Mathematics - 2013-03-26 (page 2 of 3)

Charlie

15:00

@DominicMichaelis haha you have me as your friend on facebook

Dominic Michaelis

i hardly remember my own birthday please don't be made if i forget yours

Charlie

@DominicMichaelis ok :P

CBenni

15:19

Someone adversed in numerical methods/numerical optimization here?

Dominic Michaelis

holy crap i thought BMS got low reputation today

as i looked in this reputation change and it was low

290 lol ...

CBenni

BMS?

Dominic Michaelis

brian m scott

awllower

BMS=Brave Method in Statistics.
Haha

Amith KK

appears

So yeah

I'm doing a math project

Dominic Michaelis

15:25

@awllower 7777 and capped today so the nice score will be there some time

Amith KK

And I've reached use of math in comp graphics

awllower

:D

Amith KK

have some sources to school level stuff?

awllower

You are then bestowed with good luck!

@DominicMichaelis Are you familiar with the calculus of variations?

I am taking a course on that, but find it quite difficult...

Dominic Michaelis

i know some very basics from physics

@awllower my students failed so hard in analysis

awllower

15:28

And then I looked up to some books on PDEs, as recommended, and I found the explanation that variational analysis is to find the minimal surfaces...
I am even confused more...

Oh, really!
Do you know why?

Dominic Michaelis

thats an application of it

Charlie

@DominicMichaelis Oh noes!

maybe it's the teacher's fault....

Amith KK

Anybody?

awllower

While I know barely anything about minimal surfaces.

Dominic Michaelis

@Charlie i mean those who i corrected, they wrote stuff like a function is exactly 2 times continuous differentiable iff it is a polynom of degree 2

Charlie

15:31

@DominicMichaelis oow

Dominic Michaelis

@awllower it was our motivating example in analysis 2 for cov, (rotation surfaces) as you have to minimize over an infinite dimensional space the normal stuff won't work there

awllower

Oh I see.

My professor said nothing about motivations...

He just started with some real analytical lemmas, such as Simple Vitali or so.
Even though I have taken a course on real analysis, I knew nothing about such "simple" lemmas...

Dominic Michaelis

we did make it with bubbles ?

i don't know what the correct english term is

if you have soap those little sphere stuff

awllower

and, in plain terms?

little sphere stuff, wha do you mean?

Dominic Michaelis

when you take a bath with a lot of soap in it

on the surface the white stuff

awllower

15:36

I see.

Amith KK

Um help :)

Dominic Michaelis

a soap bubble

awllower

So you start from that bubble problem?

Surprisingly, I found books on PDEs easier to understand than the book on variational analysis!

I thought that the order ought to be reversed. :D

Dominic Michaelis

jupp

and with cov we proved that a bubble forms itself like bobbles to if you take concentric circles between those

awllower

That is a nice starter I guess!

In any case, I am quite tired now, and I think I am going to read some diophantine equations before sleeping. Bye everyone!

Dominic Michaelis

15:43

but I really don't know if i could proof the euler lagrangian differential equations wihtout looking them up

good nigh

Jayesh Badwaik

@awllower are you studying from van Lint?

CBenni

can someone tell me why my question, math.stackexchange.com/questions/331529/classifying-the-reals deserved so much hate?

I might just rewrite it and remove all the fiddling with grammars, but then they will hate it for not defining what algebraic expressions should be

user20997

I'm looking for an article about IQ, written by some Russian mathematician

for the life of me can't find it, can anyone help?

It was a pdf file on his personal webpage I think

Charlie

@Karl'sstudents Hi!

Karl's students

15:59

@Charlie Karl's students are sleeping. This comment is automatically generated by a bot. By the way, Hi too...!

Charlie

@Karl'sstudents aah

@Karl'sstudents :D

user68578

Hello!

Charlie

@user68578 Hello!

