Mathematics - 2015-07-07 (page 3 of 3)

7:02 PM

since I've found no information about it, I presume it's impossible to solve a inequation system with more than 1 variable using the analytic method, right?

Ben Dover

@BalarkaSen yeah the Tor functor is definitely something else

Balarka Sen

right @BenDover. i had heard about it, but i confused that with this torsion-functor

i never did homological algebra

Karim Mansour

7:41 PM

hey

@BalarkaSen

so I want to ask a question

I want to prove [a,b] is closed so I prove complement is open that is $[a,b]^c = (-\infty,a) \cup (b,\infty)$ so I need to prove that those intervals are open and invoke the argument that union of open sets is open. So I consider an arbitrarily y $\in (-\infty,a)$

now consider B(y,r) where r = a - y we can easily prove it now

but I want to prove it aswell when I set $r = \frac{a + y}{2}$ $B(y,r) = (y - r,y + r) = (\frac{y + a}{2},y + \frac{y + a}{2})$

but I can't prove why is $y + \frac{y+ a}{2}$ is actually less than a

Balarka Sen

Remember that open means every point has a ball around it which is entirely contained in it.

Karim Mansour

yeah

I know

to be open every point has to be an interior point

and to be an interior point we have to have some ball that is entirely contained in our set.

Balarka Sen

Why do you want to do the same with $r = (a + y)/2$?

Karim Mansour

according to my drawing it should also work with $r = \frac{a + y}{2}$

Balarka Sen

Yes, it would.

Karim Mansour

7:46 PM

like I should be able to derive algebraically that $B(y,r) = (y - r, y + r) \subset (-\infty,a)$

but I don't know why its not working

Balarka Sen

but that's just algebra. $(a + y)/2 < a$

Karim Mansour

yeah I understand that

but

why is $y + \frac{y + a}{2} < a$?

Balarka Sen

no, not necessarily.

Karim Mansour

yeah exactly

I did pick that radius so if we do that we will have $B(y,r) = (y - \{y + a\}/2,y + \{y + a\}/2)$

so

Balarka Sen

ok, I misread. no, $(a + y)/2$ doesn't work. Take $(-\infty, 1)$ and $y = 1/2$, and $r = 1$.

your drawing, whatever it is, is not correct.

Karim Mansour

7:52 PM

yeah it will go outside the set

Balarka Sen

right.

Ted Shifrin

$(y+a)/2$ is the average of $a$ and $y$. The distance between them is $a-y$ (assuming $y>a$).

Balarka Sen

what you want to do, I believe, is to disect the distance.

That's $(a - y)/2$, not $(a + y)/2$

Karim Mansour

hm but how come $r = (a + y) / 2$ is half way distance between a and y always how come it goes outside the set.

Ted Shifrin

nods, having no idea what's going on

Balarka Sen

7:53 PM

hello @Ted.

hi @TedShifrin

hi @Balarka @Karim

oh I see

@KarimMansour no, that's not halfway between the distance.

Karim Mansour

no that is the average

Ted Shifrin

7:53 PM

Using words sloppily gets you confuzled.

Karim Mansour

!!

stupid me !!!

omg

ok so my drawing was according to the half way not the average ok it makes sense

Balarka Sen

all of us go through that at multiple points in our lives.

Ted Shifrin

The average is halfway between!

yes, @Balarka, stupid you :P

Karim Mansour

(a - y) / 2 should work

Balarka Sen

yeah, I mean, you have to put $(a + y)/2 - y$.

$(a + y)/2$ is just some other point outside.

Karim Mansour

7:55 PM

yeah

so you have to shift it back inside

Ted Shifrin

Huh? $(a+y)/2$ is the point a distance $(a-y)/2$ up from $y$.

Don't confuse points and distances (or points and displacement vectors).

I should probably just shaddup and leave.

Karim Mansour

yeah

Balarka Sen

I just said that (although probably didn't convey it as clearly)

Karim Mansour

not agreeing to your last statement

Ted Shifrin

You can agree with it, too :)

Karim Mansour

7:56 PM

no !

Balarka Sen

I am not agreeing with it either

Ted Shifrin

Rats.

