Mathematics - 2013-03-02 (page 1 of 3)

Jonas Teuwen

00:00

Alright.

8-). I hope so too.

My advisor replied this morning to an e-mail of mine with a quote of Goethe. The last email he replied with only using the symbol '?'.

Will Jagy

@OldJohn, a number of things are unclear. Has he ever lectured on a regular basis? You can get by all sorts of discomfort and shyness if you are experienced in front of a classroom.

Jonas Teuwen

Me? I have lectured quite a bit, but mostly basic stuff, up to complex analysis.

And in seminars on functional analysis (ergodic theory, operator semigroups and Choquet theory).

Old John

@JonasTeuwen Hi! I'm back at last

Jonas Teuwen

I don't feel that much discomfort as I know that most people do it much worse...

@OldJohn Hello! How was it?

Old John

@JonasTeuwen Fantastic, thanks!

Jonas Teuwen

00:03

Alright! It's still cold, so it didn't help much did it?

Peter Tamaroff

Darn. I keep writing "Similarily" when I mean "Similarly"

skullpatrol

Hi @OldJohn welcome back.

Old John

@skullpatrol Thanks - how's things been?

Will Jagy

I sent you both info on a conference in June in Jessica Alba, Romania. One session on harmonic analysis, still accepting abstracts.

skullpatrol

@OldJohn Fine thanks. How about you?

Jonas Teuwen

00:04

Can I also write an abstract and figure out what it means later on?

@PeterTamaroff Must be genetic. Are there any retards in the male blood line?

Old John

@skullpatrol Great holiday, but very cold here - got the heating on at full power ...

Peter Tamaroff

@JonasTeuwen HAHAHA No there aren't.

Jonas Teuwen

@PeterTamaroff Alright, must be a spontaneous mutation then!

Peter Tamaroff

@JonasTeuwen My biggest fear has become real.

Jonas Teuwen

Better than complex.

Oh boy. So lame 8-).

Otherwise, take the real part.

skullpatrol

00:07

Keep it real.

Will Jagy

@OldJohn, could be Julia Alba. Or Alba Iulia.

Peter Tamaroff

@JonasTeuwen Indeed.

BenjaLim

@OldJohn my god we haven't spoken in a while

Peter Tamaroff

@BenjaLim Yo Benjen.

Old John

@BenjaLim been away on holiday for 2 weeks - getting warm

Jonas Teuwen

00:10

"in der Beschränkung zeigt sich der Meister" < I got.

BenjaLim

@PeterTamaroff Why did you advise someone to learn stuff properly? I totally agree with this.

@JonasTeuwen I met another student of Van Neerven yesterday his name is also Jan

Peter Tamaroff

@BenjaLim Come again?

Jonas Teuwen

Don't tell people to start studying!! That way, more left for us!

@BenjaLim Jan Maas.

I talked to him in January I think.

BenjaLim

@PeterTamaroff You comment to mick.

@OldJohn getting cold here

man today is like second day of autumn and it's freezing

Peter Tamaroff

@BenjaLim Yes, what is it to it?

BenjaLim

00:12

@OldJohn Problem is there's not been much sun

so the temperature has droped

@PeterTamaroff Just sayin

Old John

@BenjaLim left a nice temperature of 21 earlier today to come back to about 4 or 5 degrees here - feels really cold

BenjaLim

fark

@OldJohn 15 degrees for us now is very cold

Jonas Teuwen

@PeterTamaroff Kahana-Khinchine inequalities are quite useful when considering infinite-dimensional generalizations of singular integral identies using randomization!!

BenjaLim

@OldJohn man the sun's not been in out in a few days now

@JonasTeuwen I felt quite uncomfortable yesterday at dinner surrounded by all these people that work in like harmonic analysis, etc

Old John

@BenjaLim it was 14 inside the house when we got back - now climbed to a lofty 16.5 ...

Peter Tamaroff

00:14

@BenjaLim What baffled me is you started with "Why did you...."

=P

BenjaLim

@PeterTamaroff I thought it was a brilliant idea.

@PeterTamaroff I completely support you

Jonas Teuwen

@BenjaLim Why?

Their poop launcher also produces brown poop.

BenjaLim

@JonasTeuwen Well they were all talking about some analysis shit which I had no clue

Peter Tamaroff

@BenjaLim Whom?