CBenni

16:29

wow

someone just posted 4 questions to Math.SE within 30 minutes

apparently all from the same assignment sheet

Charlie

@CBenni hahahahaha

CBenni

@Charlie sup ^.^

Charlie

@CBenni :D

Ariane

16:57

Hi there! I completely forgot my maths, it seems, and I think I'm going to need to know how to do this.

http://tinypic.com/r/2801kyw/6

How do I calculate a and b (namely, the X and Y lengths of diagonal movement) ?

CBenni

$\sin \alpha = \frac{b}{36}$ ;)

Ariane

Uhm, I,m sorry but I don't understand anything in that equation.

CBenni

ouch.

soo

are you still in school?

Ariane

What are dollar signs and backslashes ? And frac ? And {}

?

CBenni

oh

56

A: Should chat have TeX support?

I will leave the original post for historical reference, but as mentioned in the Update below, all four bookmarks are located on this installation page. There are four bookmarks: start ChatJax installs MathJax and starts a loop that renders $\LaTeX$ as needed. This is intended for use in chat, ...

Ariane

17:03

Could you write it to me normally? ._.

CBenni

I wrote my answer in latex

sin 15° = b/36

and cos 15° = a/36

Ariane

Sheesh, okay. I think I completely forgot the function of sin and cos outside making a wavy graph. Math is so far away. D:

CBenni

multiply both sides by 36 and you get your result for a,b

why is it? Maths is cool ^.^

Dominic Michaelis

@Cbenni i guess ariane is just far away from beeing cool ;)

caveman

good monring

Dominic Michaelis

17:06

hi

Charlie

@caveman Good afternoon

caveman

@DominicMichaelis, do you know heisenbergs inequality

Dominic Michaelis

i am afraid i don't know

Ariane

Well, the last time I did that kind of maths was in secondary 5... 5 years ago. And the little bit of college maths I did before changing programs were differentials and integrals. Which I barely remember.

Dominic Michaelis

thats no math thats calculus

Ariane

17:09

How is calculus not math?

THat's like saying optics is not physics. oo'

Charlie

@JayeshBadwaik

Dominic Michaelis

@ariane a bobby car as 4 wheels so does a racing car, still you can't compare them

Ariane

@Dominic Michaelis Both are cars, no?

Dominic Michaelis

not really zentapher.com/wordpress/wp-content/uploads/2007/03/…

Ariane

I'm pretty sure that strictly speaking, mathematics is the big category that includes algebra, arithmetics, probabilities, and everything that includes playing with numbers in a theoretical way.

Charlie

17:13

nnnnnnnnooooooooo

Tobias Kildetoft

yeah, calculus is definitely also math

Charlie

you didn't say that!

Dominic Michaelis

big categories does have classes not sets :D (sry an insider)

Charlie

@DominicMichaelis badumtss

Dominic Michaelis

oh i guess i am very unfriendly i am afraid, @ariane the math you are doing in university is much more than numbers

Ariane

17:18

@Dominic Thanksfully I won't do that. If I had completed it, the integrals ocurse would probably have been the limit of my patience and understanding.

caveman

LOL

Charlie

maaaaaan

I think you are in the wrong neighbourhood

Dominic Michaelis

me ?

Charlie

@DominicMichaelis no

caveman

Charlie

17:22

hmm......@κρανί still didn't appear :(

@DominicMichaelis Know what's odd to me?

Dominic Michaelis

that 2 is the oddest prime ?

Charlie

@DominicMichaelis odd to me is numbers that are not divisible by two

Ariane

Aaaaanyway. I'll be off. Thanks for the answers.

Arkamis

morning all

caveman

hi

Charlie

17:35

@Arkamis Hi Ed

CBenni

@DominicMichaelis they forgot actual maths in that gag

we are suprised if a explicit formula appears anywhere

Dominic Michaelis

yeah but i thought you get the point

CBenni

xD

Dominic Michaelis

non mathematicans don't see math if they stand right before it

4

Alexander Gruber

so i'm trying to write this exam problem

CBenni

17:42

hehe

Alexander Gruber

i'd written a quiz/homework problem "Prove $\operatorname{SL}_n(\mathbb{R})$ is normal in $\operatorname{GL}_n(\mathbb{R})$ and describe its quotient."