Karim Mansour

I agree with your first statement that is (a + y)/2 is a point

Ted Shifrin

I'm taking a break from sorting stuff in my kitchen and throwing stuff out.

Karim Mansour

I am gonna make some more caffe and continue solving apostol

Balarka Sen

7:57 PM

@TedShifrin Don't break your back/neck.

Karim Mansour

@TedShifrin I decided to write all the details when proving stuff and for each book I solve I will make a binder for it for later if I want to use it

Balarka Sen

@Karim Translate the geometric picture correctly into words, and you'll be fine.

Karim Mansour

yeah

Balarka Sen

Rigor is automatic once intuition is there.

Karim Mansour

yeah

Balarka Sen

7:58 PM

Slogan : "if you can't handwave, you don't understand it well enough"

Ted Shifrin

@Karim: I wrote out complete solutions of most of the exercises in the multivariable calculus part of Apostol Vols I and II (his calculus text) in the Christmas break after I'd taken a standard multivariable calculus class my first term freshman year. I wanted to make sure I knew it all more solidly, and with more theory.

You just miss being smacked, @Balarka.

Anyhow, @Karim, that was one of the folders I found in my office a month ago and threw out.

Karim Mansour

yeah I think that is good I think its also good to start doing it while undergrad so I will be quite strong when I enter grad school :D

oh !!!

Balarka Sen

@TedShifrin I shamelessly acknowledge that I do.

Ted Shifrin

@BalarkaSen I do not necessarily agree with this.

Karim Mansour

I would have loved to get it from you @TedShifrin

Ted Shifrin

8:00 PM

Long gone, @Karim.

Balarka Sen

Yes, well, it's true iff you have the power to translate handwave into rigor.

Ted Shifrin

I still know how to do those exercises, though :)

Balarka Sen

Which is all about mathematics.

Karim Mansour

hopefully this summer I am gonna get until fourier series part of the book and then next summer complete it :D

Ted Shifrin

There's a lot of serious multivariable analysis in that book, too, @Karim, which is essential for doing geometry and mathematical physics.

Karim Mansour

8:02 PM

yeah chapter 12 I am at chapter 3 now so hopefully this summer I will be at chapter 11 then next summer work on multivariable analysis

Balarka Sen

what's chapter 3 about?

Ted Shifrin

There's a lot of harder stuff coming up, @Karim.

Karim Mansour

chapter 3 is about point set topology @BalarkaSen

my goal is to get to chapter 11 fourier series and fourier integrals

Balarka Sen

cool. you know sequences?

Karim Mansour

yeah

Ted Shifrin

8:05 PM

There's actually a lot of multivariable stuff (differential) in between, @Karim. I doubt you'll make it that far.

Karim Mansour

yeah I think so but I always like to put hard goals to reach in order to push myself :D

but essentially real thing is that I will make it up to half way through through the book

Ted Shifrin

Well, soon you'll get to stuff @Balarka doesn't know. But that book has a lot of stuff in it.

Karim Mansour

yeah

Ted Shifrin

Anyhow, stop talking and get back to work.

Balarka Sen

I don't know analysis altogather.

Karim Mansour

8:07 PM

yeah brb guys

Balarka Sen

I don't even know what I don't know about analysis, but I know there's a lot I don't.

Ted Shifrin

On that note, see you later ! :)

morphic

8:23 PM

Hi @TedShifrin

I am at a logic conference at my school

Ben Dover

@KarimMansour I would recommend you to read Spanier's algebraic topology book before its too late

"Through me the way is to the city dolent;
Through me the way is to eternal dole;
Through me the way among the people lost.

Justice incited my sublime Creator;
Created me divine Omnipotence,
The highest Wisdom and the primal Love.

Before me there were no created things,
Only eterne, and I eternal last.
All hope abandon, ye who enter in!"

These words in sombre colour I beheld
Written upon the summit of a gate;
Whence I: "Their sense is, Master, hard to me!"

And he to me, as one experienced:
"Here all suspicion needs must be abandoned,

Balarka Sen

should I lol at that?

