Mathematics - 2013-06-23 (page 1 of 2)

Eduardo Alan Dávalos Peña

00:03

@anon so many thanks!

anon

bbl

Peter Tamaroff

@mixedmath How is your analysis?

Alexander Gruber

00:29

@PeterTamaroff i'll note your objection. maybe some sort of early parole could be arranged with good behavior, we'll see.

Peter Tamaroff

@AlexanderGruber Thank you.

@AlexanderGruber I have a dope proof of something.

Alexander Gruber

what's that?

Peter Tamaroff

@AlexanderGruber The asymptotics of the iteration of a function.

Alexander Gruber

which function?

Peter Tamaroff

Let $0\leq f(x)\leq x$, and for $0<x<x_0$ $$f(x)=x-ax^k+bx^\ell+x^\ell \varepsilon(x)$$ with $\varepsilon\to 0$ for $x\to 0$. Here $b,a>0$ and $1<k<\ell$. Define for a fixed $0<x<x_0$ the sequence $$v_0=x_0\\v_{n+1}=f(v_n)$$ Then $$\lim_{n\to\infty} n v_n^{k-1}=\frac{1}{a(k-1)}$$

Alexander Gruber

00:44

that is really weird, @PeterTamaroff. :p

Peter Tamaroff

@AlexanderGruber Ah?

Alexander Gruber

i'm going to try it out

dfeuer

I flagged math.stackexchange.com/questions/426495/… as off-topic a while back, and my flag was determined to be "helpful". Why is the question still here?

Peter Tamaroff

@dfeuer You got a pat on the back. That's all! =)

For it to be deleted or closed a mod or high rep users must take some course of action.

dfeuer

Pats on the back are great, but I am curious how to make "helpful" flags that actually help something.

Alexander Gruber

00:50

@dfeuer i didn't review that flag but i assume the mod that did probably read the question, disagreed with the flag, but still marked it helpful because he thought it was worth considering

amWhy

Hello all...slow weekend on math.se!

Is it slow on chat, too? :-(

mixedmath

@dfeuer So I looked at the log, and robjohn cleared that flag. What I suspect is that he asked the CrossValidated mods if they wanted the question, and they said no

(which we do before we migrate things, usually)

so what you said was helpful, but... not acted on

Peter Tamaroff

@AlexanderGruber I think I will post the proof on main.

mixedmath

@PeterTamaroff ah, that is strange

the problem you ask, that is

Peter Tamaroff

@mixedmath Why?

mixedmath

01:00

@PeterTamaroff the epsilon function in particular makes it exciting or something. Dunno, just a feeling, nothing formal

Peter Tamaroff

@mixedmath Heh, the $\varepsilon$ is slightly irrelevant. I mean, we need it, yes.

But it is not the core of the proof.

Alexander Gruber

@mixedmath the $k$ weirds me out

Peter Tamaroff

01:11

@AlexanderGruber Posted @mixedmath @anon

Guys?

@user1 Hey!

user1

@PeterTamaroff Hello, there.

Peter Tamaroff

@user1 See my post above! =D

@AlexanderGruber Dude, did you see it?

Alexander Gruber

@PeterTamaroff i'm reading it atm

user1

@PeterTamaroff I am also reading it.

Peter Tamaroff

@AlexanderGruber This is the soundtrack to do analysis

Alexander Gruber

01:18

@PeterTamaroff i'm pretty sure it's this.

Peter Tamaroff

@AlexanderGruber LOL

@AlexanderGruber Check out "Bounce".

Peter Tamaroff

01:35

@AlexanderGruber So, does it look less strange now?

Alexander Gruber

@PeterTamaroff i sang that song in concert once. :p

@PeterTamaroff yeah it does

Peter Tamaroff

@AlexanderGruber You're in a band?

Alexander Gruber

@PeterTamaroff i used to be, this was a long time ago.

Peter Tamaroff

@AlexanderGruber Heh, nice!

I play the guitar. Now I'm mostly helping my brother out since he sings, so I play the backing chords and stuff.