BenjaLim

Man Pierre has a lot of activity around him

Thierry, Dorotea, Jan, etc

phd students

undergrad

Jonas Teuwen

00:16

Dorothee?

BenjaLim

yea

Peter Tamaroff

@JonasTeuwen "Brownian motion" and "Wiener process" always make me chuckle.

Jonas Teuwen

@BenjaLim Then you say 'THIS. IS. A. DINNER. EAT. NO. MATHS.'

@PeterTamaroff Fokker-Planck?

BenjaLim

@OldJohn Did I tell you I'm the tutor for Galois theory this sem?

Peter Tamaroff

@JonasTeuwen I don't get the Planck part.

Jonas Teuwen

00:16

I have met Dorothee in Madrid.

@PeterTamaroff Plank?

BenjaLim

He's also pretty pro

Jonas Teuwen

Jan Maas is cool.

Old John

@BenjaLim Excellent! - I really enjoyed Galois theory - many years ago

Peter Tamaroff

@JonasTeuwen You wrote "Planck"

Jonas Teuwen

@PeterTamaroff In dutch it sounds like Plank.

BenjaLim

00:17

@JonasTeuwen I know he looked really intense

Jonas Teuwen

Intense?

Peter Tamaroff

@JonasTeuwen Which means?

Jonas Teuwen

He looks like a mathematician.

@PeterTamaroff Wood.

BenjaLim

@JonasTeuwen I mean like very smart. Apparently I was told his output is crazy

Jonas Teuwen

@PeterTamaroff What about the Cox-Zucker machine?

Peter Tamaroff

00:18

@JonasTeuwen HAHAHAHAHHAA

You're shitting me!

BenjaLim

@OldJohn I had a look at the assignment yesterday was not too bad for marking I guess

Peter Tamaroff

@anon What is the end of this? "Let $H$ be a proper subgroup of $G$, $G$ finite. Show $$G\neq \bigcup_{g\in G} gHg^{-1}\text{ ? }$$

Jonas Teuwen

@PeterTamaroff Nope.

Old John

@BenjaLim Hmm - I can't imagine marking stuff like that - I always hated marking stuff students had written

Peter Tamaroff

@JonasTeuwen Just googled it. Laughed once more.

BenjaLim

00:20

@OldJohn I know at first I planned with David that we would split the assignments in half

but then he said he would prefer a uniform marker

Peter Tamaroff

@OldJohn I would be a pedantic asshole if I had to mark stuff.

BenjaLim

so he said maybe one week I'll mark the assignments and he'll do the next

Old John

@PeterTamaroff I was often pretty pedantic too :)

@BenjaLim that sounds like a good idea

Peter Tamaroff

@OldJohn It does help, though.

BenjaLim

@OldJohn I hated pedantry when I had this tutor once

Peter Tamaroff

00:21

@BenjaLim Did I tell you I'm starting uni this year?

anon

@PeterTamaroff It is unclear to me what you're asking. What you've stated is, as it stands, false (take H to be maximal and G nonabelian).

BenjaLim

but it is important to distinguish between pedantry and actual points that matter in a proof

@PeterTamaroff Yes I heard.

Old John

@BenjaLim absolutely!

Peter Tamaroff

@anon Well, I'll read it again and copy it verbatim:

BenjaLim

@OldJohn Most of the time if the student gets like 80-90% right I'll give them everything

I don't want to be a pedantic arse

Old John

00:23

I had some pretty pedantic teachers in the past - like insisting punctuation was always correct when writing maths :)

Peter Tamaroff

"Let $H$ be a proper subgroup of a finite group $G$. Show that $G\neq \bigcup_{g\in G}gHg^{-1}$"

@anon

That's what it says.

Jonas Teuwen

I have access to write to one of the university domains. They wrote in the agreement that not using correct punctuation is considered abuse.

Old John

I recall once listing 3 possibilities (a) (b) (c) and ending each with a comma ...

Jonas Teuwen

And as the services are paid by the university, this means you are damaging your employer.

I had to laugh.

Old John

and was told that the last one had to be a full-stop, not a comma

Peter Tamaroff

00:24

@OldJohn I meant math related pedantry, not that kind of terrenal hell!

