Mathematics - 2015-04-19 (page 3 of 4)

12:01 PM

@Rememberme I told you if you saw that before deletion

When i first came here it was soo mathy....when I came I saw mike ted and Pedro were debating on some topological question it was soo mathy those days @Incurrence I saw it

Incurrence

@Rememberme Is this not your only account?

Remember me

I came with the name sayan I just changed it few days ago

I don't know what has happened to it these days

Incurrence

@Rememberme You mean 'not-math-chat' wise?

I guess people met eachother

Remember me

Yes not math chat wise

What do you mean by that

Incurrence

12:05 PM

Well if we came in, asked a math question, and then left, it may seem rude

So people talked about non-math and got attached to one another to some extent

Remember me

Well I have this bad feeling that this chat will die down slowly.......

Incurrence

@Rememberme It seems to be growing though

@Rememberme 36 people here

Remember me

Ya but only for now.....

Incurrence

It'll get mathy again

Remember me

I really miss David Wheeler

The question answerer

Incurrence

12:09 PM

I also miss David

He was incredibly helpful and seemed to be a genius

Remember me

I know I did disappear from chat for few weeks but David Wheeler has not been here from nearly a month......

Incurrence

Last seen 12 days ago

Remember me

He was the unsung genius of the chatroom@Incurrence

Well this chat has made some potentially big changes in my life.......
Like turning me into topology that's the biggest change this chat room made in my life

Incurrence

It got me started on textbooks

Remember me

You know how I came into topology?

lol.....

Incurrence

12:19 PM

What, that we deleted so much?

Remember me

Yup

Incurrence

Are you studying right now?

I am working on complex analysis

Remember me

Then you will be coming up against the zeta function right ?

Incurrence

No

Not at all lol

Remember me

Well Theodore W gamelin is a complex analysis book which has the zeta function @Incurrence

And if I am not wrong the statement of the Riemann hypothesis has something related complex analysis and complex numbers

Incurrence

12:23 PM

Yes indeed

But I haven't worked with it yet

Remember me

And hence comes the zeta function

It is very fascinating....... It is what made me interested into mathematics when I was in 6th grade.....@Incurrence

How old are you now?

I think 14.......

You think?

This may I will be 15

Your birthday is in may....?

When?

@Incurrence I might be talking big names here but you have come across Julia set and Mandelbrot set right ?

Incurrence

12:31 PM

Indeed

I haven't really worked with either though

Remember me

Oh great.....they are pretty great fractals

You have started topology?@Incurrence

Incurrence

@Rememberme Point set, yes

@Rememberme And a little measure theory

Remember me

You require measures for it......?

Incurrence

My measure theory was for functional analysis

I wanted to read some background on $L^p$ spaces

So I could understand the $p-\operatorname{norm}$ better

Remember me

Oh.....but why are you solo scattered ....I mean to say that you are doing complex analysis,a bit of point set then you did measures......what I was always told that you should finish on then go to another right?@Incurrence

Incurrence

12:37 PM

Well I am in uni

Taking functional analysis, complex analysis and algebra

Functional wants me to learn point set and had some measure theory stuff, complex analysis is complex analysis

Remember me

Three amazing topics......

Bit I am still in with algebra.....this is going to take some real time

Well @Incurrence you did groups right?

Incurrence

Doing them now

Remember me

I have a question......

Incurrence

shoot

Remember me

How do you use generators and relations to define a group ?

It is there in my book but I don't get it.....

Incurrence

12:41 PM

That is a presentation you refer I imagine

Remember me

You can explain me in terms of dihedral groups

Incurrence

@Rememberme I can't rigt now sorry, you can ask someone else, or I can explain on thursday

I have exam in two days and assignment in 3

Remember me

Ok fine good luck

Incurrence

But most of all I am super tired ahaha

Check that though en.wikipedia.org/wiki/Dihedral_group#Equivalent_definitions

ᴇʏᴇs

@Incurrence

Remember me

12:47 PM

Hi @ᴇʏᴇs

How are you

ᴇʏᴇs

@Rememberme I don't remember you

Incurrence

He is Sayan

With the pink avatar

ᴇʏᴇs

@Rememberme Why did you change your username

Remember me

I am sayan

Incurrence

So you won't remember him

ᴇʏᴇs

12:49 PM

lol

Remember me

Just felt like....

ᴇʏᴇs

@Incurrence Did you guys already do integration in complex

Incurrence

@ᴇʏᴇs Nope, about to soon though

This week I would say

Remember me

Contour integration....wow

ᴇʏᴇs

Yea we did contour integration a couple weeks ago

Incurrence

12:51 PM

What week are you in, and how many weeks are there?

