4:02 PM
what's the sum, @Chris'ssis?
I have a wonderful tool that give you out interesting regularized values sometimes.

@BalarkaSen it's about what I showed you yesterday. Mathematica compute it wrongly.

@BalarkaSen yeah.
@BalarkaSen Haha well that's just my "business picture".

@AlexanderGruber hmm. so what's with GL(4, 2) in the headline?

I don't really look very much like that in person. (I have a mohawk, for one thing.)

@AlexanderGruber Dr. Jekyll! Hide! I mean, Hyde!

4:05 PM
@BalarkaSen what do you mean?

yep.

@AlexanderGruber i always thought your ufl picture looked more "standard" than i might expect from you

@Chris'ssis Change the order of summation.

@BalarkaSen And then I'm done?
@BalarkaSen Too boring.

@MikeMiller yeah, my online presence is not very true to life.

4:09 PM
You do realize that I can't sacrifice a goat to statan, right? all i can do is to sprout somewhat like a thought off the top of head.

@BalarkaSen :D

what's your favorite proof of A8 \cong GL(4, 2), @alex?

@BalarkaSen there are a few other sequences that I put up there (or was going to and forgot about) that were in the same line... conjugacy sizes in GL(4,3) GL(4,4) etc

@AlexanderGruber ah.
most of them has exceptional isomorphism though, if you want to include a lot GL-type groups.
in fact, i wonder if all simple groups are of the type PSL(m, n)? surely i am mistaken?

@MikeMiller When I first got my UFL faculty website I had this as my faculty picture for a month before somebody made me change it.

4:12 PM
@AlexanderGruber lmao

@BalarkaSen um, yeah, there are many other simple groups

@AlexanderGruber kick out the sporadic and lie groups.
give me a counterexample.

@BalarkaSen well, you kicked out your PSLs too, then. :p

@AlexanderGruber what?
oh.
heck.

@BalarkaSen Imagine the whole thing on a big square (similar to the chess board ...) and then finish it without pen and paper.

4:16 PM
@alex here
this is a nice proof.
@Chris'ssis Imagine what?

@BalarkaSen the terms of the double series ...

@Chris'ssis oh that. no, i am not interested right now.
:16009253 nor do i.

maybe "suspect" would have been better than "expect"

ah, but they're both simple

4:18 PM
them fancy harvard types might wanna think about some diction classes

simplicity is a rather rare phenomenon

but it'd be foolish after looking at a bunch of psls with isomorphic groups.

@MikeMiller yeah there's only one or two exceptions of nonisomorphic simple groups of the same order

but i have no intention to go and solve it right now.

there is an MO question somewhere about that.

4:19 PM
i forgot for a second these were simple, and he was just saying "well, these groups both have order 201600, ergo they're obviously the same."

@MikeMiller I hate simplicity proofs.

to be honest i'm not a huge fan of the theory of simple groups in general

The geometric proofs of isomorphism of groups with GL-type gives more arithmetic informations than solid-core group theoretic proofs.

i don't hate it, but it's not my favorite part of finite group theory

the only part of finite group theory i ever really liked was the theorem that a finite cancellative semigroup is a group

4:21 PM
I will see if I can find a completely algebro-geometric proof of $A_8 \cong \text{GL}_4(\Bbb F_2)$
@MikeMiller haha
Ore's theorem.

it's such a fun argument

@BalarkaSen i'd prefer to see an entirely group theoretic one

the only ore's theorem i know is in graph theory

i.e. no rep theory

@AlexanderGruber you could write down an explicit isomorphism :)

4:22 PM
@MikeMiller no doubt. :p

there's your entirely group theoretic argument

@MikeMiller fair enough =P

character theory is cute too but it never really gripped me.

@MikeMiller Oystin Ore proved that result.
AFAIK.

so do most group theory students, @BalarkaSen

4:24 PM
character theory is one of those things that gives you a few really nice tools to use but isn't that interesting on its own (imo)

sure enough, i was referring to the history.
=P

that's a somewhat unpopular opinion among finite group theorists, too

@AlexanderGruber the easy consequences of schur orthogonality are what i like most.