Random Variable

8:43 PM

@DanielFischer You alluded to the possibility that one could understand the boundary behavior of the Maclaurin series for $\exp \left(\frac{z-1}{z+1} \right)$ if one had a semi-explicit formula for the general term. What did you mean by "semi-explicit"?

Daniel Fischer

@RandomVariable Something like a series representation. Then it might be possible to get useful estimates.

Random Variable

@DanielFischer At the moment I still have nothing.

Ted Shifrin

9:11 PM

@morphic: mr eyeglasses, have you changed names yet again?

hi @DanielF

Daniel Fischer

Hi @Ted.

Ted Shifrin

hope you're doing ok :)

Daniel Fischer

More or less. The heatwave is over, now we can live again.

Ted Shifrin

It's still horrid here, but I move cross country to waterless land soon.

Hippalectryon

btw @DanielFischer if you want you can remove all those starred music videos, I'm not sure if they belong on the math star board

Daniel Fischer

9:16 PM

Then it will at least be dry. That's better than breathing boiling water, isn't it?

Ted Shifrin

howdy, @Hippa

Hippalectryon

@TedShifrin o/

Ted Shifrin

not if there's no water to bathe, cook, or drink, @DanielF :D

Daniel Fischer

@TedShifrin Bottled water?

Ted Shifrin

That only addresses a small fraction.

Hippalectryon

9:19 PM

Nah, bath with bottled water :3

Ted Shifrin

@Hippa: Then I can't afford to pay my rent.

Daniel Fischer

Then don't move to California, move to Canada. They have water, and not as humid hot summers as Georgia.

Ted Shifrin

Too late, @DanielF. Besides, Canada doesn't want us Muricans.

Daniel Fischer

@TedShifrin Hey, they just let you win the world cup.

Ted Shifrin

LOL ... Not a sport I follow, but, yes, I heard about that.

Mike Miller

9:25 PM

@DanielFischer Bullshit. I just took a nap and after half an hour, I sweat so much my body is only 5% water.

Balarka Sen

hello @Mike.

Ted Shifrin

@MikeM ... That I do not believe.

Daniel Fischer

5% water, 65% beer?

Ted Shifrin

That 110º day in San Jose was plenty sweaty, @MikeM.

Your addition is interesting, @DanielF ... oh, there's plasma.

Mike Miller

@DanielF: I wish. Give me another four hours.

Ted Shifrin

9:28 PM

So, @MikeM, how was Ciprian's talk?

Mike Miller

It was good, of course. Painted a nice picture.

Ted Shifrin

Can you interpret all the nuances?

Chris's sis the artist

I shut down, extremely tired.

Hippalectryon

Plot twist : @Chris'ssistheartist is a computer

Ted Shifrin

@Hippa: Sounds like your computer ... always overheated and broiling.

Mike Miller

9:30 PM

It's not an easy paper. He didn't go into those. First half was about the relevant 80s work.

Ted Shifrin

Wow, that's like ancient Kirby history. :)

Hippalectryon

@TedShifrin 86°C atm

Ted Shifrin

toasty warm, @Hippa.

Hippalectryon

I could cook someone in there :=)

Ted Shifrin

I volunteer you.

Hippalectryon

9:32 PM

But in the village, who cooks the cooker ?

Then if you have to cook the barber, given that the barber can't shave himself... hum..

Ted Shifrin

You don't need to be shaved.

Mike Miller

Glewski-Stern, Matumoto. Obstruction to having a triangulation lives in $H^5(M;\ker \mu)$, $\mu$ is the Rochlin homomorphism. If there's a homology sphere $\Sigma$ of order 2 in the homology cobordism group, with $\mu(\Sigma) = 1$, then that obstruction is always trivial. Otherwise it can be nontrivial.

Hence, 3-dim topology is relevant to this high-dim problem.

I think this only applies in dimension at least 5. There are non-triangulable 4-folds.

Ted Shifrin

To whom are you addressing this, @MikeM?

Mike Miller

You.

Ted Shifrin

I was afeard of that.

Mike Miller

9:40 PM

You seemed vaguely interested.