We are on 7/16 I believe

Remember me

@ᴇʏᴇs is it complicated

ᴇʏᴇs

@Rememberme No, the things we learn are fairly simple since this is an introductory class

We are on 10/16

Incurrence

@ᴇʏᴇs So pretty much same rate I guess

Remember me

So how do you integrate in complex....just the gist

Incurrence

@Rememberme I think you take a parametrisation around the singularities is the gist of it

Remember me

12:55 PM

Okay.

ᴇʏᴇs

I have one question on my homework I'm unsure about but the prof. explicitly said we can't share it outside of class

Remember me

Is it some kind of a secret method @ᴇʏᴇs

ᴇʏᴇs

@Rememberme Yes

Will Hunting

@ᴇʏᴇs @Incurrence Hello.

ᴇʏᴇs

Hi @JasperLoy

Incurrence

1:00 PM

Hello William

We have 37 chat members

Remember me

Why did he say not to share it outside the class....pretty weird....because I have always heard that mathematicians work in collaboration

Hi @WillHunting

ᴇʏᴇs

@Rememberme Bcause he doesn't want us to get help from other people

Remember me

Oh got it now .....

Good luck on it @ᴇʏᴇs

Will Hunting

@Rememberme Hi Sayan.

ᴇʏᴇs

@JasperLoy how did you know it was him

Will Hunting

1:03 PM

@ᴇʏᴇs I know everything. I just pretend not to know some things.

Remember me

He is will hunting @ᴇʏᴇs

ᴇʏᴇs

Oh

Will Hunting

I am thinking of not coming to this room anymore, still thinking.

Remember me

I think Julian Rachman will also have the same reaction as @ᴇʏᴇs

Why @WillHunting

Will Hunting

@Rememberme I talk too much rubbish and many people dislike me.

@Incurrence 39 now.

Incurrence

1:07 PM

The number of people here is disturbing me for some reason

@WillHunting I have also considered this

It is one of my greater sources of procrastination

anonymous

How do I find the factorial of a decimal?

Will Hunting

@Incurrence I did not feel disturbed but now I am.

Henrik

@anonymous:as in ½!

anonymous

Yes.

Will Hunting

@Incurrence Why do you think so many are here?

Henrik

1:10 PM

In that case you need some extension of the factorial to the reals, the one used most often (by far) is the gamma function

I believe wikipedia has an article on it, and there are several questions (with answers) on here

Incurrence

@WillHunting No idea

But I am tired as f

Will Hunting

@Incurrence I think I come here mostly to talk to you and @ᴇʏᴇs.

Incurrence

@WillHunting It's probably good to be exposed to the math though?

Will Hunting

@Incurrence Why were there so many removed messages?

Incurrence

Reasons

Will Hunting

1:16 PM

@Incurrence I don't need to be exposed to it. I know enough math.

@ᴇʏᴇs Have you considered not coming here anymore?

Incurrence

@WillHunting But you haven't been exposed to everything, like path homotopic equivalence

Just fun little things

Will Hunting

@Incurrence Well, that's what you think. =)

Incurrence

Oh okay hahahaha

You were DavidW and then you stopped coming here

Will Hunting

No, I am not David.

ᴇʏᴇs

@JasperLoy No

Incurrence

1:21 PM

Secret safe with me JL

aka

DW!

Will Hunting

I am Will Hunting.

Every day, I hunt for the will to solve my problems.

That is what my name means.

@ᴇʏᴇs Yesterday when you asked me my birthday I thought you wanted to give me a present LOL.

@Incurrence DW never came here regularly anyway.

Incurrence

But he was awesome - he has been coming here for 3 years periodically. So he must be a secondary account

Will Hunting

The nature of this room has changed a lot over the 4 years I was here.

People come and people go.

Incurrence

Yes I can imagine, and likely a bad way

Will Hunting

Yes, a bad way, because it is more serious now.

@Incurrence The answer to why there are 38 users in this room is because they forgot to leave the room.

@Incurrence In the past, we used to talk much more rubbish and there were much fewer flags.

Incurrence

1:32 PM

@WillHunting What really? It is more serious?

2

Will Hunting

@Incurrence Yes, indeed.

Incurrence

@WillHunting But it autoleaves after 10 minutes if you turn off your pc, and very few people leave the pc on 24h

Oh wtf

They changed the chat system

Seen 9h ago

Will Hunting

@Incurrence Well, many people use their school computers, LOL.

Incurrence

Wow they changed the system

It no longer autokicks

Only 14 are in here

12

9

Will Hunting

@Incurrence You can be a private investigator, LOL.

Incurrence

1:35 PM

11 is the correct count

Will Hunting

I miss some friends I had in here. They left the site long ago.

@Incurrence Your textbook challenge is too challenging. Don't have to follow my list, which I might change anyway. Read what suits you best.