@AlexanderGruber Today we were doing this one

amWhy

I get so discouraged sometimes...I think I'm going to have to spend less time on math.se...It has become "too" important to me (too much time) !! Okay...now let's see if I can manage that...I don't want to have to pull a "jasper"!! ;-)

Peter Tamaroff

01:44

@amWhy What be oozing your chillies?

amWhy

@PeterTamaroff hehehe I like your "lingo"! I just put too much importance/time into the site...And take too much too personally...

Peter Tamaroff

@amWhy What is "lingo"? I guess you don't mean "...a comprehensive software designed to make building and solving linear, nonlinear and integer optimization models faster, easier and more efficient."

amWhy

"lingo" is short for "language"...particularly used in the context of describing one's dialect and slang...

Peter Tamaroff

@amWhy Aha!

amWhy

@PeterTamaroff I have to watch my slang (lingo is a "slang" term)...on such an international site...I've found myself needing to explain my usage of "slang" a few times now.

Peter Tamaroff

01:50

@MarianoSuárez-Alvarez Ahoy.

@amWhy Hmm, I know a little slang, and sometimes I fish out words from my head I didn't even know I knew. It is kinda weird, because I don't speak English on a daily basis, but I have studied English for a long time, so many many stuff has sunk on meh brainz.

amWhy

@PeterTamaroff :-) (+1 for your post)

Peter Tamaroff

@amWhy Thanks.

Kasper

02:13

hi all

Kasper

02:32

hi @vvavepacket

vvavepacket

@Kasper hello!

Kasper

how are u doing ?

vvavepacket

im doing some exercises in the math book

Kasper

haha nice !

which one ?

vvavepacket

um How to think like mathematician by Houston.

@Kasper Lord_farin told me to finish this first so us to clear my mind when reading Ross works

Kasper

02:35

hm.. that may be a good idea

I'm building a math blog

vvavepacket

oh thats great

is it online?

Kasper

yes, I just finished a version that looks a little bit like something :)

euclidthegame.com/mathexchange/1.php

if you click on the menu it should move away

vvavepacket

what is this language

lemme guess

german?

let me guess kasper

Kasper

no german :p

vvavepacket

w8. i think i know this

it sounds like it came from somewhere in amsterdam

when i read it, the pronounciation sounds like amsterdammyy

Kasper

02:41

yes !! :P

that's correct

vvavepacket

:D

what is the name of language if you dont mind

Kasper

dutch

I'm from the netherlands

vvavepacket

oh glad to know that

@Kasper you rarely skype right?

it just sits on your computer

Kasper

yes, I never skype actually :p

vvavepacket

i think dutch is one of the hardest

to learn

Kasper

02:44

I don't know, I think french is most difficult

but that's me :p

vvavepacket

i think dutch is between german and english

what you think

Kasper

I think that may be correct

But what do you think about this concept:
Splitting a math book, in small parts, and making a blog of it like this.
Then you have comment section where people can help each other out to understand the math book better

vvavepacket

thats a great idea

+1 for me.

u know why?

Kasper

why ?

vvavepacket

coz people from all over the world might b reading the book, and they can be in different chaptersl. so there must be a way for them to interact chapter by chapter

says person 1 is in chap 4, person 2 is in chap 1

so person 1 can leave a comment and share something. and by the time person 2 jumps to chap 4, they can interact.

that way, records on how people treat a chapter will be save, and can be viewed later.

overall, people will go to it and add ideas.

ideas will add up, and be consolidated overtime. so new people can go and view it, and after they finish the chapter, check their answer, verify the results and share something

Maths Lover

02:51

hi

vvavepacket

hi fawzy

@Kasper what do you think

Maths Lover

hi , kasper seems to be telling you about his blog

Kasper

@vvavepacket yeah it would be awesome if things like that would happen

@MathsLover euclidthegame.com/mathexchange/1.php new update

you can click on the menu to slide away

vvavepacket

is that link intended only for dutch people

Maths Lover

yes , this is great

vvavepacket

02:52

i want to participate but can't comprehend it:9

Maths Lover

@vvavepacket , learn Dutch :D

Kasper

@vvavepacket I think in holiday I will add some english book

vvavepacket

@MathsLover arabic + dutch

Maths Lover

Cool haha!

but it seems that arabic is more difficult than dutch !