Ted Shifrin

Yes, vaguely. It far surpasses my knowledge.

Balarka Sen

what's the homology cobordism group?

the homology theory you build up with cobordism?

if so, then you're saying that "manifolds can't be triangulated because of the 5-th cobordism group"? (although I don't know what the Rochlin hom is)

John Sheridan

10:20 PM

anyone here ever studied stochastic processes?

Khallil Benyattou

Strongly considering taking it next year, @John.

John

cough

John Sheridan

I'm looking for a good reference for this study, I was wondering if anyone knew the book Durrett and the book of Karlin

Samuel Yusim

yo people, what's up

Karl Kronenfeld

don't like being pinged randomly @john?

John

10:27 PM

@KarlKronenfeld I don't particularly mind; I just figured people should know when they're doing it :p

Khallil Benyattou

Aha, sorry @John!

Karl Kronenfeld

Ah, I operate under the assumption that everybody is omniscient but has evil intensions, @John.

Khallil Benyattou

What's up, @SamuelYusim?

John

2 mins ago, by John

@KarlKronenfeld I don't particularly mind; I just figured people should know when they're doing it :p

:)

@KarlKronenfeld Oh I am, and I do, I just can't let on yet.

evinda

Hey @Ramanewbie

Samuel Yusim

10:39 PM

not much @KhallilBenyattou, how about you?

Ramanewbie

Hi @evinda

evinda

How are you? @Ramanewbie

Ramanewbie

@evinda Fine what about you ?

evinda

@Ramanewbie Ok... How is your time? :)

Ramanewbie

@evinda Great, I'm still in Ireland playing snooker and fishing

evinda

10:45 PM

@Ramanewbie Nice... When will you go back?

Ramanewbie

@evinda I go back to France in 305 weeks

evinda

@Ramanewbie :o You mean days?

Ramanewbie

@evinda 3.5 weeks lol.
The '0' is just next to the '.' on the keyboard @evinda

evinda

@Ramanewbie Aaa I see :D

@Ramanewbie Are the children nicer now?

Ramanewbie

@evinda They' re are still quite rude with their parents but they're nice to me

evinda

10:48 PM

@Ramanewbie Aha...

What job do the parents have? @Ramanewbie

Ramanewbie

@evinda The father is a truck driver for MAXOL (Irish petrol company)
But idk what the mother does... She doesn' t work those weeks but she might simply be on holidays

evinda

@Ramanewbie I see...

@Ramanewbie Do they teach you irish?

Ramanewbie

@evinda No... This language looks quite complicated to me

evinda

Do they speak fluently english? @Ramanewbie

Ramanewbie

@evinda Of course, yes. Everyone speaks English in Ireland.
They don' t even speak Irish well...

evinda

10:54 PM

@Ramanewbie Aha!

@Ramanewbie Do you often speak with your parents via internet?

Ramanewbie

@evinda Not really... They don' t have Facebook or Skype or whatever. I just send them a few emails sometimes

evinda

@Ramanewbie Ah I see...

No, I am in Crete. @Ramanewbie

Ramanewbie

@evinda Then arent you on holidays ?

evinda

@Ramanewbie No, I live there.

Ramanewbie

@evinda Great I didnt know that !

evinda

11:00 PM

Have you been there? @Ramanewbie

Also are you in contact with your brother? @Ramanewbie

Mike Miller

how's your graph thing going @Samuel

evinda

Hi @SamuelYusim

Hi @KarimMansour

Samuel Yusim

hi @evinda

Karim Mansour

Hi @evinda

evinda

How are you? @SamuelYusim @KarimMansour

Samuel Yusim

11:10 PM

also @MikeMiller I'm currently typing up formal versions of some stuff on cographs that will ideally be in the first draft of our paper

Karim Mansour

good how about you @evinda

evinda

@KarimMansour Ok

Samuel Yusim

I've never been so careful writing something

Karim Mansour

been doing analysis @evinda

Mike Miller

haha

the best advice i think is to just write first

and then edit

Samuel Yusim

11:11 PM

also @evinda pretty good lately

evinda

@KarimMansour And did you like it?