Incurrence

brb shower

Ted will be on soon lol

robjohn

1:48 PM

@Chris'ssis what's the news?

@Incurrence autokicks?

Will Hunting

@ᴇʏᴇs @Incurrence I think maybe I won't come to this room anymore. I may still hang out in room 168 and we can still email. Bye.

robjohn

@MikeMiller I don't know if I've ever "left" this room, but most other rooms I do.

ᴇʏᴇs

@JasperLoy :(

robjohn

@WillHunting why not?

A.P.

2:06 PM

Hi all. If you think this answer to an old question is correct, could you please upvote it, so that I can flag this exact duplicate? (I only need one, as far as I understand, though more are of course welcome)

Incurrence

It use to autokick peoplke when not 'seen' for 10 minutes or some close number @Robjohn

E.g. you need to leave your computer on

Now it doesn't kick people for a longer amount of time, or ever

The change happened 11hours ago I would conjecture

@Robjohn

Happening to all chat rooms it seems

robjohn

@Incurrence As long as my computer is connected to the room, I stay connected. If I turn my computer off, I will be disconnected. I assume these people still have their computers on.

Incurrence

@robjohn They don't though

Since otherwise we get 'seen 1m ago' over and over

Whereas it has seen: 10h ago and they are still there

And there is 38 of them lol

robjohn

@Incurrence There have always been people who show long times in the seen 1h ago

Incurrence

Hmmm perhaps I never noticed

ᴇʏᴇs

2:18 PM

My computer is off right now

robjohn

@ᴇʏᴇs good try ;-)

ᴇʏᴇs

hehe

Incurrence

@robjohn Have you ever seen so many users online here at one time?

robjohn

@Incurrence Yes, but not recently. When I started there would be large numbers of people here.

@ᴇʏᴇs I don't see any of your questions closed recently.

@ᴇʏᴇs Oh, it was deleted by Community.

Incurrence

@robjohn How do I find all solutions $z$ to $\cos z = i$?

Semiclassical

2:26 PM

@Incurrence: the substitution $x=e^{i z}$ may be useful, if you know euler's formula for cosine

Incurrence

$$\cos z = i$$
$$\frac{e^{-zi}+e^{zi}}{2i}=i$$
$$e^{-zi}+e^{zi}=-2=2e^{i\pi + 2\pi k},\quad k\in \Bbb Z$$

robjohn

@Incurrence Solve $e^{iz}+e^{-iz}=2i\iff e^{2iz}-2ie^{iz}+1=0$ with the quadratic formula

Incurrence

Is that for $\sin$ above?

Sorry I asked a similar question yesterday

I am confused robjohn

Oh damn

I see

I thought the denominator in both cases was 2i

Chris's sis

2:53 PM

What can we say about the maximum possible area of the rectangle below?

and what happens with that maximum area divided by the angle $\theta$ when $\theta \to 0$?

r9m

@robjohn AWESOME!! :D

@Chris'ssis if you have an elementary solution to that ... I'll worship you on a sinking war-ship ! :D ;)

2

Chris's sis

@r9m Yes, I have. :-))))) (I wonder why ... maybe I'm just lucky)

r9m

@Chris'ssis then be prepared to be worshiped under said conditions :P Awesome!!

Chris's sis

@r9m :-)))))))))))

David Wheeler

3:26 PM

i may lose my connection at any moment

Chris's sis

3:54 PM

Test for convergence$$\sum _{n=1}^{\infty } \frac{1}{\displaystyle \frac{((2 n)\text{!!})^2}{((2 n-1)\text{!!})^2}-1}$$

Well, maybe it's too easy though ...

One is allowed to only use high school tools (anything about Stirling's approximation, say)

Cortizol

Hi @DanielFischer. One question: if we have some family $\{f_{i}\}_{i \in I}$ of entire functions and we know that for every $z \in \mathbb{C}$ set $\{f_i(z)\}$ is countable, is it then also $I$ countable?

Daniel Fischer

@Cortizol Not sure. I think I have seen a counterexample, but I may misremember and it was a counterexample to something similar but different. I'm off to cook dinner in a moment, but I'll try to remember what it was.

Cortizol

@DanielFischer Ok. Thank you.

Mary Star

4:16 PM

Hello @robjohn @DavidWheeler !!

We have the initial and boundary value problem $$u_t=u_{xx}, 0<x<\pi,t>0\\u_x(0,t)=u_x(\pi,t)=0\\u(x,0)=f(x)$$

We are looking for solutions of the form $u(x,t)=X(x)T(t)$.

