Mathematics - 2014-06-10 (page 3 of 4)

@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

Balarka Sen

@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?

Alexander Gruber

@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.

Mike Miller

4:12 PM

@AlexanderGruber lmao

Alexander Gruber

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

Balarka Sen

@AlexanderGruber kick out the sporadic and lie groups.

give me a counterexample.

Alexander Gruber

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

Balarka Sen

@AlexanderGruber what?

oh.

heck.

forget about it.

Chris's sis

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

Balarka Sen

4:16 PM

@alex here

this is a nice proof.

@Chris'ssis Imagine what?

Chris's sis

@BalarkaSen the terms of the double series ...

Balarka Sen

@Chris'ssis oh that. no, i am not interested right now.

:16009253 nor do i.

Alexander Gruber

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

Chris's sis

@BalarkaSen Then why do you ask me about series?

Mike Miller

ah, but they're both simple

Alexander Gruber

4:18 PM

them fancy harvard types might wanna think about some diction classes

Mike Miller

simplicity is a rather rare phenomenon

Balarka Sen

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

Alexander Gruber

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

Balarka Sen

@Chris'ssis i asked about the divergent series you were talking about.

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

Alexander Gruber

there is an MO question somewhere about that.

Mike Miller

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."

Balarka Sen

@MikeMiller I hate simplicity proofs.

Alexander Gruber

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

Balarka Sen

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

Alexander Gruber

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

Mike Miller

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

Balarka Sen

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.

Mike Miller

it's such a fun argument

Alexander Gruber

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

Mike Miller

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

Alexander Gruber

i.e. no rep theory

Mike Miller

@AlexanderGruber you could write down an explicit isomorphism :)

Alexander Gruber

4:22 PM

@MikeMiller no doubt. :p

Mike Miller

there's your entirely group theoretic argument

Balarka Sen

@MikeMiller fair enough =P

Mike Miller

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

Balarka Sen

@MikeMiller Oystin Ore proved that result.

AFAIK.

Mike Miller

so do most group theory students, @BalarkaSen

Alexander Gruber

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)

Balarka Sen

sure enough, i was referring to the history.

=P

Alexander Gruber

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

Mike Miller

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

Alexander Gruber

@MikeMiller yeah, exactly

Studentmath

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

Balarka Sen

4:24 PM

@AlexanderGruber that'd be a lot boring. so less informations on algebraic/geometric objects. bleh.

@Studentmath which question?

Chris's sis

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

Mike Miller

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

Balarka Sen

@Alexander Fun!Fun!

Ah, now it worked.

Alexander Gruber

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

Balarka Sen

@AlexanderGruber haha.

Mike Miller

4:31 PM

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

N3buchadnezzar

@MikeMiller What about rolling in radioactive waste?

Mike Miller

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

Studentmath

@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]

N3buchadnezzar

How picky

Mike Miller

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"

Alexander Gruber

4:33 PM

@MikeMiller you could cut it yourself

N3buchadnezzar

Ask a girl to do it

Mike Miller

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

Alexander Gruber

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

Mike Miller

that's in my price range.

Balarka Sen

@MikeMiller Interesting.

Mike Miller

4:35 PM

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

Alexander Gruber

what are you getting done?

Mike Miller

i'm cutting some hair off.

i have too much of it.

Alexander Gruber

fair enough.

Balarka Sen

@MikeMiller Don't cut your eyes out though

Or cut open your head.

Mike Miller

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

Balarka Sen

4:36 PM

@MikeMiller you're cutting hair and chatting the same time?

Alexander Gruber

@MikeMiller better start drinkin 'shine.

N3buchadnezzar

@AlexanderGruber Whats the joke?

Mike Miller

@AlexanderGruber can you convert comments to answers?

Alexander Gruber

@MikeMiller i can delete comments and post answers

Mike Miller

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.

Alexander Gruber

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

Mike Miller

darn

@AlexanderGruber should i just put this as an answer?

Balarka Sen

@AlexanderGruber thank god not the monstrous moonshine.

Alexander Gruber

@MikeMiller sure

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

Balarka Sen

probably, hahaha

Mike Miller

some people who drink moonshine are monstrous

Balarka Sen

4:43 PM

have you drank moonshine while studying modules, @alex?

it'd be close enough then.

Alexander Gruber

@BalarkaSen nope.

@MikeMiller case in point.

Balarka Sen

I am taking a leave from my school tomorrow.

Need to digest sieves.

Mike Miller

stay in school kids

Balarka Sen

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

Mike Miller

no

Balarka Sen

4:46 PM

ah, you're all algebraic. i forgot.

