Mathematics - 2012-06-29 (page 2 of 3)

there's a tendency (imo) for "calculations" to be about specific numbers, computations for more general symbolic things, and "determine" more general still to abstract objects and features rather than just expressions

robjohn

@FrankScience You have to be careful about how you define uniformly distributed. Depending on the continued fraction, an irrational number can have clumps at some levels.

@FrankScience without further context, I would say yes.

Frank Science

Now it's studying discrepancy.

$D(\alpha,n)=\max_{0\le\nu\le1}|s(\alpha,n,\nu)|$

robjohn

@FrankScience consider what anon says. I am sure many share his opinion.

Frank Science

5:39 AM

What's imo? I can't get it in Google.

I have seen such word many times, but I can't get it.

where $s(\alpha,n,\nu)=\sum_{0\le k<n}([\{k\alpha\}-\nu]-\nu)$.

$[P]$ is Iverson bracket.

robjohn

@FrankScience In My Opinion

Frank Science

Well.

I use IMO to refer to the International Mathematical Olympiad.

robjohn

@FrankScience Often it is IMHO

Frank Science

@robjohn Now I know.

robjohn

H=Honest

Frank Science

5:43 AM

The property of irrationals and continuants confuses me.

robjohn

@FrankScience have you looked into continued fractions further than definitions?

Frank Science

$D(\alpha,n)=o(n)$.

and $D(\alpha,n)$ is not $O(n^{1-\epsilon})$ for some $\alpha$.

@robjohn I get it from CMath.

Eugene

@robjohn soon enough. i need to read papers so not that much french

Frank Science

$D(\alpha,n)=o(n)$ implies that $\{n\alpha\}$ is uniformly distrubuted.

robjohn

@FrankScience what is an Iverson Bracket when applied to a real number? Usually they are applied to a truth value.

Frank Science

5:55 AM

@robjohn Sorry, it should have been $[\{k\alpha\}<\nu]$.

user19161

6:16 AM

So often I want to answer a question only to find that one has been posted before I can submit mine.

Frank Science

--> So often do I want to ...

user19161

@FrankScience Wait, are you trying to correct my English?

Frank Science

@JasperLoy Am I right?

anon

makes more sense to me the way jasp wrote it

user19161

@FrankScience This warrants some thinking.

user19161

6:23 AM

English is not as straightforward as many think, so it's just like math.

Frank Science

So stop using English, use the formal language instead, say, first-order logic.

user19161

By the way I saw the meta post about someone trying to remove the essential parts from his question. I looked at the edit history and I don't think it's vandalism. meta.math.stackexchange.com/questions/4520/…

user19161

@FrankScience Wait, so you just started studying calculus and you know about first order logic? Hmm, you must be the next Fields medallist.

Frank Science

@JasperLoy Maybe impossible.

user19161

@FrankScience OK, a few more years then.

Eugene

6:27 AM

what is .... .....?

user19161

One of the edits above could be an accident, not vandalism. The rest are just OP's way of expressing himself.

Eugene

@JasperLoy IMO he deserves the suspension, sir

Frank Science

@JasperLoy Only know about, not know first order logic. It's somewhat popular science, not scientific, say, the proof for Godel's incompleteness theorem.

user19161

@Eugene But like I said, there is a high chance it is not vandalism. In fact I would not think it is if not for the meta post.

Eugene

@JasperLoy ok, sir

user19161

6:30 AM

@FrankScience That's why I never read these popular books. They teach you nothing and just waste your time and money.

user19161

Half of them are written by silly authors who know nothing about the topic itself.

user19161

Then people read them and then think they know everything about it already.

Eugene

@JasperLoy and the other half are written by genius awesome authors?

Frank Science

@JasperLoy Some are good.

user19161

@Eugene Yes, but still I am not the type to read such books.

user19161

6:32 AM

@FrankScience Yes, books are just like food. Some are good, some are bad.

Eugene

@JasperLoy and both are edible.

user19161

@Eugene Yes literally and metaphorically.

Frank Science

@JasperLoy Incidentally, where's your high school? (nationality)

user19161

@FrankScience Singapore.

Frank Science

@JasperLoy Cool.