@MikeMiller yeah, exactly

Wow. This is a really great questions. Feels elementary, really horrid to do elementary, yet one trick and it gets so much easier

4:24 PM
@AlexanderGruber that'd be a lot boring. so less informations on algebraic/geometric objects. bleh.
@Studentmath which question?

@G.T.R this is the question you might meet at an oral exam $$\sum_{n=1}^{\infty} \frac{1}{n^2} \left(1+\frac{1}{2^2}+\cdots+\frac{1}{n^2}\right)$$

need to decide what to do for the rest of my day.

@Alexander Fun!Fun!
Ah, now it worked.

@BalarkaSen the http:// fairy had mercy upon you

@AlexanderGruber haha.

4:31 PM
i need a haircut but the only places near me are bizarre and expensive korean salons.

I only want to remove some of my hair, @N3buchadnezzar

@Balarka You have 25 marbles, 15 red, 10 blue. They are placed randomally along a circle. Let X be the number of blue marbles with red marble on both sides along the circle, find E[X] and Var[X]

How picky

to justify "bizarre": one of these places advertises something called "orange hair" as one of their services. no further information or price. just "orange hair"

4:33 PM
@MikeMiller you could cut it yourself

Ask a girl to do it

i seem to have found a place on yelp that does haircuts for 8 bucks.

it's not actually too hard to do, i picked that up about a year ago and it's been working out great

that's in my price range.

@MikeMiller Interesting.

4:35 PM
@AlexanderGruber i graduate on saturday, being my own guinea pig will have to wait

what are you getting done?

i'm cutting some hair off.
i have too much of it.

fair enough.

@MikeMiller Don't cut your eyes out though

i'm approaching mullet territory, @AlexanderGruber, so you know how much danger there is in this

4:36 PM
@MikeMiller you're cutting hair and chatting the same time?

@MikeMiller better start drinkin 'shine.

@AlexanderGruber Whats the joke?

oh, but i can do that too.
i posted a comment on one question that i'd rather change into an answer, but the question isn't worth bumping, so i didn't know if a moderator could do stuff without bumping stuff.

4:40 PM
@N3buchadnezzar mullets are associated with people from mountain country, who also drink moonshine
@MikeMiller no, most everything we do bumps stuff too actually

@AlexanderGruber thank god not the monstrous moonshine.

@MikeMiller sure
@BalarkaSen i've drank moonshine while studying finite group theory before, does that count?

probably, hahaha

some people who drink moonshine are monstrous

4:43 PM
have you drank moonshine while studying modules, @alex?
it'd be close enough then.

@BalarkaSen nope.
@MikeMiller case in point.

I am taking a leave from my school tomorrow.
Need to digest sieves.

stay in school kids

Have you ever been in to that part of nt, @Mike? Sieves?

4:46 PM
ah, you're all algebraic. i forgot.

I know Erathosthenes Sieve, lol

i am not all algebraic

@JasperLoy It's the beginning of the theory.

i am just not into analytic number theory :)

You are bidirectional I remember @MikeMiller

4:47 PM
@MikeMiller yeah, you're differential to some extent.

that's
what?
i am going to go take a shower

The attracting part of sieves is that to learn them you need almost no background in advanced stuff in math at all.
Plus, they are applicable to a large variety of estimations. Universality of sieves is what makes analytic nt interesting.

I did not know that my disc drive does not work with DVD-RW, only DVD+RW.

@MikeMiller good luck

This is very strange. I thought both of them would work.

4:54 PM
This is what I hate about Ramanujan.

@BalarkaSen don't approve of synesthesia?

Oh no, he had a religion. That must make him a bad person / bad at mathematics.
What I hate about Ramanujan is Turberkolosis.

@AlexanderGruber what's that?

Is it real

@nablablah No it's imaginary.