$X'(0)=0\\X'(\pi)=0$

$u_t=u_{xx} \Rightarrow \frac{T'(t)}{T(t)}=\frac{X''(x)}{X(x)}=-\lambda$

$X''(x)+\lambda X(x), 0<x<\pi\\X'(0)=X'(\pi)=0$

$T'(t)+\lambda T(t)=0, t \geq 0$

Why do we take at the last two lines $0<x<\pi$ and $t \geq 0$ respectively ? Why do we take for $x$ as at the problem an open interval and for $t$ we take greater or EQUAL to 0 ??

evinda

4:28 PM

@DanielFischer I want to write an algorithm that runs in time $O(|V| \cdot |E|)$ and calculates the transitive closure of a directed graph $G=(V,E)$. Could I show you what I have tried so that you tell me if it is right?

@DanielFischer That's what I have tried: pastebin.com/6hQC8XHD

ADG

4:48 PM

anyone in for a friendly talk

ᴇʏᴇs

Depends how friendly

Chris's sis

@r9m @robjohn have you seen this one? $$\int_0^1 x^x +(1-x)^{1-x} \ dx \ge \sqrt{2}$$ A simple solution is required.

ADG

@ᴇʏᴇs LOL

@Chris'ssis @Chris'ssis @Chris'ssis @Chris'ssis @Chris'ssis little buddy do you know AM,GM HM?

ᴇʏᴇs

lol

ADG

lolly pop

@Chris'ssis $\int_0^1 x^x+(1-x)^{1-x}\ge(1-0)\min(x^x+(1-x)^{1-x})=1*\sqrt2=\sqrt2$

@Chris'ssis reply

Chris's sis

5:02 PM

@ADG OK

@ADG If I ask a question it doesn't mean I don't know how to answer it (btw).

Semiclassical

hi chat

@Chris'ssis: working on any interesting integrals lately?

user314

Why does AmWhy have 1 reputation?

Semiclassical

5:17 PM

per the top of that page, apparently their account has been suspended

oof, and for a year

Chris's sis

@Semiclassical I told you I discovered a new integral representation of the catalan's constant? I just worked on different versions of that integral.

Semiclassical

if you did, i'm afraid i'm forgetting

ah

Chris's sis

@Semiclassical I discovered it yesterday.

Semiclassical

ahh

neat

Chris's sis

@Semiclassical I think to publish it, or to add it to my book without publishing it ...

Not sure what to do now.

Semiclassical

5:21 PM

yeah, dunno how that all works

plus there's always the nagging worry that it's been done -somewhere- in the last few hundred years of mathematical literature

Chris's sis

@Semiclassical Sure. I did a lot of reserach for it, and found it in no other part.

Semiclassical

ahh

what kind of an integral representation is it, out of curiosity? (i'm fine with generalities rather than details)

Chris's sis

@Semiclassical double integral involving trigonometric functions.

Semiclassical

ah

Mary Star

In my notes there is the following:

Periodic conditions:

$\exists T$ period, $f: \mathbb{R} \rightarrow \mathbb{R}$
$f(x+T)=f(x),\forall x \in \mathbb{R}$

$\lim_{x \rightarrow T^{-}} f(x)=f(T)$

$I$ per. $T$
$\forall x \in I \Rightarrow x+T \in I$

Coud you explain to me what the last two lines mean?? @DanielFischer @robjohn

Semiclassical

5:31 PM

oh, a practical Mathematica question for you. do you know much about how to make NIntegrate run as efficiently as possible?

Chris's sis

No, I don't.

Semiclassical

nuts. thought i'd ask.

Chris's sis

I'm out to bring some food to needed people. BBL (in 1.5-2 hours)

Semiclassical

later

robjohn

@MaryStar They're your notes. What were you thinking when you wrote them? I can't really figure out what you meant.

Karim Mansour

5:49 PM

hmm

hey guys

evinda

Hi :)

Mary Star

@robjohn I didn't write them... The prof gave them to us...

robjohn

@MaryStar Then you'll need to ask the prof. I can't really figure out what the last line is supposed to mean.

Mary Star

I suppose that $I$ is the domain of $x$. Does "$I$ per. $T$" that $T$ is the period??
And why would the following stand?? $\forall x \in I \Rightarrow x+T \in I$ @robjohn

AbstractionOfMe

6:29 PM

René Descartes

René Descartes (/ˈdeɪˌkɑrt/; French: [ʁəne dekaʁt]; Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician and writer who spent most of his life in the Dutch Republic. He has been dubbed the father of modern philosophy, and much subsequent Western philosophy is a response to his writings, which are studied closely to this day. In particular, his Meditations on First Philosophy continues to be a standard text at most university philosophy departments. Descartes' influence in mathematics is equally apparent; the Cartesian...

I don't understand this diagonal lemma.

Not that that's surprising considering I am an idiot compared to people who inhabit math.SE.

Remember me

This is a kind of record...... 46 people in this room now amazing!!!!

Hi @BalarkaSen