Tobias Kildetoft

@AlexanderGruber when you say write, do you mean you are making them, or doing them?

Alexander Gruber

meaning they have to notice that $\mathbb{SL}_n(\mathbb{R})$ is the kernel of $\operatorname{det}$, and conclude $\operatorname{GL}_n(\mathbb{R})/\operatorname{SL}_n(\mathbb{R})\cong \mathbb{R}^*$

@TobiasKildetoft i mean making them.

Tobias Kildetoft

ok

Alexander Gruber

so i want to put this on the exam, but i don't want it to be exactly the same as the one on the quiz

Tobias Kildetoft

17:45

pick a different field

what is the general topic for the class?

Alexander Gruber

it's just group theory, junior undergrad level

Tobias Kildetoft

take a finite field perhaps

Alexander Gruber

they don't know about finite fields or extensions yet. i could maybe do $\mathbb{C}$ though.

Tobias Kildetoft

or maybe do sortof a dual and ask about the center

Alexander Gruber

hm that's a good idea

Tobias Kildetoft

17:46

though I guess the quotient there is not as easy to describe

Alexander Gruber

its the kernel of some homomorphism into projective space right?

(i mean, other than the quotient space)

Tobias Kildetoft

you could also take a more tricky (but generally useful) one and ask about the quotient of the normalizer of the diagonal matrices by the diagonal matrices themselves

Alexander Gruber

that's interesting.

Tobias Kildetoft

maybe by giving them the normalizer directly as the set of monomial matrices

CBenni

@AlexanderGruber what if one of your students is in here? ;)

Alexander Gruber

17:48

@CBenni then at least they're studying ;)

CBenni

the person who made my topology exam frequents this chat too

I was hoping to find some clues xD

Tobias Kildetoft

@AlexanderGruber since that example is a special case of the Weyl group

Vrouvrou

hi

help me please

0

Q: Question on measurability of multifunction*

If $(T,\mathcal{A})$ is a measurable space , $X$ a meatrizable separable space. $F$ a multifunction from $T$ to compacte subsets of $X$. We want to prove that $F$ is measurable if $\forall C\in X$ ,$C$ closed,$F^{-1}_+(C)=\lbrace t\in T; F(t)\cap C\neq \emptyset\rbrace \in \mathcal{A}$ In my...

Alexander Gruber

@TobiasKildetoft i like that a lot actually, but i think i may make it homework. (this is an in class exam so they only have like an hour.)

Tobias Kildetoft

@AlexanderGruber ok

it can be made more or less difficult by varying how much they are given

Alexander Gruber

17:52

what do you think would make it easiest?

Tobias Kildetoft

if you tell them what the normalizer is and ask them to show that the quotient is isomorphic to the symmetric group (possibly with a hint mentioning how the symmetric group sits inside the matrix group)

@AlexanderGruber hardest is of course to just ask them to describe N_G(T)/C_G(T) where G is the matrix group and T is the set of diagonal matrices

or to ask them to show that it is the symmetric group to make it have a more precise answer

that will take a lot of work and calculations

another option is to introduce congruence subgroups of $SL_n(\mathbb{Z})$

(these are all based on doing something with matrix groups of course)

Alexander Gruber

hm, yeah. definitely a homework question i think. these guys just learned quotients maybe a month ago.

Tobias Kildetoft

ahh, then yeah

describing the normalizer and centralizer of the diagonal matrices is a good exercise, but it takes a lot of work

Alexander Gruber

i should just give them a single sheet of paper with "Prove $A_5$ is simple" written on top and let them freak out for a minute :)

caveman

haha

Tobias Kildetoft

18:01

@AlexanderGruber no, do the same for $A_6$

Alexander Gruber

hahahaha

Dominic Michaelis

a lil question if a matrix is symmetric positiv definit, every submatrix is symmetric positiv definit in the gauss elemination

Tobias Kildetoft

or even better, for $PGL_n(\mathbb{R})$

sorry, that should have been $PSL$ of course

Dominic Michaelis

is it true a matrix is positiv definit if every diagonal entry of R is positive?