ˈjuː.zɚ79365

@AlexanderGruber I really wish that moderators would stop dismissing flags-to-close as helpful while leaving the question open. Flags to close are in a category separate from flags for a moderator attention. Questions flagged in this way automatically go into the Close Vote queue for 3K+ users, who decide what to do with them. That is, unless a mod clears the flag, preventing the peer review from happening.

One problem with moderators handling flags to close is a bias for inaction: moderators prefer not to use their binding votes (and rightly so). Leaving the flag in place allows the decision to be made by five reviewers, who are not constrained by having a binding vote.

vvavepacket

03:02

guys, whats wrong with goldbach conjecture?

Kasper

I'm going to sleep, enough work for today

Maths Lover

@vvavepacket , the wrong is that no one could prove it !

good night @Kasper

vvavepacket

is it hard to prove?

@mathslover مع السلامة

i mean, how do we prove bach?

how do we prove goldbach conjecture? what are the steps

anon

how do we perform cold fusion? what are the steps

totally serious question

I expect an answer in this chatroom

Peter Tamaroff

@anon Are you on crack?

anon

03:12

no, I am a satirical genius

Bageer

If we had the steps it wouldnt be a conjecture

Peter Tamaroff

@anon \mewikis " It has been rejected by the mainstream scientific community because the original experimental results could not be replicated consistently and reliably, and because there is no accepted theoretical model of cold fusion."

@anon BTW

vvavepacket

@peter why is that goldbach conjecture cant be prove

Peter Tamaroff

@vvavepacket What?

vvavepacket

@Peter edited

Peter Tamaroff

03:17

@vvavepacket You're telling me you read/heard "Goldbach's conjecture cannot be proven"?

vvavepacket

@Peter, sorry, i really mean whats wrong with Goldbach conjecture, why is that until now, no one can show proof for it

Bageer

Because it is hard

Peter Tamaroff

@vvavepacket I have no idea.

Maybe @WillJagy can explain, dunno.

vvavepacket

@WilJagy help us

Bandeira Gustavo

03:51

@anon lol.

@vvavepacket Someone made a proof of something related to it, no? Minor and major arcs for goldbach conjecture?

Bageer

that was the weak goldbach i think.

Bandeira Gustavo

04:33

@Bageer Goldbach without work-out.

Bageer

@BandeiraGustavo work-out?

Bandeira Gustavo

05:33

@Bageer Yes. In the poledance.

Bageer

@BandeiraGustavo In the poledance? I am not sure if it is just me, but you are not making any sense.

@BandeiraGustavo Up to any math?

anon

it worked

Alexander Gruber

06:32

@ˈjuː.zɚ79365 stop flagging questions that don't require moderator attention then. those are for questions which require urgent attention

ˈjuː.zɚ79365

06:43

@AlexanderGruber Only the first of the options says "needs moderator attention". The flags to close are the second category.

Bitrex

07:26

Goldbach's conjecture is false, there's a counterexample around 10^80

skullpatrol

08:21

@Bitrex Link please :-)

@anon Do you honestly believe Jordan deserved to be susended for an hour from the chatroom?

Bitrex

@skullpatrol I evaluated it with mah quantum computer

just checked every integer out to infinity :)

anon

no, but an hour in the chatroom is not a big deal otoh. it's the mainsite suspension that's more curious and more significant - I don't know what the reason was.

Bitrex

If Jordan hated math before, I bet he really hates it now!

anon

he's been through this cycle more times than you know. in a sense, you could say he's a veteran.

Bitrex

After years of being a "math hobbyist" I am finally buckling down and studying a real analysis text

It is pretty challenging, particularly for an oldie like me :(

Bandeira Gustavo

08:33

@Bagger It depends.

JohnDoe746

08:58

anyone around with a little CoV experience?

Patrick Da Silva

@PeterTamaroff : Sure! Let's discuss it here

BenjaLim

09:21

@MarianoSuárez-Alvarez are you around? I have a question about pure dimension

somehow I am not able to prove that if $Y$ is an algebraic set of dimension in $\Bbb{P}^n$ of pure dimension 1 and of degree $1$, then it has to be a linear variety. I know that $Y$ is irreducible though.

I can see this is true in $\Bbb{P}^2$

I tried inducting on $n$ and then like projecting onto a hyperplane

but it didn't work out

Patrick Da Silva

09:39

an algebraic set "of dimension"? Of dimension what?

