4:04 PM
HAI MAIK
@mike
Im watching pacificvrim

4:34 PM
@PedroTamaroff Silly movie.
@BalarkaSen Is your appointment over? When it is?

@Sawarnik Not just silly ... bogus with a capital B :P

I'm having a terrible time visualizing this problem. Can anybody offer any insight?
A national singing contest has five distinct entrants from each state. Use a generating function for modeling the number of ways to pick $20$ semifinalists if there are at most three people from each state.
I want to say that I need to solve $e_{1}+e_{2}+e_{3}+\cdots+e_{50}=20$ where $0\leq e_i\leq 3$, but then I feel like i'm not counting some of the contestants.
If I go with that, I'd have $(1+x+x^2+x^3)^{50}=20$
But the contestants are distinct, not the same.

1 hour later…
5:51 PM
Hullo.

@MattN. Hi! Hope you are doing well.

@JasperLoy Hi there. Well, not too bad I guess. Got a broken knee and sinusitis and hay fever but otherwise I'm good. What about you? Making any progress with that OCD?

@Sawarnik Yes, but I have another tomorrow.

@MattN. Hmm, trying to, trying to...

I don't know but on chat you seem pretty normal. Is it really that bad?

5:53 PM
The sum'll come out... tomorrow... betchcha bottom!

@MattN. Yes, I dare not say the number of years I have not worked.

Talk to you later, byes!

Why star all the nah's?

@JasperLoy Yes but was there really no way you could have? I notice with my knee that I don't do certain things that I could probably do.
@JasperLoy I have no idea.
"nah" is way after my (SE-)time.

@MattN. Maybe I could have, but I don't have the confidence. A few times I did try to find some work, but it got worse.

5:55 PM
@JasperLoy Maybe the wrong work?

Anyway, I hope to be well enough to start studying soon, I still hope to go to grad school.

But anyway, I'm not here to advise you. You'll know best.
Sure.

Well, there are people who are debilitated their whole lives from mental illness, so it's scary.

Yes.

Nash took twenty years to recover from his schizophrenia.
But at least he proved the Nash embedding theorem, I have proven nothing, lol.

5:57 PM
You still may : )

Yeah, maybe one of the millennium problems, haha.

You can either come up with the famous Loy conjecture or alternatively state and prove the Loy theorem.

Same for you, the N. conjecture or the N. theorem.

We'll see.
I'm actually aiming much lower.

Have you decided on your speciality topic?

5:59 PM
Just want to be a lecturer and have enough free time to work on stuff.
No, actually I find this decision impossible to make.

Yeah, everything seems so interesting.

Exactly.

Maybe choose what you are best at.

It'll be a more important topic once I decide on a PhD. For the MSc's I guess it's not really all that important.
I've been wondering though about how you can make the optimal choice for a PhD supervisor.

Yeah, in fact I never understood why they make people write theses for the BA and the MA.

6:02 PM
To learn how to write a thesis. Obviously : )
There's enough other stuff to learn during your PhD I suppose.

I think at the lower levels it is more important to take courses as there is so much to learn.

Also true.
This conversation is too serious.

Anyway, I had to write something for my BA, which I did.

Which subject?

I wrote something about Lebesgue integration in R^n.
It was an uncommon approach that in the end turns out to be equivalent to the usual one.

6:04 PM
Measure theory. Nice.
Caipiranha!
Do you drink?

Nope, only occasionally.
I don't smoke at all.

Me neither.
It makes no sense.
But drinking does: it's a kind of blissful state you reach.

How about drugs? I don't do drugs, lol.

I don't either. But if someone gave me a packet of amphetamines I'd take it!
For sure.

The panelty for drug trafficking here could be death.
@mike I did a google and am trying to figure out which image is yours, lol.
Hey @seaturtles, how is school?

6:14 PM
meh

Meh is one of your fave words.

hmm, the starboard is interesting this morning

Yes, but so far all wrong. I will write the correct version, remember to star it.
Nah.
Nobody is starring it, sad panda.

Starred.
Sorry, was afk. Had to get dinner going.
I feel like I'm turning into a cook.
Thinking about signing up for cooking classes.
Crickets.

HAI @MattN. @seaturtles

6:29 PM
Tumeni videos.

Tumeni. \loves

@PedroTamaroff HAI = Hello awesome internetters?
Hai = yes in Japanese.

Yes, this is dog.