@JasperLoy Did you take part in mathematical competitions?

user19161

6:37 AM

@FrankScience I have many secrets I don't share here, but country is OK to share.

Frank Science

@JasperLoy Sorry.

user19161

@FrankScience Why are you saying sorry? :-)

Frank Science

@JasperLoy I asked about your secret. It's somewhat impolite.

user19161

@FrankScience Erm, not really. I am not really good in math.

user19161

@FrankScience That's not a secret. You can ask me anything you want, I may or may not answer but I will never lie.

Frank Science

6:38 AM

@JasperLoy Thanks.

user19161

What about you @frank? Do you take part in math competitions?

Frank Science

@JasperLoy Yes.

user19161

@FrankScience IMO?

Eugene

@JasperLoy i thought you were a grad student no?

user19161

@Eugene I'm not a grad student, but I might be in future.

Frank Science

6:41 AM

@JasperLoy There are only 6 students in China who is able to take part in IMO.

Eugene

@JasperLoy are you in the NUS?

user19161

@Eugene I'm not a student now. Finished undergrad long time ago.

Frank Science

@JasperLoy I find that most students are clever than I.

@JasperLoy Those who took part in MO.

Eugene

@FrankScience in your opinion only 6 students in china are able to take part in math competitions? =P

Frank Science

@Eugene No, I meant IMO.

Eugene

6:43 AM

@FrankScience yes, in your opinion.

user19161

Among the people on MSE, so far I only shared my secret with Ben.

Eugene

that's what i said

Frank Science

@Eugene No, IMO is abbreviation for International Mathematical Olympaid.

Eugene

@JasperLoy that you are in fact batman?

user19161

@Eugene No, Jonas is Batman.

Eugene

6:43 AM

@FrankScience yes i know. i was just trolling

@JasperLoy ah. then you are the joker.

user19161

Maybe I'll share my secret with others in future too if I feel like it.

user19161

@Eugene You must be Catwoman.

Frank Science

@JasperLoy In MO the problems are elementary but a bit tricky.

user19161

@FrankScience What do you mean by elementary?

Frank Science

@JasperLoy It's exactly high-school mathematics.

user19161

6:46 AM

@FrankScience Ah yes I know. I just wanted to know what you were thinking.

Eugene

@JasperLoy well only the joker knows batman's identity. so the logical conclusion is that you are the joker

user19161

How did the triangle question get three answers in a minute or so?

Frank Science

@JasperLoy So it's very impossible for me to get a good idea of mathematics.

user19161

@FrankScience Well, you may get a good overview by browsing The Princeton Companion to Mathematics edited by none other than Timothy Gowers.

Frank Science

thx.

user19161

6:51 AM

But I'm not asking you to buy the book. Don't waste your money on such things while you are a student.

Frank Science

I know.

And buying is impossible.

Only a few English books are available.

anon

@Eugene I just remembered a question I had before you were around in chat.

Is there a name for an $x\in\Bbb Z_p$ such that its truncation to $\Bbb Z/p^r\Bbb Z$ results in a primitive root, for every $r$? What's interesting is that every p-adic integer can be approximated arbitrarily well by powers of any partciular such p-adic.

user19161

@FrankScience If you have all the money in the world, you can ship them from amazon.com. Note the if part.

anon

I guess the same idea applies to $\Bbb F_q[[T]]$, mod various $T^{\large q^r}-T$...

Eugene

7:11 AM

@anon i've never heard of a name being given to such an object but i imagine it'd be somewhere along the lines of "ultra-mega primitive root"

anon

heh heh

Eugene

sorry.

anon

I wonder if they could have uses in approximation of p-adic integrals...

Frank Science

9:52 AM

Why notation $\partial z/\partial x$ is mostly used?

anon

as opposed to..?

Frank Science

$\partial/\partial x=D_x$, but the second one seems easier to write again and again.

Martin Sleziak

Many people write $f_x$ instead of $\frac{\partial f}{\partial x}$.

And $f_{xx}$, $f_{xy}$ etc.