BenjaLim

10:15

of dimension 1

Patrick Da Silva

ah okay :P

skullpatrol

11:24

Vivian

haha

skullpatrol

:D

Dominic Michaelis

13:20

Oh dear how emberassing

skullpatrol

huhu

Dominic Michaelis

huhu

there was a newspaper article about a nine year old who wants to go to university and study

and they said he is a over genious and they took a picture of an integral problem on a blackboard which he solved in "a few minutes" and the solution is plain wrong

look on the blackboard luzernerzeitung.ch/nachrichten/zentralschweiz/luzern/…

skullpatrol

13:38

Let him go to university and fail, lots of people do.

Dominic Michaelis

i mean how emberassing is that, when you are hyped but every freshman can see you totally failed ?

skullpatrol

I agree :D

(-:

jul8

14:15

hey, short question: considering the differential quotient $\frac{f(x+h)-f(x)}{h}$ for $h\rightarrow0$ can $h$ be negative and positive, right? And also in a neighborhoud of e.g. 1 we can't assume $h>0$, right? thanks!

Dominic Michaelis

it can be both

jul8

thx

just wanted to be sure ;)

user1

@jul8 I don't understand your second question. The limit itself has $x$ fixed.

Bandeira Gustavo

@skullpatrol "

skullpatrol "Let him go to university and fail, lots of people do." - XD XD

Bitrex

14:30

@DominicMichaelis I was watching MIT's differential equations videos a while back and according to the professor in one of the videos half the class made the same mistake on some part of an exam

differentiating instead of integrating

and in one video he asks what the antiderivative of $\frac{1}{1 + x^2}$ is and there's a dead silence for 15 seconds as nobody answers

user1

@Bitrex Makes me wonder if I have ever inadvertently made that mistake...

Bitrex

@user1 I know I have and still do!

Alexander Gruber

@ˈjuː.zɚ79365 the only time questions should be flagged to close is if they are very clear cut cases, e.g. obvious duplicates (user asks the same question over and over), contest questions, racist rants. stuff where unilateral moderator close votes are needed. normal grey area close votes should be left to the community.

Vivian

@Alexander, Laozi, the profile photo

Alexander Gruber

14:45

@Vivian haha, close. it's Yu the Great.

Vivian

@Alexander, ach so

@Alexander, very interesting. Why did you put him, nothing about math?

Alexander Gruber

15:07

@Vivian i just like the picture, to be honest. :)

ˈjuː.zɚ79365

@AlexanderGruber I agree: normal closing should be done by community, not the moderators. Which is why flags to close are not called flags for moderator's attention. They automatically put the flagged question into the Close Review, where the community of 3K+ decides what to do with them.

The flag is automatically dismissed when the reviewers vote to close. No moderator action is needed at all.

Alexander Gruber

@ˈjuː.zɚ79365 oh right you're talking about the 10k+ close flags

sure, i agree with you then.

Alexander Gruber

16:49

@Vrouvrou You have previously been instructed by multiple users not to repost links to chat to questions you have posted on main.

JohnDoe746

If someone could spare a second, ... math.stackexchange.com/questions/424903/…

@ Alexan: oh, sorry. didn't know that

Peter Tamaroff

@AlexanderGruber Success.

Alexander Gruber

@JohnDoe746 see point 3 here

JohnDoe746

AlexanderGruber: yeah, my fault. i should learn how to read. :/

Alexander Gruber

@JohnDoe746 no problem.

Patrick Da Silva

17:22

Yes

Peter?

Little Child

18:34

Can someone tell me what Taylor's Series for Complex Numbers is ??

@robjohn

robjohn

@LittleChild I am not sure what you are asking

Little Child

Taylor's Series .. what is it ???

robjohn

Taylor series

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point. The concept of a Taylor series was formally introduced by the English mathematician Brook Taylor in 1715. If the Taylor series is centered at zero, then that series is also called a Maclaurin series, named after the Scottish mathematician Colin Maclaurin, who made extensive use of this special case of Taylor series in the 18th century. It is common practice to approximate a function by using a finite number...

Little Child

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

So .. how do I calculate that for Complex Numbers ?

robjohn

@LittleChild The same way you do for real numbers

Take the derivative.

@LittleChild Do you know how to get the Taylor Series for real functions?