CBenni

no

only for diagonal matrices ^.^

Tobias Kildetoft

18:02

@AlexanderGruber $PGL_n$ is of course only simple as an algebraic group

Alexander Gruber

"Prove $O_{p^\prime}(G)Z(J(S))\unlhd G$ for any $p$-stable and -constrained group $G$"

Tobias Kildetoft

or just ask them to prove FT

maybe one of them gets an idea that allows for an elementary and short proof

if not you can just fail them all and laugh at them

Alexander Gruber

i have nightmares that that will happen someday

CBenni

make them solve $P\stackrel{?}{=}NP$

2

Alexander Gruber

and it will be something i've overlooked thousands of times, "no that's silly FT is really hard"

caveman

18:05

@CBenni, in a group theory course :D

Alexander Gruber

@caveman hahaha

Tobias Kildetoft

@AlexanderGruber well, I am still secretly hoping that it will be possible to prove that groups of odd order are PR-groups directly without using solvability

Alexander Gruber

@TobiasKildetoft did you read the $D^*$ paper?

Tobias Kildetoft

@AlexanderGruber no

CBenni

@caveman well yeah, maybe there is a group theoretical proof?

caveman

18:07

lol

CBenni

if they find one, take it, publish it, profit

caveman

my question is getting lots of computer power thrown at it math.stackexchange.com/questions/337053/…

Alexander Gruber

@TobiasKildetoft glauberman and solomon found this new subgroup last fall which i think has a lot of promise for simplifying all that stuff

Tobias Kildetoft

@AlexanderGruber by new subgroup you mean general type of subgroup?

Alexander Gruber

right, a new characteristic subgroup in odd order $p$-groups

if i remember correctly it is the subgroup generated by all subgroups $A$ with the property that whenever $\langle A,x\rangle$ has nilpotence class $2$, $x$ centralizes $A$

Tobias Kildetoft

18:11

@AlexanderGruber and where A has class 1 or 2?

Alexander Gruber

oh right, 1

Tobias Kildetoft

interesting

Alexander Gruber

they did a big simplification of $Z^*$ with it and they're looking for a way to connect it to Stellmacher's analog for $\Sigma_4$-free groups

i've been thinking about it too, i think it's gonna be a big thing

Tobias Kildetoft

what is $Z^*$?

Alexander Gruber

it's a theorem of glauberman, related to his $ZJ$ theorem

Tobias Kildetoft

18:14

ok

not sure I know ZJ either

Alexander Gruber

$ZJ$ was essentially the first big step towards the odd order theorem

it's somewhat technical but the paper is quite well written

Dominic Michaelis

is it true that for any symmetric regular matrix $A$ in the LU decomposition $A=L U$, $U=D L^T $ holds ?

Tobias Kildetoft

@DominicMichaelis what is D?

Dominic Michaelis

an arbitrary diagonal matrix (which you get from the decompositino)

Tobias Kildetoft

@DominicMichaelis so it is not arbitrary

Dominic Michaelis

18:28

jupp a diagonal matrix such that $A=L D L^T $ holds

Dominic Michaelis

18:45

why is it possible to get up to 100 flaggs a day?

Charlie

@κρανίοπεριπολία Hi!!!

κρανίοπεριπολία

@Charlie Hi, how are you?

Charlie

@κρανίοπεριπολία I'm fine, and you???

κρανίοπεριπολία

@Charlie Fine thanks.

Charlie

@κρανίοπεριπολία good!

κρανίοπεριπολία

18:50

:)

Charlie

:D

pourjour

19:37

hi

caveman

hi

Charlie

@pourjour Hi Soufian!

pourjour

@caveman how are you?

@Charlie hi Mari

Charlie

@pourjour comment vas vous?

pourjour

@Charlie bien et toi?