Yo, dawg, wassup?
Ooooh, this makes me miss Trevor Phillips and the gang.
</3
GTA 5 was way too short.

Never played that one.
=D
I ended up in Vice City.

6:33 PM
Never played any of the other GTAs.

WAT.

True story.

@MattN. You should play Vice City.

I used to be a Nintendo person. More or less. And I don't think there are any GTAs on Nintendo devices.

@MattN. YAY. I have SNES.
Still working.
Have my Super Mario World.

6:35 PM
@PedroTamaroff And you should get GTA 5 and get to know Trevor Phillips. : D
@PedroTamaroff Poor me. I don't have mine anymore because it was lost when I moved once.
Nor do I have my 80ies Game Boy.

@MattN. hi there

Change of topic this is too sad.
@Complexanalysis Hello

what have you been upto ? @MattN.

trying to read some measure theory @MattN.

6:37 PM
Do you have a book or is it lecture notes?
@PedroTamaroff Actually, I think I'll rename my account to Trevor Phillips.

@MattN. wikipedia :P

The sound track is also wicked. Let me show you.
@Complexanalysis : )
@PedroTamaroff e.g. Me gusta : )

"The Black Angels".

Especially if you listen to it while you are speeding, running over motorbikes and being chased by police : D
@PedroTamaroff You know it?

@MattN. Nope. Just translatin'.

6:40 PM
The king and I.

@JasperLoy, I know how you feel.

@MattN. Prove $$\sum_{n,m= 1}^{\infty} x_{nm} =\sum_{n=1}^{\infty} \sum_{m=1}^{\infty} x_{nm} =\sum_{m=1}^{\infty} \sum_{n=1}^{\infty} x_{nm}$$ for $x_{\alpha} \ge 0$ .

@PedroTamaroff or this.
@Complexanalysis Gimme a minute need to get mathjax up and running.

@Complexanalysis Do you need help with that?

@PedroTamaroff Sure :-)

6:45 PM
@Complexanalysis Sure you need help?
So, the important thing to observe is we want to work with $\sup$s.

@PedroTamaroff Sure sure :D

@PedroTamaroff lets go !

So, we can prove that $$\sum_{i\geqslant 1} \sum_{j\geqslant 1}x_{ij}=\sum_{i,j\geqslant 1}x_{ij}$$
And the other part follows by symmetry.
Agreed?

W00t. I did it. Now for the sums.

6:48 PM
?

Oh, Pedro is at it. Okay : )
I'll bbl.

@MattN. Sorry, did you want to do it?

No, too drunk. Just want to sit and drink more.
bbl

@Complexanalysis
OK.
So, note that $$S=\sum_{i,j\geqslant 1}x_{ij}=\sup \left\{\sum_{(i,j)\in F}x_{ij}:F\subseteq \Bbb N^2\text{ finite }\right\}$$

@PedroTamaroff We might be able to prove the first equality , but how

6:53 PM
In a similar fashion, $$b_j=\sum_{i\geqslant 1}x_{ij}=\sup\left\{\sum_{i\in F_j}x_{ij}:F_j\subseteq \Bbb N\text{ finite }\right\}$$

@PedroTamaroff How can you say that there is $S$ such that the first equality holds ? Putting it other way , you are telling me that $\sum_{i,j} x_{ij}$ is defined as the $\sup$ over the finite indexing set .

@Complexanalysis Aha.
That's how one defines that sum.

@PedroTamaroff What do you mean by Aha ? just to get your expression right :-)

That's what I'm saying.
Or you can prove it equals that.
Whenever $x_{ij}\geqslant 0$.
@Complexanalysis Aha = Nod.
So, by the above, note that for each $j$; $$\sum_{j\geqslant 1}x_{ij}\leqslant \sum_{i,j\geqslant 1}x_{ij}$$
So, $$\sum_{i\geqslant 1} \sum_{j\geqslant 1}x_{ij}\leqslant \sum_{i,j\geqslant 1}x_{ij}$$