Mike Miller

(the editing part is essential, of course, but be wary of early perfectionism)

Karim Mansour

yeah

Samuel Yusim

yep, definitely

Karim Mansour

I like analysis algebra and topology

they are very nice

evinda

11:11 PM

@SamuelYusim In which semester are you?

@KarimMansour Nice

Karim Mansour

hopefully by the time I go to grad school I will understand them perfectly

Samuel Yusim

@evinda I just finished my second year and I'm on summer break

evinda

@SamuelYusim Did you go well in the exams?

Samuel Yusim

yeah, they all went fine. I took a course that was maybe too hard for me but I didn't do atrociously on the final so I'm taking it as a win

I exaggerate when I say I just finished, though. it was actually a couple months ago now

evinda

@SamuelYusim Which one?

@SamuelYusim How many semesters are left?

Karim Mansour

11:15 PM

which course @SamuelYusim ?

Samuel Yusim

I took a course called set theory and model theory, and it was pretty tough

Karim Mansour

I heard about it

what is the prereq ?

user159870

Hello everyone!

Karim Mansour

@SamuelYusim ?

Samuel Yusim

it required an abstract algebra course, but that was more for maturity than anything else

set theory and model theory both don't really "follow" from any other mathematical subject

but you can't just jump in because the complexity of the proofs will make lots of stuff incomprehensible

Karim Mansour

11:21 PM

no

no @user159870

user159870

Do you have an other profile or aren't you subscribed? @KarimMansour

Karim Mansour

no I don't have facebook @user159870

its waste of time

user159870

Are you busy? @KarimMansour

Karim Mansour

yeah

user159870

Do you have a girlfriend? @KarimMansour

Or are you too busy? @KarimMansour

Karim Mansour

11:24 PM

yes

I do have a gf

user159870

How long is your relationship? @KarimMansour

Karl Kronenfeld

Oh, I so badly want to you to interview/interrogate me @user159870.

Karim Mansour

1 year and half a month

user159870

Congrats! @KarimMansour

Karim Mansour

thank you

user159870

11:27 PM

@KarlKronenfeld It's just for fun!
Do you have a girlfriend?

Karl Kronenfeld

@user159870 Certainly

user159870

@KarlKronenfeld and how long is your relationship?

Karl Kronenfeld

@user159870 Like all mathematical relationships, it has neither a beginning nor an end.

4

Karim Mansour

ahahaha

user159870

HAHAHHAHHAHAHA

Richard

11:30 PM

Please don't attempt to dox each other. It's a massive fail of rule #1

Karl Kronenfeld

rule 1?

user159870

You have a nice picture @Richard

Karl Kronenfeld

I am pretty sure that is how userblah would talk in person

the respect part, on the other hand..

Richard

@user159870 - Buffy approves of your approval

I had a girlfriend who was a mathematician. She was a non-Euclidian. She said she couldn't carry on because there was no point.

Karim Mansour

haha

lool

Richard

11:33 PM

After a while, we just led parallel lives.

user159870

HAHAHAHAHAHAHAHHAHAHAHA

Karim Mansour

hahahaha

user159870

You are really funny!

Richard

She'd go hyperbolic at the least thing

Karl Kronenfeld

100% true, I did a google search.

user159870

11:36 PM

Is your gf a mathematician? @KarimMansour

David Zhang

Hey guys, quick question.

Karl Kronenfeld

Is it about our partners, David?

user159870

Tell us @DavidZhang

You are welcome

David Zhang

Nah, just a notation thing. Is 2n! usually interpreted as 2 * (n!) or (2n)!?

user159870

I think it is 2*(n!)

@DavidZhang

David Zhang

11:38 PM

Ah, ok. I thought so too, but I wanted to check with someone else

user159870

@KarlKronenfeld HAHAHAAAAHHAAHAHAHA

Karl Kronenfeld

@user159870 ?

user159870

Because you asked David if his question was about our partners although he wasn't discussing with us before about this topic. @KarlKronenfeld

Karl Kronenfeld

But then he asked about notation! BAHAHA!

user159870

HAHAHAHAHA

Transcript for

$Mathematics$ Mathematics