Charlie

19:39

@pourjour bien bien

pourjour

@Charlie good :D

Charlie

@pourjour :)

pourjour

can someone please help with this:
if $\forall (a;b;c) \in \mathbb{Z}$ as $(a,b)=1$ how to prove that:
$(a,bc)=(a,c)$

caveman

im ok today

pourjour

@caveman great :)

caveman

19:46

bbl

pourjour

@caveman if (g|a and g|b) then g =1 isn't it?

caveman

20:11

back

@pourjour, yeah because (a,b)=1

user19161

20:22

Hey @amWhy I see you have a new avatar!

Charlie

@JasperLoy hi Jasper

amWhy

@JasperLoy Yes, but I changed back a few minutes ago!

user19161

@Charlie Hey hey.

user19161

@amWhy To what?

Charlie

@JasperLoy :)

amWhy

20:23

My blue question mark...the one just before this...

user19161

@amWhy Oh, but I think the yellow one is cuter.

amWhy

@JasperLoy You think?

user19161

@amWhy Yes, sometimes I do.

amWhy

@JasperLoy Okay...I'll change back ;-)

@JasperLoy hahahahahaha

user19161

@amWhy It's up to you.

κρανίοπεριπολία

20:24

@amWhy I liked your keyboard one...why did you change?

user19161

I just emailed the great John Lee to ask if he could include a proof of the uniformisation theorem in the second edition of his riemannian manifolds book, and he said it was too hard to be included in a book at that level!

user19161

Oh well, it must be really hard then, considering the fact that that is a GTM.

amWhy

@JasperLoy Cool!

@κρανίοπεριπολία I'll use it again...

κρανίοπεριπολία

@amWhy :-)

user19161

@amWhy I just got second editions of his topological manifolds book and his smooth manifolds book!

amWhy

20:27

@JasperLoy Wow!! How do they compare to first edition?

user19161

@amWhy Much more material. I did not buy the first edition, of course.

amWhy

@JasperLoy Good choice on waiting, then!

user19161

@amWhy Yes, the second edition of his riemannian manifolds book will only be out earliest end of next year.

Charlie

:\

κρανίοπεριπολία

@Charlie Hi

amWhy

20:29

@JasperLoy end of 2014?

Charlie

@κρανίοπεριπολία Hi

user19161

@amWhy Yes. Anyway you should just use whatever avatar you like.

κρανίοπεριπολία

@Charlie Did you get bored?

Charlie

@κρανίοπεριπολία no

κρανίοπεριπολία

@Charlie I did ;)

Charlie

20:31

oh

amWhy

@JasperLoy I just have fun trying out a few ... this one is cute, but seems kind of "silly"...maybe I'll save it/wear it when I'm in a silly mood!

Charlie

just got a bit down, suddenly

user19161

@amWhy Well, one of my all time favourites is the Justin Bieber pic.

amWhy

@JasperLoy I don't know if I remember that one?

user19161

@Charlie You need to watch Step Up then, and I just found out that Channing Tatum actually married Jenna Dewan after the movie was filmed!

user19161

20:32

@amWhy Yeah, not sure if you have seen it before.

κρανίοπεριπολία

@Charlie like I said ...obsession is not good.

user19161

@κρανίοπεριπολία How is life pal?

Charlie

@JasperLoy I already watched

@κρανίοπεριπολία what did i do?

κρανίοπεριπολία

@JasperLoy Fine thanks and you?

user19161

@Charlie Yeah I have the VCD too.

user19161

20:34

@κρανίοπεριπολία Same as always. Have you watched Step Up?

Charlie

@JasperLoy I like dance movies

user19161

@Charlie I watched it only because Channing Tatum is so cute.

Charlie

geez

κρανίοπεριπολία

@Charlie Not you, I'm talking about Arkamis and PF

user19161

@Charlie Anyway, I cannot dance at all, even though I can sing.

Charlie

20:35

@κρανίοπεριπολία ah, ok

user19161

@κρανίοπεριπολία Who is PF?

Charlie

@JasperLoy I like this

@JasperLoy pink floyd

κρανίοπεριπολία

@JasperLoy No I haven't.

user19161

@Charlie Ah, I don't really appreciate dancing.

Charlie

I love doing this

user19161

20:37

@Charlie Is that you?