JohnDoe746

18:52

@robjohn i saw you had lots of tags in your profile but couldn't find CoV. Does this mean you don't like it?

robjohn

@JohnDoe746 CoV?

JohnDoe746

@robjohn calculus of variations

robjohn

@JohnDoe746 I've answered a number of calculus of variations questions. Perhaps they were mistagged.

JohnDoe746

@robjohn do you have time to look at another one? i'm not sure if i understood it

@robjohn posted few days ago; if you get bored ;)

Little Child

19:15

@robjohn No, I do not know how to do that for reals. I will learn that right away !

How do I take derivative of complex number ?

robjohn

@JohnDoe746 That question is hard to understand. The formula you are looking at is a formula from CoV, but the question about $F$ does not appear to have anything to do with CoV. $F$ is dependent on the functional being minimized and whether $F$ is convex in the third variable is dependent on the functional.

JohnDoe746

@LittleChild taylor series is a representation of a function as an infinite sum [...] you are talking about functions, not numbers here

Little Child

oops .. my bad. I meant functions :)

robjohn

@LittleChild derivatives are not taken on complex or real numbers, they are taken on functions.

Little Child

Yes, that too

functions on complex numbers

I dont seem to understand how to find limits and derivatives of these complex functions

I can do that for real functions, though :)

robjohn

19:20

@LittleChild before you learn about Taylor Series, you should be familiar with derivatives.

Little Child

I can do that on real functions. Didn't find a good resource for derivatives of complex functions

I did Google..

robjohn

@LittleChild The definition is the same $f'(z)=\lim\limits_{h\to0}\frac{f(z+h)-f(z)}{h}$

Chris's wise sister

Greetings

Little Child

Hello, sis :)

Chris's wise sister

@robjohn hi

@LittleChild hi

Little Child

19:22

oohh .. so say I have z = $a + b_i$

robjohn

@LittleChild you just need to take the limit over all complex $h$ near 0.

Little Child

and .. I need to get its derivative

that will be ?

robjohn

@LittleChild I don't see a function there

Little Child

oops..

f(z) = $z^2$

robjohn

@LittleChild use the definition

Little Child

19:24

f(z+h) = $(z+h)^2$

robjohn

what is $(z+h)^2$?

Little Child

$z^2 + 2zh + h^2$

$\frac{z^2+2zh+h^2-z^2}{h}$

$\frac{2zh + h^2}{h}$

robjohn

@LittleChild as $h\to0$?

Little Child

$\frac{2z + h}{1}$

JohnDoe746

@robjohn well, $\cal F$ is the usual functional you use. Now you know that $\cal F$ is seq. weakly. l.s.c. and we are in $\bb R$ so this is equivalent to $F$ being convex.

Little Child

19:26

yeah .. I avoided that

so .. we have limit as .. 2z...

which is the same as derivatives for reals .. ?

robjohn

@JohnDoe746 The functional depends on the variational problem being done.

Little Child

Let's go mad on this one ..

robjohn

@LittleChild why do you think it would be different?

Little Child

f(z) = $4z^2 + z - i$

is that a valid function ??

Because .. it is complex .. I assumed its solution to be complex (I mean the English complex ... tough .. tricky)

robjohn

@LittleChild yes

Little Child

19:29

so $i$ is a constant ? and derivative of a constant is 0 ?

robjohn

@LittleChild yes, you can get that from the definition

Little Child

YEEEEHAAAA !! gets his pogo stick and hops around

Can you gimme some problems to solve ? on derivatives of complex numbers ?? :)

I never expected it to be this easy, sir. I was expecting to have to rummage through a tome with some cryptic Greek symbols trying to get my head around this :)

@robjohn so by extension , integration is also the same ????

JohnDoe746

@robjohn well, "dacarogna - direct methods in the CoV" says in his Theorem 3.15, that if $\cal F$ is s.w.l.s.c. then $F(x,z,p)$ is convex in p.

Chris's wise sister

@robjohn Could you take a look on another proof of mine to a problem we discussed in the past? I wonder if there are some shortcuts to the way I used this time. I'd appreciate some feedback from your side. :-)

robjohn

@LittleChild you need to be careful. Antidifferentiation is essentially the same (with some caveats), but contour integration has other considerations.