Frank Science

Here's one exercise, where writing $\partial/\partial x$ is horrible:

$$x^2\frac{\partial^2w}{\partial x^2}+y^2\frac{\partial^2w}{\partial y^2}+z^2\frac{\partial^2w}{\partial z^2}+yz\frac{\partial^2w}{\partial y\partial z}+zx\frac{\partial^2w}{\partial z\partial x}+xy\frac{\partial^2w}{\partial x\partial y}=0$$

Substitute $(x,y,z)$ with $(t,u,v)$.

Write the transformed equation.

It's very horrible to write $\partial/\partial x$, etc, again and again. You can try it.

Jonas Teuwen

@MartinSleziak I write $\partial_x f$.

Never $f_x$. Seems like a component to me! 8-).

Frank Science

10:02 AM

I was writing $\partial/\partial x$, etc, again and again, until I decided to stop.

Jonas Teuwen

Me too. I was like bloody monkey, what is the difference if I just write $\partial_x^2$ or whatever? Nothing!

Then I took a Sobolev space course, and there they did the same. Good.

Frank Science

Try the preceding exercise with your notation.

David Wheeler

you know what i hate? i hate it when i google some math topic, and it links to a forum post that looks promising. i go to the the forum, and then discover i wrote the post, and don't remember it at all.

Jonas Teuwen

@FrankScience There is not really a problem? Then how do you write it?

Frank Science

@JonasTeuwen eh?

Jonas Teuwen

10:05 AM

$D_\alpha$ is more like for multiindexed differential operators.

Anyway: lunch! Be back soon.

David Wheeler

in some book i read, the partial wrt the first variable was written $D_1f$

i think that is even better than $D_xf$

Frank Science

Try this

David Wheeler

i think that writing $\partial f/\partial x$ encourages the confusion of a function with its value...not a terrific idea.

Frank Science

I think the computation is somewhat large.

Is it conventional that $\vartheta_z=z\dfrac\partial{\partial z}$?

Clash

10:24 AM

how can you have a function $f$ that is monotone decreasing in an interval and in this same interval, $f'' > 0$?

anon

1/x on (0,inf)

Clash

damn, thanks

anon

geometrically, f''>0 in a nutshell means the tangent lines to f are turning counterclockwise as x increases

which is still possible, obviously, when f'<0, ie f is decreasing

Jonas Teuwen

@DavidWheeler Yes, then you can use multiindices.

Clash

@anon nice, that does help me understand it! thanks!

Gigili

10:30 AM

@DavidWheeler Aaaaaaaa, David!

Clash

@anon I assume f'' < 0 means the opposite, the tangent lines are turning clockwise as x increases?

Uh-oh, gotta run.

@Clash yes

cool, thanks!

f' is the slope of the tangent lines, so f''>0 means the slopes are increasing, which amounts to counterclockwise turning

Jonas Teuwen

10:31 AM

@anon Scary things you are talking about... these stacked primes and stuff. Just like pointer-pointers.

Clash

@anon nice, I was trying to write exactly that here, but you summed it up much better than me

BenjaLim

11:53 AM

@anon I am worried

that because of all of the algebra overload

anon

I often worry.

BenjaLim

when doing all this algebraic topology stuff

My visual thinking is completely out

I am thinking in terms of everything algebraically

should I be worried? @anon

anon

dunno :<

BenjaLim

hmmm

@Eugene should I be worried?

Eugene

@BenjaLim why?

BenjaLim

11:57 AM

@Eugene look what I wrote above

Eugene

@BenjaLim i know i saw. do you need visual thinking for AT?

BenjaLim

maybe yes

Eugene

@BenjaLim well like i said i've never done AT so i'm not an authority to ask on this

BenjaLim

ok

Eugene

sorry

Old John

12:16 PM

Hi folks

Mark Dominus

12:47 PM

Good morning. Does anyone here know enough about formal semantics to be able to tell me if the raven paradox is resolved by Angelika Kratzer's theory of "if" as a modal modifier instead of as a two-place operator?

I see that se.philosophy does not have a "semantics" tag, which is worrisome.

Old John

@MarkDominus Sorry Mark - formal semantics is not my area :-(

Mark Dominus

1:04 PM

Well, I threw it onto se.phil anyway, although I don't expect much.