@PedroTamaroff Okay , i think i can prove that breaking it into two cases , ie when the sum is divergent and when the sum is convergent and arguing that there exists $(N,M) \ge (n,m) \in \mathbb N \times \mathbb N $$\ for every \epsilon > 0 6:58 PM @Complexanalysis So, what you should aim to show is that for each \varepsilon >0; you can make$$\sum_{i\geqslant 1} \sum_{j\geqslant 1}x_{ij}\geqslant \sum_{i,j\geqslant 1}x_{ij}-\varepsilon$$ya @PedroTamaroff @Sawarnik There? how do you define \sum_{j \ge 1} x_{ij}? Okay ok , i got it . @PedroTamaroff just got confused with the notations . @Complexanalysis Good. Sorry, I was diverted a second. @Complexanalysis Maybe you can read this and ask me? Heya 7:09 PM Hullo @PedroTamaroff ya i got it , next step i want to know is when can i extend this theorem for a sequence even with the negative terms ? @N3buchadnezzar Have you learned PNT? @Complexanalysis No, you can't. Negative stuff fucks things up. But, you can do it when the sum converges absolutely. Tonelli's theorem. @PedroTamaroff if the sum converges absolutely then the Tonelli theorem holds again. @Complexanalysis Yiss. Do you know a little measure theory? 7:17 PM @PedroTamaroff Yiss Preciousess. @PedroTamaroff nothing apart from some definition . I like it though . It's a really nice subject. @BalarkaSen Prime number theorem yeah? And you still haven't linked me to that Katsumura paper... I haven't studied it much, just a tiny bit. 7:18 PM @PedroTamaroff Do you know it well ? We have been using two weeks now learning the basics to understand the proof @PedroTamaroff How much have you learnt ? @N3buchadnezzar Are you gonna go Selberg? Or the other way, i.e., no \zeta zero on 1-line? @Complexanalysis Well, a decent amount from one viewpoint. I read Shilov's book "Integral, Measure and Derivative." @BalarkaSen Both 7:20 PM Cool and good. @BalarkaSen Here you go. @PedroTamaroff Not seeing vids from ytubes. @PedroTamaroff How is the book ? they can make you EVIL!! @BalarkaSen 'i have read the outline of both proofs they seem still somewhat heavy 7:21 PM @N3buchadnezzar Yeah, those heavy guns. But I like the 1-line proof very much. You should first go through Merten's theorem. Here we go. @Complexanalysis It's pretty nice. @BalarkaSen You do realize it was all just a joke, right? What book, @N3bu? @PedroTamaroff I realized alright, but a bit later. =P As you might have guessed. apostol 7:23 PM @N3buchadnezzar Nice one. What have you covered up until now? up to 11 skipping quadratic residues and that I don't have a copy myself (not now, at any rate) and I never read Apostol throughly (my ideal is I&K) so I don't know what 11 has on it. @N3buchadnezzar OMG, don't do that! You'll need characters and what-nots In L-theory @PedroTamaroff I am trying to go through Terry tao's book . lecture notes to be precise @Complexanalysis Don't know that one. @Complexanalysis In Measure theory? I don't know of one. 7:26 PM They say Folland is a good book. I started reading it. @Pedro Recommend a book in alg topo. I figured I don't like the diff geo POV Ok . @PedroTamaroff @BalarkaSen Hatcher is "The Book"; apparently. @PedroTamaroff Okay, so I need a bit Homo and Cohomo from D&F, right? @PedroTamaroff ya , Hatcher is supposed to be the main book . 7:28 PM But you cannot expect to read that one if you don't know topology. I guess. @PedroTamaroff I am learning the basics. But I don't believe that much DGPOV is really nessesary for alg topo, is it? @BalarkaSen What the hell is DGPOV. Differential Geometric Point Of View You need to know topology. I know, but do you need differential geometry to approach topology thoroughly? You know, people say one can attack it through algebra. Just like the way we approach NT from PT, you know. 7:32 PM I don't think so. But you can read Spivak's Calculus on Manifolds for a first start on Diff. Geo. Spivak got a Calc, that I knew, but Calc on Mani? I didn't know that. Yes. But wouldn't it be a lot off-the-tangent for me to dive on Diff. Geo.? @PedroTamaroff Do you know what is the problem with the jordan measure which makes us to go for lesbegue measure ? I mean, I like NT. Especially