BenjaLim

@OldJohn The other day I had to present my solutions to my lecturer

for the thing on algebraic number theory

man he asked so many questions

Old John

@BenjaLim how did it go?

BenjaLim

and a lot of times I was not allowed to even look at my solutions and present the proofs

anon

@PeterTamaroff Oh, nevermind about my supposed counterexample.

Jonas Teuwen

Did you eat him alive?

BenjaLim

00:25

@OldJohn He said at the end that what I presented was about 20% of a PhD qualifying exam at berkeley and I passed :)

Carpediem

@Anon You might find this interesting: math.stackexchange.com/questions/121526/…

Old John

@BenjaLim good!!

BenjaLim

@OldJohn thanks to the support from you too!!

anon

@Carpediem did you mean to direct that to Peter?

Carpediem

Yes sorry

Peter Tamaroff

00:26

@anon So my question stands: what is the end of proving that?

BenjaLim

@anon Hey, we haven't met in a while :)

Carpediem

@PeterTamaroff math.stackexchange.com/questions/121526/…

Jonas Teuwen

@PeterTamaroff Shall I write you a two line recommendation letter for Cambridge?

Peter Tamaroff

@Carpediem Yes, thanks.

@JonasTeuwen How would you do that?

Jonas Teuwen

@PeterTamaroff 'Peter is an intelligent, but surprisingly ugly young man. He would fit right in between the British in Cambridge.'

Old John

00:27

@BenjaLim My support was negligible!

anon

@PeterTamaroff does "end" mean "purpose" or "goal" or "motivation" here?

Old John

Time I got some sleep - might be the only way to get warm :((

anon

I would guess, to contrast with the situation with taking intersections.

Peter Tamaroff

@anon Yes. As in "To what end..."

Old John

bye all

Peter Tamaroff

00:29

@anon Well, $\cap gHg^{-1}$ is a subgroup, but it might take some particular presets for it to be $G$, right?

@JonasTeuwen I shall append a picture of myself and refute your claim.

I'm off to eat now.

user19161

@PeterTamaroff Peter is very handsome, if I were a girl I would fall in love with him.

Jonas Teuwen

@PeterTamaroff Where is the refutation?

user19161

@JonasTeuwen The refutation is my claim above.

Jonas Teuwen

Is that some kind of very weak 'ad populum'?

peoplepower

@PeterTamaroff It also fits in a slightly more general framework: For any transitive action of a finite group $G$ on $S$, with $2\leq |S|<\infty$ there is an element of $G$ which fixes no element of $S$.

BenjaLim

00:37

@OldJohn @JonasTeuwen @PeterTamaroff bye!

@anon bye!

Peter Tamaroff

@BenjaLim Bye dawg.

@JonasTeuwen The picture, obviously.

@peoplepower OK.

@peoplepower So I assume I can prove the above claim (about the union of the $^gH$) by finding some appropriate transitive action?

peoplepower

@PeterTamaroff Yes.

Peter Tamaroff

@peoplepower Gooooood. I'm off the action hunting.

Carpediem

@PeterTamaroff What is a solution to the "damped" equation (in the context of differential equation ?) Is it when the discriminant is positive?

Peter Tamaroff

@Carpediem Oh, you can find the solution using integrating factors.

More specifically

$$x'+kx=f(t)$$

$$x'e^{tk}+ke^{tk}x=e^{tk}f(t)$$

$$(e^{tk}x)'=e^{tk}f(t)$$

Carpediem

00:52

@PeterTamaroff Well I am considering the differetinal equation mx"+bx'+kx=0

Peter Tamaroff

@Carpediem I see.

Carpediem

There where a series of questions when b=0

Peter Tamaroff

@Carpediem You can reduce it to $y''+uy=0$

Did you know that?

Carpediem

yes yes

this is what we call undamped equation

Peter Tamaroff

OK. So what do you want?

Carpediem

00:53

I just wanted to make sure that "damped" equation is when the discriminant is positive

when you write the characteristic equation

Peter Tamaroff

OK, please remind me what damped means.

Carpediem

this is my question :)

Peter Tamaroff

Oh.

But there must be some definition.

Carpediem

I can't seem to find it neither in my book or online

@PeterTamaroff Do you want me to specify some of the questions before leading to this one ?