Jasper Loy

I know Erathosthenes Sieve, lol

Mike Miller

i am not all algebraic

Balarka Sen

@JasperLoy It's the beginning of the theory.

Mike Miller

i am just not into analytic number theory :)

Jasper Loy

You are bidirectional I remember @MikeMiller

Balarka Sen

4:47 PM

@MikeMiller yeah, you're differential to some extent.

Mike Miller

that's

what?

i am going to go take a shower

Balarka Sen

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.

Jasper Loy

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

Alexander Gruber

@MikeMiller good luck

Jasper Loy

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

Balarka Sen

4:54 PM

Ah, snap

This is what I hate about Ramanujan.

Alexander Gruber

@BalarkaSen don't approve of synesthesia?

N3buchadnezzar

Oh no, he had a religion. That must make him a bad person / bad at mathematics.

What I hate about Ramanujan is Turberkolosis.

Balarka Sen

@AlexanderGruber what's that?

nabla blah

Is it real

Balarka Sen

@nablablah No it's imaginary.

Alexander Gruber

4:57 PM

synesthesia is, basically, when one sense gets tangled with another sense

like if you can taste music or something

N3buchadnezzar

Seeing colors etc

Alexander Gruber

a lot of people have it with numbers and colors

Balarka Sen

@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.

Alexander Gruber

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.

N3buchadnezzar

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

Balarka Sen

4:59 PM

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

Alexander Gruber

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

Balarka Sen

@AlexanderGruber Fair enough.

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

Alexander Gruber

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

nabla blah

Is he good at math?

Alexander Gruber

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

Balarka Sen

5:00 PM

@AlexanderGruber huh?

utter stupidity.

Alexander Gruber

@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

Balarka Sen

OK, have to goes.

Going to digest sieve theory.

N3buchadnezzar

@BalarkaSen You should be more open minded >.<

Alexander Gruber

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

Studentmath

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

Alexander Gruber

5:03 PM

@Studentmath what are Haredis?

N3buchadnezzar

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

Alexander Gruber

@N3buchadnezzar yeah, that's true.

N3buchadnezzar

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,

Alexander Gruber

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

Jasper Loy

@AlexanderGruber Is his name Zach?

N3buchadnezzar

5:05 PM

However most religions has some very good norms they tend to follow

Alexander Gruber

@JasperLoy Nope, Chris.

N3buchadnezzar

@AlexanderGruber His sister frequents the chat then

Alexander Gruber

@N3buchadnezzar Maybe they should be introduced.

Jasper Loy

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

Alexander Gruber

@JasperLoy i know the feeling, i visited there once

N3buchadnezzar

5:08 PM

"Who is this?" It is your sister! "Hmmmmmmmmmmmmm"

Mike Miller

woo

i hit 4k

Jasper Loy

@MikeMiller Time to retire and delete your account.

Mike Miller

no thanks

what I really need is 10k

Jasper Loy

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

nabla blah

Hi @JasperLoy

Hippalectryon

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

Jasper Loy

@nablablah Hi Bart.

Chris's sis

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

nabla blah

@JasperLoy I am at a church now

Jasper Loy

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

nabla blah

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

Jasper Loy

5:15 PM

@nablablah As long as that helps to pay for bread.

nabla blah

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

Mike Miller

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

Alexander Gruber

@MikeMiller you're catchin' the addiction

Mike Miller

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

Jasper Loy

@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.

N3buchadnezzar

5:30 PM

@AlexanderGruber All you need is 20 ;)

Mike Miller

4020.

that's close to 420

Chris's sis

@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.

N3buchadnezzar

@nablablah How do you type those eyes?

robjohn

@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

Chris's sis

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

robjohn

5:42 PM

@Chris'ssis I didn't stop, Mathematica did

Chris's sis

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

robjohn

@Chris'ssis what version?

Chris's sis

@robjohn 8.0

robjohn

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

Chris's sis

@robjohn Yes.

robjohn

5:52 PM

I'll restart my Mathematica and try again

@Chris'ssis It still spits it back unevaluated

Chris's sis

:16011386

G.T.R

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

robjohn

@Chris'ssis I am running 8.0.1.0

Alexander Gruber

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

Chris's sis

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

Daniel Fischer

5:59 PM

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

Alexander Gruber

@JasperLoy go to somewhere in the South in the states.

@N3buchadnezzar this should be the icon for mod messages

robjohn

@Chris'ssis that is true.

Jasper Loy

@AlexanderGruber Why is that so?

Ilan Aizelman WS

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

G.T.R

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

Alexander Gruber

6:02 PM

@JasperLoy weather's nice and girls are pretty.