ANT and TNT. 7:35 PM @Complexanalysis It isn't a measure to start with. =D IIRC it is not countably additive. @BalarkaSen Oh it it just all of us has already had number theory @PedroTamaroff What is IIRC ? We have learned a bunch about L functions and Dirichlet Characters @N3buchadnezzar That's fine then. What have you learned on field theory? I have taken an introductory course in Algebra but alas do not remember much from it 7:37 PM Field theory is important in learning L-automorphs. @BalarkaSen I just think you need to learn a few more basics things before launching up. Had anything on algebraic geometry? @PedroTamaroff Ineqs perhaps, but that's just if I ever learn topology. I really hate inequalities. Even diophantine approximation of TNT because of that. Heh taking complx analysis and topology along with ant CA is good. And important. Alas I think I will never grasp topology. @BalarkaSen WAT. 7:41 PM @BalarkaSen ãƒ½à¼¼àºˆÙ„Íœàºˆà¼½ï¾‰ Are you not HAUSDORFF enough? ãƒ½à¼¼àºˆÙ„Íœàºˆà¼½ï¾‰ @Pedro Someone told me that there are number theoretic approaches on learning topology. Do you think it's true? @BalarkaSen No. @PedroTamaroff Odd. A topologist (professional, yes) himself said so. @PedroTamaroff WYSIWIS @BalarkaSen Well, you asked for my opinion. Just pick a topology book and read it. And if you don't understand it read it again. =) One in a million opinion =) Dang my internet connection. @PedroTamaroff He says perspective matters. I wonder what that means ... 7:45 PM @BalarkaSen You should read my professors notes, they are very elementary @BalarkaSen I wonder too. @N3buchadnezzar nah @PedroTamaroff His name is Mahan Mitra, you can google him on the internet. I don't understand any of his works however. what does even opinions mean? 7:48 PM I just wonder why \text{PSL}(2, \Bbb{C}) pops out everywhere. Anyone good with gradients? In physics, there are several kinds of dipole: *An electric dipole is a separation of positive and negative charges. The simplest example of this is a pair of electric charges of equal magnitude but opposite sign, separated by some (usually small) distance. A permanent electric dipole is called an electret. *A magnetic dipole is a closed circulation of electric current. A simple example of this is a single loop of wire with some constant current through it. *A current dipole is a current from a sink of current to a source of current within a (usually conducting) medium. Current dipoles a... How did they get the field? So, I am trying to find an involution in {\rm SL}(2,5). @PedroTamaroff what is involution ? @Complexanalysis An element for which x^2=1. It is sometimes confused for an idempotent, which is an element for which x^2=x. =) @PedroTamaroff A\in F^{n \times n} such that A^2=I ? 8:01 PM No. Matrices in \Bbb Z_5^2 with A^2=1 and \det A=1. =D In general {\rm SL}(n,k) is the group of n\times n matrices over the field with k elts with determinant 1. Yup . Hello everybody @Complexanalysis So$$\begin{pmatrix}-1&0\\0&-1\end{pmatrix}$$does the job. Is Mike in? I have to prove this involution is unique. @Mike just entered. 8:04 PM I should say @Mike, I suppose. ãƒ½à¼¼àºˆÙ„Íœàºˆà¼½ï¾‰ @Pedro Unique up to what? looking for a, b , c, d such that ad-bc =1 ? @Complexanalysis And four more equations, over \Bbb Z_5. @Mike Unique. Just that. @Complexanalysis Not such a hard find. Looking to make ad-bc = 1 is a bit easier then looking for ways to reduce global warming. 8:06 PM Well that ain't true. @Mike, Sorry I'm probably out of context here. @Mike ORLY. There is probably a context where making the det 1 is difficult. Well then Rotman is pulling me legs. @Pedro what does ORLY mean? 8:07 PM @Pedro How did you define involuntion? @Mike x^2=1, x\neq 1, I guess. Ah, okay. I didn't see the second part earlier. :D @Mike, what's your grad school news? nada @Mike, here's the difference in a nutshell between a career in the corporate world and a career in academia. In academic life, the main determinant of your future is how well you do. In corporate life, the main determinant is how well the company does. If a mathematician is working in industry, then if the company is doomed, the job is doomed even if the mathematician is a Fields medallist. If the mathematician is working in academia, then even if the dept. is not highly ranked the mathematician will do well if good results are forthcoming. Perhaps the above is trite and banal, but to me it's a crucial distinction. 