Peter Tamaroff

Well, your equation models a spring, yes?

Carpediem

00:55

Yes

Peter Tamaroff

@Carpediem Let's see.

Carpediem

The first question was to determine x in the case when b=0

then I had to express the kinetic energy ie $$\frac{1}{2}m(x')^2$$

Then I had to prove that:

$$\frac{1}{2}m(x')^2+\frac{1}{2}kx^2=c$$, such that c constant

Then they tell us to consider the total energy E=E(t) given in the previous question, but using a solution to the "damped" equation

Peter Tamaroff

OK.

For $b=0$ we have $mx''=-kx$

Multiply both sides by $x'$.

Carpediem

This is E' right ?

Peter Tamaroff

$x=x(t)$

Carpediem

01:01

@PeterTamaroff

Peter Tamaroff

Yes?

Carpediem

Why do you want to multiply both sides ?

Peter Tamaroff

What is $\frac{dx}{dt}(x')^2$?

Similarly, what is $\frac{dx}{dt}x^2$?

Carpediem

That is what we obtain when we differentiate $$\frac{1}{2}m(x')^2+\frac{1}{2}kx^2$$

Peter Tamaroff

@JonasTeuwen

@Carpediem Think it the other way around.

$$x''+kx=0$$
$$x'x''+kxx'=0$$
$$(2x'x'')+k(2xx')=0$$

Now integrate that.

Carpediem

01:05

Ok but what expression for x(t) shoud I use ?

Peter Tamaroff

Don't you want to get to

8 mins ago, by Carpediem

$$\frac{1}{2}m(x')^2+\frac{1}{2}kx^2=c$$, such that c constant

?

You're one step away.

Carpediem

But what you wrote is in the case of the undamped equation.

Peter Tamaroff

You told me to assume $b=0$, didn't you?

I might have misunderstood.

What is $E(t)$?

Carpediem

@PeterTamaroff No that is what I did in the beginning. I already did that.
We are assuming now b>0

Peter Tamaroff

And where do you wanna get to?

Carpediem

01:09

We want to find an expression for the total energy E(t) but using a solution x(t) to the damped equation

(assuming damped equation is when b>0)

Peter Tamaroff

OK; what is $E(t)$? The "total energy".

I have little knowledge of physics.

Carpediem

Yes as in: $\frac{1}{2}m(x')^2+\frac{1}{2}kx^2$

Peter Tamaroff

That is $E$?

Carpediem

Yes

Peter Tamaroff

OK.

But we already said we can reduce $x''+bx'+mx=0$ to $u''+\beta u=0$, which we already solved!

Just do that.

Carpediem

01:12

But I need to express E' in terms of b and x'

Peter Tamaroff

I don't understand, you said $E$ is defined as $\frac{1}{2}m(x')^2+\frac{1}{2}kx^2$. It can be something different from that?

Carpediem

It is defined as above

But when b=0 it is constant

Now we are considering the case where b>0

And we want to express E' in terms of x' and b

Peter Tamaroff

Oh, OK. So you can just find $x$ and be done with it, yes?

Carpediem

That is what I thought but I wanted to see if there was any alternatives?

Peter Tamaroff

OK, I have found something in my notes that might be helpful.

Take $x''+ax'+mx=0$.

Assume $y=uv$ with $u$ such that $wu'+au=0$. This means $u=\exp(-ax/2)$

Then we obtain the equation $v''+\frac{4m-a^2}{4}v=0$

If $\Delta <0$, the solution is

$x(t)=c_1 e^{\sqrt{k}t}+c_2 e^{-\sqrt{k}t}+C$

where $-k=\Delta$

Carpediem

01:20

I think delta is always negative: we are considering the cases where b=0 and b>0

I never mention b<0

Peter Tamaroff

For $\Delta >0$, it is $c_1\cos \sqrt kt+c_2\sin \sqrt kt+C$

Oh, no wait

$k=\frac{a^2-4m}{4}$ in the first case.

Carpediem

Thank you

I have to go now

Charlie

@PeterTamaroff Whatever

Oooow....

Charlie

01:45

@anon

Carpediem

01:59

@PeterTamaroff Actually we were thinking too hard

We know that $E'=x'(mx"+kx)=x'(-bx')=-b(x')^2$

That's it

@charlie

Charlie

@Carpediem Hi CarpeDiem!

