

Bonne nuit, @Astyx. A tout à l'heure :)

Good night

Last midterm, I got lucky and did a homework problem which ended up being one of the questions

The night before

But yeah anyway, the days of tests are temporarily behind me so I'll just leave that topic to rest

I used to get annoyed when I explicitly told my students that they should expect a certain kind of problem (typically one I showed in class and assigned homework on) ... and then numbers of them would do garbage.

That's related to a question I asked some time ago math.stackexchange.com/questions/2107666/…

@MeowMix may I suppose you finished the little integral gave you?

(the one by Ramanujan I mean)

Hi @ShaVuklia

Interesting, @Sophie.

If there is someone in chat I wanna greet then that's you! @ShaVuklia

I'll be back later.

Used to? So you got used to it after some time?

Aight, see you @Ted!

robjohn is not around

Old & good times are gone (of course, why old and gone again together? maybe to emphasize the fact itself)

Let me think what question to ask ...

(pretty undecided today)

Let me briefly build up an inequality with zeta values ...

@Don'tdisturb I was busy (and unmotivated), sorry

I did answer one of Balarka's questions, however

Prove that $$3\zeta(2)\zeta(5)+\frac{3}{4}\zeta(3)\zeta(4)-6 \zeta(7)>0$$

Develop a technique to build up a useful series that uses the left-hand side of the inequality and then prove it (inequality) holds

yeah, it looks like ill need to do infinite series

The left-hand side is about 0.0426983

@Don'tdisturb I'm so sorry, I actually left the chat, because I'm off to bed! Luckily Stack notifies me. I'm going to bed early, so I'll have a lot of energy for mathematics this weekend! I will see you around! Bye!:)

@ShaVuklia hehe, sure. I'll do the same soon. :-) Take care.

@Don'tdisturb are you an undergraduate?

or graduate?

That is an interesting question.

I initially wanted to do something like switch the two torii in the Heegaard decomposition but that requires $p = q$

Forget that. That's not degree -1

Ehhh, doesn't any orientable 3-manifold admit an orientation-reversing homeomorphism?

No

I can't seem to come up with one.

Did a @Ted just appear?

I don't think any do.

?

S^3 clearly admits an orientation-reversing diffeom. Am I misinterpreting what you mean?

sorry, internet's slow on this end