8:21 PM @Mike So yeah, the system is easy to solve. Hello How to I convert a plane in Cartesian coordinates (z=k) into spherical coordinates? (p=?) @Mike I think I got it. @PedroTamaroff what did you get ? @Complexanalysis I have to show that the quarternions are iso to the 2-Sylows of {\rm SL}(2,5). @PedroTamaroff the order of SL(2,5) is ? half of GL(2,5) ? 8:36 PM @Complexanalysis No, a fourth. Because 5-1=4. In general {\rm GL}(n,k)=(k-1){\rm SL}(n,k). Reason Use the determinant map \to F^{\times} that has size k-1. No i don't get , SL is group with determinant 1 and GLN is group with det -1, 1 right ? @PedroTamaroff @Complexanalysis No. \rm GL is all invertible matrices. @PedroTamaroff Oh oh , i got it . I got confused with the Orthogonal group . SIGH I cannot make W|A compute matrices mod 5. 9:02 PM @DanielFischer How can I show a 2-Sylow of {\rm SL}(2,5) cannot be abelian? Or cyclic. I have shown a 2-Sylow of that has a unique element of order 2. @PedroTamaroff SL(2,5) is the 2\times 2 matrices over \mathbb{F}_5 with determinant 1? The groups of order 8 are D_8,Q_8,C_8,C_2\times C_4,C_2^3. Thus, I am left with Q_8 or C_8. @DanielFischer Yes. I have found elements in SL(2,5) with x^2=-1, but wasn't able to find Q_8 inside it =P Even noncommuting elts with x^2=y^2=-1. But they were bad noncommuting. I need [x,y]=-1 too. @PedroTamaroff If nothing else helps, brute force will, SL(2,5) isn't large ;) @DanielFischer Heh, 120 elts is big enough for me. =D I am trying to see if I can show the 2-Sylow isn't cyclic. Thus, I have to show it is not abelian. Because it already has a unique element of order 2. During by search, I learned SL(2,5) is one of the three unique nonsolvable IC groups. @PedroTamaroff Don't$$\begin{pmatrix}2&0\\0&3\end{pmatrix};\quad \begin{pmatrix}0&4\\1&0\end{pmatrix}$$do the desired? 9:10 PM @DanielFischer I didn't come across those. =P I tried \begin{pmatrix}2&0\\0&-2\end{pmatrix}, \begin{pmatrix}2&0\\1&-2\end{pmatrix},\begin{pmatrix}2&1\\0&-2\end{pmatrix}, \begin{pmatrix}3&0\\1&-3\end{pmatrix}... among others. @DanielFischer They do. I'm so jealous =D @DanielFischer Wait. @DanielFischer How did you find them?$$\begin{pmatrix}i&0\\0&-i\end{pmatrix};\quad\begin{pmatrix}0&-1\\1&0\end{pmatrix}‌​$i\leadsto 2$@DanielFischer Ah, right. =) Now I have to show$A_4$doesn't embed in$SL(2,5)$. @DanielFischer grrreat :D 9:20 PM @DanielFischer That proves$S_5\not\simeq {\rm SL}(2,5)$, since$D_8$is a$2$-Sylow of$S_5$. Yep. Regarding$A_4$, does$Q_8$contain a$V_4$? @DanielFischer No,$Q_8$has three copies of$C_4$and one of$C_2$. @DanielFischer I meant$A_5$. Sorry. =) Same argument, the$2$-Sylow subgroups of$A_5$are$V_4$. @DanielFischer$V_4\leqslant A_4\hookrightarrow A_5\$.
@Mike Hello.

GRRrrnh, @Pedro

9:35 PM
@Mike Yo took a nappy?
@seaturtles Hey there.

herro

so, you prefer the sea to hot cocoa?

I have never heard I not cocoa turtles

@Mike Are you high?
@robjohn

9:50 PM
@PedroTamaroff It doesn't want to stay Pedro

@robjohn How can I adjust the size of the pic here

there

@robjohn You saw my question?
I am considering a bounty on it now.

@PedroTamaroff I don't know if SE supports IMG tags in HTML. If it doesn't, then you have to resize the image then reupload.
@Sawarnik why is it important? You're assuming the actual question was stated wrong, aren't you?
@Sawarnik maybe I am thinking of the wrong question again

@robjohnI think you are thinking of the correct one. The thing its not always false, sometimes its true. Tats my question, when its true? It is not important, no simple math question is. Actually, I am considerably fascinated by the question. My attempts have failed till now. I just pinged you if had any idea. No problem :)

9:57 PM
@Sawarnik Hang on, I will write and answer

Ok.
I maybe on and off though. My exam starts in 4 hours, and I have 2 [biology] chapters to do.