Carpediem

@charlie Nice seeing someone around

Just finished my differential equation problem set :)

Charlie

@Carpediem Yes, I was feeling a little alone

@Carpediem Excellent

Carpediem

I still like algebra more

matrices, euclidien spaces,...

Charlie

Good, good

Carpediem

02:11

I am going to see now the documentary on Fermat's last theorem you where talking about earlier

Charlie

@Carpediem me?

it was user58512

Carpediem

@charlie Oh sorry then

Charlie

@Carpediem Don't worry :)

@Carpediem where will you watch it?

Gustavo Bandeira

@Charlie Cê foi suspensa?

Charlie

@GustavoBandeira pois é

Gustavo Bandeira

02:22

@Charlie Isso que dá chingar o RobJohn.

Charlie

@GustavoBandeira num xinguei o robjohn

Gustavo Bandeira

O que tu aprontou?

Charlie

mandei o gitgud ir se fud#r

Gustavo Bandeira

Haha

Notei:

2 days ago, by Git Gud

@PeterTamaroff Not much. She wanted me to tell her where I was from because I knew she's from Brazil. But I didn't say anything. It was amusing.

Peter Tamaroff

@Carpediem Blimey.

Gustavo Bandeira

02:25

@Charlie Mas só porque ele num disse de onde era?

@PeterTamaroff Portugesliño.

Peter Tamaroff

@GustavoBandeira Ah?

Charlie

@GustavoBandeira num foi nada, tava só brincando poxa

Gustavo Bandeira

You used to say something like that when we spoke portuguese.

@Charlie Haha

@Charlie Bem feito. Tu vivia fazendo mistério de quem tu era e onde morava, encontrou um espelho agora! Há!

Charlie

tô cagando e andando

pouco me lixando

:)

anon

@Charlie eh?

Charlie

02:31

@anon nothing, just calling you

it's a bad habit, it's hard to drop it

Gustavo Bandeira

@Charlie Eita. Agressiva.

Charlie

sim de vez em quando

מה הזמן מסמן לי
זה הכל שאריות של החיים

Gustavo Bandeira

@Charlie Rivaldo sai desse lago.

Charlie

???

Gustavo Bandeira

@Charlie youtube.com/watch?v=SxVCFGrNHWc

Charlie

02:38

what a piece of shit

Gustavo Bandeira

^

Charlie

aaaaaaaaaaaaaaaaaaaaa

Frank Science

Is it too difficult for an ordinary freshman to understand the properties of $p$-adic number?

Charlie

@anon could you answer ^?

Peter Tamaroff

@FrankScience I don't think so.

Frank Science

02:52

@PeterTamaroff Since I'm an ordinary freshman, is there any reference for me?

Peter Tamaroff

I asked this a while ago, @FrankScience

There is this which anon linked to.

Frank Science

Well, thanks.

Is there any prerequisite?

Well, I'm considering $\sum_{k=m}^\infty a_kp^k$, not just integers.

Suppose $m\ge0$, which leads to $p$-adic integers, It's not hard to show that the metric space is sequential compact.

Peter Tamaroff

@FrankScience Well, a little number theory and a little analysis seems enough.

anon

@FrankScience nope

Frank Science

I did some search work on two's complement in computer, which led me into the theory about $p$-adic numbers.

user19161

03:13

I actually am beginning to think that mick is really 14.

Frank Science

*I'm actually

Peter Tamaroff

@JacobBlack Of course he is... or somewhere near.

user19161

@PeterTamaroff Initially I thought he was just telling a lie, but I think it may be the truth after all.

Peter Tamaroff

03:33

Should I make this CW?

@JacobBlack

@robjohn

@anon

@Charlie

user19161

@PeterTamaroff Why CW? It's your solution!

Peter Tamaroff

@JacobBlack Well, because it doesn't really answer the OP.

user19161

As long as you know the answer yourself and nobody has posted it as an answer, you can post it as an answer.

user19161

But if it is not an answer, then it should not even be posted as an answer.

Peter Tamaroff

@JacobBlack OK, it is strongly related to the question

user19161

03:35

But if you do post it as an answer for whatever other reason, you can just explain yourself in the post.

user19161

CW or not, well, no difference to me.