4:57 PM
synesthesia is, basically, when one sense gets tangled with another sense
like if you can taste music or something

Seeing colors etc

a lot of people have it with numbers and colors

@AlexanderGruber I am not sure about that, but what I don't approve is too much religiousness.
That's why my classical hero is Erdos : There is no god, there is always a SF.

my first girlfriend associated two with yellow, three with orange, four with blue, five with orange again, six with green. that's all i remember.

Ramanujan also had too much turberkolosis in his life, he should have tried to cut down on that.

4:59 PM
And you don't have to believe in god, but you should believe in the book.

@BalarkaSen well, it doesn't seem to have affected his mathematics too much. ;)

@AlexanderGruber Fair enough.
I can't argue about algebraic number theorists' father's mathematics being affected by religion.

my officemate is a very devout Christian, one of the first math students I've met who is.

Is he good at math?

@nablablah yeah, he's very good at it.

5:00 PM
@AlexanderGruber huh?
utter stupidity.

@nablablah i think it helps him actually, he's got a lot of serenity. He comes in every day and teaches in the morning, studies the Bible during lunch, then does research till he goes home

OK, have to goes.
Going to digest sieve theory.

@BalarkaSen You should be more open minded >.<

if I had half the consistency he did i'd have published books by now

I know few Haredis who do the same, though they do get mocked by their own society for that, sadly

5:03 PM
@Studentmath what are Haredis?

@AlexanderGruber Hard to know how much of that is his persone, versus religion / growing up.

Oh look a hindu who is working hard, that must be because he is hindu.
Oh look at a guy with a metal t-shirt slacking of, that must be because of the music he listens too,

well, it's the way he acts that makes me think it has to do with his religion

@AlexanderGruber Is his name Zach?

5:05 PM
However most religions has some very good norms they tend to follow

@JasperLoy Nope, Chris.

@AlexanderGruber His sister frequents the chat then

@N3buchadnezzar Maybe they should be introduced.

I am very sad that I did not go to Cambridge for my undergrad. It is one of the biggest disappointments in my life.

@JasperLoy i know the feeling, i visited there once

5:08 PM
"Who is this?" It is your sister! "Hmmmmmmmmmmmmm"

woo
i hit 4k

@MikeMiller Time to retire and delete your account.

no thanks
what I really need is 10k

I am very sad. I wonder when I will recover from my OCD and live a normal life again.

Hi @JasperLoy

5:13 PM
@G.T.R Lol à ce qui paraît içi sur une classe de MP une de PC une de PSI seul 2 MP sont admissibles aux mines :C

@nablablah Hi Bart.

@G.T.R I prepare an even nicer question ... This one $$\sum_{n=1}^{\infty} (-1)^{(n+1)} \frac{1}{n^2} \left(1+\frac{1}{2^2}+\cdots+\frac{1}{n^2}\right)$$

@JasperLoy I am at a church now

@nablablah You should go only if you believe in God. Don't just listen to your mum.

@JasperLoy My mom subleased my room to someone and they moved in yesterday

5:15 PM
@nablablah As long as that helps to pay for bread.

@JasperLoy I feel guilty taking food from the kitchen without permission

@nablablah You should sleep under the new person's bed to creep them out

i think my answer here was about books at a higher level than the OP is looking at. oops

@AlexanderGruber However, there isn't really a place I want to go badly for grad school now.
I saw a few lhf today, but I don't feel like answering them.

5:30 PM
@AlexanderGruber All you need is 20 ;)

4020.
that's close to 420

@robjohn Mathematica fails again to compute an Euler sum, the one above (newly created).
@robjohn Mathematica says it's $\displaystyle \frac{\pi^4}{72}$, but no, it cannot be true since the partial sum is far away from that result.

@nablablah How do you type those eyes?

@Chris'ssis How did you give that series to Mma to get that result?
Sum[(-1)^(n + 1) HarmonicNumber[n, 2]/n^2, {n, 1, Infinity}] can't figure it out

@robjohn you need to wait for a while ... (this is what I used)

5:42 PM
@Chris'ssis I didn't stop, Mathematica did

@robjohn hmmm, interesting. Mathematica gave me that result.