Charlie

@JasperLoy no

pourjour

@Charlie angle $\dfrac{\pi}{2}$

user19161

I see that you capped yet again @amWhy.

Charlie

@pourjour yup

@JasperLoy I'll take a pic like that

pourjour

:)

user19161

20:39

@Charlie Yeah you can show me after that!

Charlie

hehe

κρανίοπεριπολία

21:17

haha

Charlie

hihi

κρανίοπεριπολία

hoho, huhu, and sometimes hyhy.

Charlie

XD

κρανίοπεριπολία

:D

Charlie

;)

κρανίοπεριπολία

21:26

};)

Charlie

O;)

κρανίοπεριπολία

XD

Charlie

:)

caveman

21:49

how to prove $$\int f(x) dx = \int \hat f(\lambda) d\lambda$$

I got it wrong

is $\hat f(\lambda) = \hat f(-\lambda)$ for real $f$?

Jonas Teuwen

22:06

Do you know the inverse Fourier transform?

caveman

I have proved $FFf(x) = 2 \pi f(-x)$

pourjour

can someone please give me some ressources about the cramer's rule and modulo like in this post

math.stackexchange.com/questions/296987/…

caveman

and $$\int F f(x) g(x) dx = \int f(x) Fg(x) dx $$

I don't get how $$\int f(x)^2 dx = \int [Ff(x)]^2 dx$$

this doesnt make sense

The Substitute

Off topic question: Is there a standard name for sets like the Cantor Middle Thirds Set? Are they Cantor-like sets? Cantor trees? Trees?

caveman

just say homemorphic to the cantor set

Jonas Teuwen

22:14

Fat Cantor Sets.

Depending on the context.

@caveman FUBINI.

The Substitute

@JonasTeuwen even if the size of the gaps between the intervals, and the number of children from each interval isn't constant?

@caveman but I don't think every tree will be homeomorphic to the cantor set

caveman

what do you mean then

The Substitute

What's the name for the generalized set for which the cantor set is an example. I.e., there is a beginning interval, say [0,1], and we break it into a_1 intervals of the same length, where the gaps between the intervals can vary. Further, the number of intervals emanating from each of the a_1 intervals is not constant.

Jonas Teuwen

@TheSubstitute In what bloody sense.

caveman

"a_1"?

I think that's still homemorphic to the cantor set anyway

just call it whatever you want

The Substitute

22:22

* a_1 many intervals.

user19161

@JonasTeuwen Hey Jonas, I miss you bro.

The Substitute

I think "Fat Cantor Sets" is what I was looking for.

Jonas Teuwen

@JasperLoy Hi!! :-))).

I just sit in the library all day.

8AM-10PM.

user19161

@JonasTeuwen And study mathematics?

Jonas Teuwen

@JasperLoy I don't study, I absorb 8-).

Yes, or sleep.

user19161

22:29

@JonasTeuwen Well done bro, I am so proud of you.

Jonas Teuwen

Thanks! 8-).

κρανίοπεριπολία

Don't they have access to wifi in there?

user19161

@JonasTeuwen I hope to meet you some day in the future.

user19161

@κρανίοπεριπολία Hmm, I should think so. All universities should have it.

caveman

How do I prove $$\int f(x)^2 dx = \frac{1}{2 \pi} \int [Ff(x)]^2 dx$$ for $Ff(x) = \int f(t) e^{-tx}dx$

pleasehelp

Jonas Teuwen

22:42

Are you fuqing joking?

@JasperLoy Yes! Perhaps that can happen, the company doctor suggested I have an intermediate stop in Singapore when I would go to Australia.

Peter Tamaroff

@JonasTeuwen What's up?

Jonas Teuwen

Nothing.

Should be for in 1-2 years.

As I am too messed right now.

But can travel around closeby, say <5000km.

caveman

@PeterTamaroff, can you help me with fourier transform

Peter Tamaroff

22:57

@caveman Dunno about it, but let's give it a try.

caveman

here math.stackexchange.com/questions/342180/…

Transcript for

$Mathematics$ Mathematics