Peter Tamaroff

@JacobBlack I think what I posted was an exercise in Spivak.

But I had never done it.

user19161

@PeterTamaroff Now I see what you posted is not an answer, haha. Well, if I were you, I would just delete it.

Peter Tamaroff

@JacobBlack Buuuuu!!!

user19161

@PeterTamaroff Delete!

Peter Tamaroff

03:39

@JacobBlack Damn you!

user19161

@PeterTamaroff HAHAHAHA!

Peter Tamaroff

@JacobBlack You unvoted! Damn you twice!

user19161

@PeterTamaroff Yes, I also removed the upvote the other day for the post where you used the same k.

Peter Tamaroff

@JacobBlack I corrected that.

user19161

@PeterTamaroff OK, it's slightly better now, so upvote.

Peter Tamaroff

03:42

@JacobBlack Accept the idea was correct, but the notation was off. I think it is worth to have a good idea vs bad notation than the converse.

user19161

@PeterTamaroff Well, in this case, it is not bad notation but wrong notation, therefore wrong answer.

Peter Tamaroff

@JacobBlack GUSFRABA

user19161

@PeterTamaroff Sounds like Gustavo, lol.

user19161

So guys currently I am taking some meds which I hope will help me...

Peter Tamaroff

@JacobBlack With what?

Frank Science

03:44

Do you know Bernoulli polynomials?

user19161

@PeterTamaroff Well, with my secret conditions.

Peter Tamaroff

@FrankScience Aye.

@JacobBlack Hehehe, nailed it!

user19161

@PeterTamaroff I edited cos I misinterpreted your question.

user19161

Or maybe that is what you meant!

user19161

In which case, the answer is water.

Peter Tamaroff

03:46

@JacobBlack I was ambiguous on purpose.

Frank Science

Crankeries.

user19161

@PeterTamaroff Pedro is a genius!

Peter Tamaroff

@FrankScience Ah?

user19161

@FrankScience We're all nuts here, tru dat...

Peter Tamaroff

@JacobBlack Is it something psychological?

user19161

03:47

@PeterTamaroff Well, my secret conditions are what I told you in the email.

Frank Science

@PeterTamaroff I'm reading an article about a crank.

user19161

@FrankScience Who?

Frank Science

@JacobBlack You don't know.

Peter Tamaroff

@JacobBlack Yes, I know. I mean, what are the medicines supposed to do? Prevent you from making the same mistake again?

@FrankScience Why don't you share?

Frank Science

@PeterTamaroff It's not in English.

user19161

03:48

@PeterTamaroff Well, well, never mind.

Peter Tamaroff

@FrankScience What is it in?

user19161

@PeterTamaroff Probably Chinese.

user19161

@peter That was a good advice you gave to mick, lol.

Frank Science

He was saying that he was prior to any mathematical professor.

user19161

@FrankScience What do you mean by prior?

Peter Tamaroff

03:50

@JacobBlack I had had enough, was slightly tipsy.

Frank Science

@JacobBlack superior.

user19161

@PeterTamaroff Yes.

user19161

@FrankScience Ah, never seen prior used in that way.

user19161

@FrankScience It's true many of these math profs aren't very good.

Peter Tamaroff

@FrankScience Who was?

user19161

03:52

@PeterTamaroff The crank.

Frank Science

@PeterTamaroff The crank. Did you meet any crank?

Peter Tamaroff

@FrankScience No, I haven't.

user19161

@FrankScience Yes, a few on this site. Usually they ask about the Riemann Hypothesis.

Frank Science

@PeterTamaroff This one is different from others. He might know something about algebraic geometry or so, but his behavior indicates that he's a crank.

Peter Tamaroff

@FrankScience Well, there are Cranks and Crank Hatchlings. Take mike as an example. He can be saved.

Frank Science

03:57

@PeterTamaroff He wastes all the time in arguing that he's valuable and significant.

@PeterTamaroff He claims that the society is totally unfair and the professors are only aiming at making money.

Peter Tamaroff

@FrankScience The guy you're reading about?

Frank Science

@PeterTamaroff Yeah.

Transcript for

$Mathematics$ Mathematics