@Chris'ssis what version?

@robjohn 8.0

@Chris'ssis so am I... and you used that same expression?

@robjohn Yes.

5:52 PM
I'll restart my Mathematica and try again
@Chris'ssis It still spits it back unevaluated

:16011386

@DanielFischer how do you say in German when someone is resilient and won't let go, but in a positive way

@Chris'ssis I am running 8.0.1.0

@N3buchadnezzar i been hoverin' around 20k for quite some time now ;)

@robjohn 8.0.0.0 It's better to give nothing than a wrong answer.

5:59 PM
@G.T.R "hartnäckig", but that can be both, positive and negative, and also neutral.

@JasperLoy go to somewhere in the South in the states.
@N3buchadnezzar this should be the icon for mod messages

@Chris'ssis that is true.

@AlexanderGruber Why is that so?

Back with some questions, would love to get some help: math.stackexchange.com/questions/829554/orthogonals-u

@Chris'ssis how long did you wait for the output to appear ?

6:02 PM
@JasperLoy weather's nice and girls are pretty.

@Chris'ssis returns the same as Robjohn on Mathematica 9.0

@G.T.R some minutes, maybe $5$.

i approve 100%

@AlexanderGruber Ah OK. I hope I find someone there and get married and live there happily ever after.

@JasperLoy Yeah man, go for it

6:05 PM
@Chris'ssis I will look again at this answer to see if I can get this sum

@Chris'ssis In the notation of that question, this sum is $A(2,2)$

@robjohn sure, that's true

6:22 PM
@MikeMiller Too Abstract! :O

Darn.

@Ilan taking a look, don't hold you breath
@Alexander Ultra-Orthodox

I can't get my galois theory right.

@Ilan Seems like you got a reply. That formula is standard, can be easily proven and I believe it is somewhere in the book, if not in the theorems than there is an exercise proving it
If you can't find it ask in the course's forums, they will direct you to the exercise.
You can quote exercises in the tests and works.

6:42 PM
How to load latex in the chat?

see "$\LaTeX$ in chat" on the starboard ---->

thought you might

@seaturtles Which one is your third account?

@seaturtles Oh, I had lost it :) thanks
Is there any way to visualize the multivariable functions chain rules?

6:46 PM
@DanielFischer Bonus points if $\int_0^\infty |f(t)| dt$ also converges

@robjohn I have amazing news ... What Mathemtica showed me is just a "truncated" answer. (I mean just a part of the real answer)

@G.T.R Then I don't know a better way than a sum of bump functions that become narrower.

$\frac {dy}{dt}=\frac{\partial f}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial f}{\partial y}\frac{\partial y}{\partial t}$, is there any way to visualize $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$ parts, what are the interpretations of them?
For instance, I can interpret $\frac{\partial y}{\partial t}$ as the velocity of y axis, but what about $\frac{\partial f}{\partial y}$ ?

@robjohn the way is already established, but I'll need time to put all on paper. I think there is work to do for some (many?) hours ... I also need to explain many things.

@MrWho Yep.
It's all in Piskunov.

6:57 PM
$\frac{1}{x \sin ^2(x)+1}$ @DanielFischer

@Chris'ssis For $A(2,2)$?

@robjohn Yes.

@G.T.R Alors ? :)

@Chris'ssis I am working on a series only method for $\displaystyle\sum_{n=1}^\infty\sum_{j=1}^\infty\sum_{k=1}^\infty\frac1{(j+n)^2}‌​\frac1{(k+n)^3}$

6:59 PM

@G.T.R Isn't integrable, it's $\geqslant \frac{1}{x+1}$. If you make it $\frac{1}{1+x^2\sin^2 x}$ it might work, but one would have to look to make sure.

@Nico combien en chimie ? :P

@BalarkaSen Hello, could you dig something?

@G.T.R 7...et toi ?

7:00 PM
@robjohn Ah, OK. You work on the series I previously posted. Did you see any way to get that elementarily?