G.T.R

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

Chris's sis

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

Alexander Gruber

i approve 100%

Jasper Loy

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

Alexander Gruber

@JasperLoy Yeah man, go for it

robjohn

6:05 PM

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

Freddy

@IlanAizelmanWS i would like to help you, but i don't have any idea about your question :)

robjohn

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

Chris's sis

@robjohn sure, that's true

Mike Miller

what is this guy asking?

MrWho

6:22 PM

@MikeMiller Too Abstract! :O

Balarka Sen

Darn.

Studentmath

@Ilan taking a look, don't hold you breath

@Alexander Ultra-Orthodox

Balarka Sen

I can't get my galois theory right.

Studentmath

@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.

MrWho

6:42 PM

How to load latex in the chat?

sea turtles

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

Mike Miller

@seaturtles I appreciate your comments on that question

sea turtles

thought you might

Jasper Loy

@seaturtles Which one is your third account?

MrWho

@seaturtles Oh, I had lost it :) thanks

Is there any way to visualize the multivariable functions chain rules?

G.T.R

6:46 PM

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

Chris's sis

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

Daniel Fischer

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

MrWho

$\frac {dy}{dt}=\frac{\partial f}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial f}{\partial y}\frac{\partial y}{\partial t}$, 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 $\frac{\partial f}{\partial y}$ ?

Chris's sis

@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.

Balarka Sen

@MrWho Yep.

It's all in Piskunov.

G.T.R

6:57 PM

$\frac{1}{x \sin ^2(x)+1}$ @DanielFischer

robjohn

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

Chris's sis

@robjohn Yes.

Nico

@G.T.R Alors ? :)

G.T.R

@Nico admissible et toi ?

robjohn

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

Nico

6:59 PM

@G.T.R admissible. Félicitation

Daniel Fischer

@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.

G.T.R

@Nico combien en chimie ? :P

Swadhin

@BalarkaSen Hello, could you dig something?

Balarka Sen

@Swadhin Dig? What?

Nico

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

Chris's sis

7:00 PM

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

G.T.R

5.25...

Swadhin

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

G.T.R

Combien en français @Nico

Swadhin

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

robjohn

@Chris'ssis I'm working on it.

Balarka Sen

7:01 PM

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

Chris's sis

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

Hippalectryon

@Nico alors les notes des mines ?

Nico

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

Swadhin

@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

Balarka Sen

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

Swadhin

7:03 PM

@BalarkaSen I am 14 now...

Balarka Sen

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

Swadhin

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

G.T.R

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

Balarka Sen

Oh. OK.

Hippalectryon

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

Balarka Sen

7:05 PM

@seaturtles @seaturtles @seaturtles

Nico

@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

Hippalectryon

@Nico SMA Anthony

Nico

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

Hippalectryon

@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 :)

G.T.R

@Nico Paris dans le 5ème

sea turtles

7:09 PM

@BalarkaSen ?

Nico

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

Hippalectryon

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

Nico

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

Hippalectryon

St louis ou H4

Un des deux

Nico

Une bonne prépa de toute façon :-p.

Hippalectryon

7:12 PM

Yep

G.T.R

@Hippalectryon t'en as oublié un mais bon

Hippalectryon

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

Nico

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

G.T.R

oui oui

Hippalectryon

@G.T.R je me suis basé sur letudiant.fr/palmares/classement-prepa/maths-spe-mp.html

G.T.R

7:13 PM

privacy concerns

Hippalectryon

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

Nico

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

G.T.R

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

Hippalectryon

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

Lol

Nico

Louis le Grand ça rigole pas alors hahaha

Jasper Loy

7:42 PM

This chat is dead.

Hippalectryon

De produndis mathematicus ....

Studentmath

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 $\binom{15}{2}*\binom{10}{1}*\binom{22}{13,9}$?

Mike Miller

damnit @DanielFischer I was about to answer that

Daniel Fischer

@MikeMiller Which one?

Mike Miller

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

Daniel Fischer

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.

Studentmath

I think it's right..

Daniel Fischer

@Studentmath What?

Mike Miller

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

Daniel Fischer

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

Mike Miller

But then the third line is true, @DanielFischer

(because of the question in the OP!)

Nikolaj Kyed

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?

Mike Miller

@NikolajKyed Yup, I think that's it.

@DanielFischer Your connectedness comment should be an answer :P

Nikolaj Kyed

@MikeMiller Okay, I'm in the need of some homework help. If you're able to, could you take a look at my question and tell me what probability it is? math.stackexchange.com/questions/829680/…

Transcript for

$Mathematics$ Mathematics