Henning Makholm

@anon: would you consider voting to undelete this question so we can close this repost without work shown as a duplicate?

Ragib Zaman

1:35 PM

Hi all.

$$ \huge \text{IS ANYBODY OUT THERE?} $$

Mark Dominus

Bon jour.

Ragib Zaman

Anything interesting happening?

Jaakko Seppälä

I was asked what is a geometric intuition of a curve with negative arithmetic genus. Can anyone help me?

Ragib Zaman

Certainly not me unfortunately.

The "T"s that MathJaX renders are slightly too short.

vastutsav

3:42 PM

hi

finite

4:49 PM

Hello

Mats Granvik

yes, hello

finite

Does anyone know why the pullback of a short exact sequence of locally free sheaves on a curve to a smooth one is still exact?

I think, it because of vanishing of Tor on a smooth curve but I dont see how to connect Tor with pullback. Perhaps that's the question.

ok, its not so hard to see

unNaturhal

5:19 PM

Hi guys!

Could someone help me to study a function?

robjohn

5:48 PM

@RagibZaman Listening to Pink Floyd?

N3buchadnezzar

6:11 PM

@robjohn Its awesome!

robjohn

@N3buchadnezzar When I saw Ragib's large message, I heard Pink Floyd :-)

N3buchadnezzar

@robjohn Comfortably numb =)

robjohn

@N3buchadnezzar Isn't that "Is there anybody in there"?

N3buchadnezzar

It is, therefore I did not asking him whether it was from that song or not. But Ragib`s message reminded me of that song-

unNaturhal

6:30 PM

"All in all you're just a...nother brick in the wall!!"

Mark Dominus

@robjohn It's both.

user19161

@unNaturhal What function?

user19161

I only know the zero function well.

Mark Dominus

Zero functions are closed under addition, multiplication, and composition.

They also form a vector space over the reals.

user19161

It's also a linear map.

Mark Dominus

6:45 PM

And it the unique function that is both even and odd.

unNaturhal

@JasperLoy $$y = e^{x-|x^2-x|}$$

user19161

You know everyone is bored when chat degenerates to this.

unNaturhal

To this.. what?

user19161

@unNaturhal To talking crap.

unNaturhal

@JasperLoy ...

robjohn

7:41 PM

@JasperLoy I have trouble fully factorizing it.

I have obviously seriously misjudged this question :-D

user19161

7:58 PM

@BenjaLim There are many things I can't visualize too. Don't worry. Not everything is meant to have a geometric interpretation.

user19161

@robjohn Hmm, of all the people in this room, I like your humour the best. :-)

Dylan Moreland

@robjohn Animations are always popular.

robjohn

8:17 PM

@DylanMoreland The other answer had outdone mine by 6:1. two more votes have been cast now, so it is not so one-sided. It seems that the descriptive answer beats the mathematical answer there.

N3buchadnezzar

@robjohn I felt so distant when a college teacher said that parametric equations was far to abstract for his class..

robjohn

@N3buchadnezzar That is really strange. Even in High School we did parametric equations.

N3buchadnezzar

8:32 PM

Exactly

I guess I need to turn the "Fate in the human race lever" another notch down.

Matt N.

8:51 PM

@DylanMoreland Hi Dylan, are you there?

I'm asking because I just posted an answer about something I recently learned (today, so I'm still a bit shaky) and I was hoping you might have a look.

It's this thing here.

Mark Dominus

@robjohn The question was about the human perception, which your answer addresses only obliquely, if at all. You needed to have a section explaining how the mathematics can be interpreted to give an answer about what the noise sounds like.

Matt N.

Haha! Mark Dominus' pinned message made me lol just now.

Mark Dominus

Also, you treated the specific phenomenon of beating, but the question wasn't asking specifically about beating.

I think what you wrote is a really nice answer to a different (and probably better) question than the one that was actually asked.

Peter Tamaroff

@MarkDominus I think that question is not really math related.

Mark Dominus

It has 87 views and no votes to close.

My own view is that Matthew Conroy hit the nail on the head: "we hear both frequencies, not some sort of average of the two."

Peter Tamaroff

9:08 PM