5.25...

@BalarkaSen Sad, you have been so busy that you forgot what you promised me...

Combien en français @Nico

about Bachelor's degree at Mahan Mj's univ..

@Chris'ssis I'm working on it.

7:01 PM
@Swadhin Oh, right, right. I kinda had a look at it, but didn't find anything.

@robjohn OK. I'm glad you like it. A mathematician told me to publish it and give my name to it. :-)

@Nico alors les notes des mines ?

@G.T.R 14en français, 17 maths 1 et 15maths 2, physique 1 14, physique 2 15,5 voilà mes notes ^^

@BalarkaSen uh-hunh...then I might have to find a bachelor's degree from some place else...sad but reality! Anyways...I will live with it

@Swadhin You? Aren't you a high schooler?

7:03 PM
@BalarkaSen I am 14 now...

@Swadhin Yeah. So what's with the BSc at this age?

@BalarkaSen some future planning from some bright place...

17 en français, 12 maths 1 et 12.5maths 2, physique 1 12, physique 2 13,5 anglais 18. T'es trop fort @Nico :P

Oh. OK.

@Nico D'ailleurs t'es dans quelle prépa ?

7:05 PM
@seaturtles @seaturtles @seaturtles

@G.T.R L'anglais sorry, 13...vu ton niveau en anglais je n'avais aucun doute pour toi lol. Merci, mais t'es tout aussi bon je pense ;)
@Hippalectryon Faidherbe lille ,et vous ? @G.T.R

@Nico SMA Anthony

@Hippalectryon Connais pas, c'est cool ?^^

@Nico Le niveau des élèves est pas top top mais les profs sont très bons donc si on veux plus dur il suffit de demander :)

@Nico Paris dans le 5ème

7:09 PM
@BalarkaSen ?

@Hippalectryon C'est ce qui compte les profs, @G.T.R Paris 5ème ne me donne pas ta prépas..

@Nico Je lui ai demandé il m'as donné un hash SHA1 :c

@Hippalectryon Lol. Pq ? Ce n'est pas un secret si ? Je parie sur saint louis alors.

St louis ou H4
Un des deux

Une bonne prépa de toute façon :-p.

7:12 PM
Yep

@Hippalectryon t'en as oublié un mais bon

@G.T.R dans le 5e et dans les 5 meilleurs prépas de France ? (tu m'avais dit ça je crois)

@G.T.R Pq tu ne veux pas le dire ?

oui oui

7:13 PM
privacy concerns

@G.T.R T'es quand même pas à stan ??? :O

@G.T.R Bizarre mais pq pas..`

@Hippalectryon ah t'as pris le mauvais Louis en fait

@G.T.R Ah oui je voulais dire LLG pas StLouis
Lol

Louis le Grand ça rigole pas alors hahaha

7:42 PM

De produndis mathematicus ....

Hrm, is my combinatorical logic correct:

The total options of ordering 15 red marbles and 10 blue marbles along a circle is $\binom{25}{15,10}$; The total options of ordering 15 red marbles and 10 blue marbles so that a specific blue marble has red marble on each side of it is $\binom{15}{2}*\binom{10}{1}*\binom{22}{13,9}$?

@MikeMiller Which one?

The one you just commented "More general result" at.

7:51 PM
Ah, that.
I'd have voted to close as duplicate, but the answer was not upvoted. At the new one, there is now an incorrect answer, @Mike, adding a correct one wouldn't necessarily be bad.

I think it's right..

@Studentmath What?

@Studentmath I'm fairly sure the second line doesn't imply the third ($a_n = 1/\log n$ is probably a c/e)

@MikeMiller Make it $1/(\log n)^2$.

But then the third line is true, @DanielFischer
(because of the question in the OP!)

7:57 PM
When I have to show a distance defines a metric in $R^2$. Do I have to show that it's non-negative and non-zero, it's symmetric and something with the triangle inequality I believe. Is that correct?

@NikolajKyed Yup, I think that's it.