Little Child

19:34

What on earth are those ??

@robjohn Now, derivatives have some formulas for reals .. do they apply for complex, too ?

$\frac{dx^2}{dx} = 2x$

robjohn

@LittleChild too much to go into until you know more about complex analysis. Contour integration deals with integration over paths.

Little Child

I heard in one lecture that Limits in complex functions is different from limits in reals

@robjohn

robjohn

@LittleChild for the most part. It depends on how you extend the functions to the complex numbers. But if you use polynomials, the formulas stay the same.

Little Child

hmm.. seems like I can finally get Complex Analysis into my head :)

robjohn

@LittleChild well, limits in complex numbers are like limits in $\mathbb{R}^2$

Little Child

19:37

The next lecture is on Taylor's Series for Complex functions.. I should learn that first for real functions ??? :)

robjohn

@LittleChild That is usually the way it is done

Little Child

hmm... and if I can do that on real functions, the procedure stays the same for complex functions ??

what I mean is ... I am working on reducing my steep learning curve here :)

Let me sum it up:
**derivatives** stay the same for complex and real functions *work reduced*
**Taylor's Series** remains the same *work reduced*
**integration** has its subtleties. *work*

@robjohn

Peter Tamaroff

@LittleChild Derivatives certainly don't stay the same!

Little Child

uhh ?? why ??

rules of derivatives for real functions do not apply ?? :)

Peter Tamaroff

@LittleChild Yes, but the story is very different. Let me find a question on MSE:

Little Child

19:46

find some basic one .. or a reference-for-beginners would do :)

Peter Tamaroff

Hmm... this?

This too

Little Child

Added to favorites. Will check it in the morning

getting late here :)

skullpatrol

Hi @HenningMakholm long time no see.

@HenningMakholm how are you?

Henning Makholm

20:01

Someone went through and upvoted my 5 top questions in a span of about 200 seconds. Now waiting for the serial-vote detector to kick in ...

Peter Tamaroff

@HenningMakholm Think it'll be reversed?

Henning Makholm

@PeterTamaroff Wouldn't surprise me, but I don't know exactly where the threshold is.

Peter Tamaroff

@HenningMakholm Hmm... doesn't look like something bad. You surely deserve them.

skullpatrol

Maybe someone just likes your style.

Peter Tamaroff

20:18

@HenningMakholm

JohnDoe746

Anyone of you guys interested in calculus of variations? i posted a problem a few days ago and i'm having a little trouble with it.

Henning Makholm

@PeterTamaroff Yes? Imagine I wrote something falsely modest there. :-)

Peter Tamaroff

@HenningMakholm Heh. I wonder if you know about Stokes theorem and friends.

Henning Makholm

@PeterTamaroff Hm, no, not by far. I've never really understood exterior derivatives.

Peter Tamaroff

@HenningMakholm Ah, OK.

skullpatrol

20:33

@HenningMakholm have you read the graphic novel "Logicomix"?

Kasper

21:45

hi all

Kasper

22:29

@vvavepacket Hi :)

vvavepacket

HI!

Kasper

how are you doing ?

still enjoying your math journey ?

@vvavepacket are u there ?

vvavepacket

@Kasper yes Im reading a math book.

@Kasper yes of course! enjoying it!

but I got a dilemma

Kasper

hm.. tell me

by the way, I finished my blog, it know look decent:
http://euclidthegame.com/books/LA2/H3/Sectie%203.1/1-1.php

in chrome

vvavepacket

you see Ill be completing my undergraduate as an electrical engineer. but i love math. i mean theres no way for me to become a mathematician like you

ok im checking your blog..

I mean look at you, you got a full blown math degree unlike me

Kasper

22:39

yeah, it will be kind of hard to combine, but can't you switch to math major ?

vvavepacket

i cant

Kasper

hm.. that sucks

Is the navigation working on that website ?

vvavepacket

yeah

i can navigate

Kasper

nice !

vvavepacket

:)

Kasper

22:44

I've now everything finished, to upload more books.

I can't of have the template, that will work with every book.

Now I just need to split the pdf's, and the rest works automaticly.

vvavepacket

cool

Kasper

for some reason I love to see math really big projected on my screen :)

Transcript for

$Mathematics$ Mathematics