Mathematics - 2013-02-24 (page 3 of 4)

robjohn

16:01

@Argon You mean $(3)$?

user58512

16:12

hello

Akram Hassan

Hey gus

user58512

hi @AkramHassan

Akram Hassan

what's up @user58512?

hi @robjohn?

user58512

im confused

user19161

So am I.

Orange Harvester

16:21

I am just fused having carried out too many cons.

Khromonkey

@JacobBlack what is wrong with my answer?

user19161

@Khromonkey Which one?

Khromonkey

the one about the gp

Akram Hassan

guys, Apostal or Spivak, for "really" understanding calculus?

user58512

Spivak

Orange Harvester

16:23

spivak

user19161

Why Spivak?

user58512

because i haven't read apostal

Ethereal

Spitvak.

user19161

@Khromonkey Your first sentence is already wrong, so I did not read further.

Ethereal

Apostol is better.

Khromonkey

16:26

why?

think it is correct

user19161

The form of a GP is a, ar, ar^2,...

Khromonkey

i divided by a

user19161

It is not 1, a, a^2,...

user19161

Then the writing is not clear.

user19161

Even if it is 1,a,a^2, the formula is wrong.

Orange Harvester

16:28

@Ethereal Why do you think so?
I personally found Apostol not coherent, especially in the starting. There is no big picture about where we are going. In spivak, I could predict and work out what happens in the later chapter on my own. I could not do similarly in Apostol. I found it rather, here is the stuff, and here is how to do it.

Khromonkey

is it?

user19161

Read carefully.

Akram Hassan

Apostol seems really pure

which i like

Khromonkey

its correct

user58512

its.caltech.edu/~mamikon/VisualCalc.html

loopy

Ethereal

16:30

@OrangeHarvester I found it hard.

My opinion doesn't matter, but still...

Orange Harvester

@Ethereal Spivak?

Khromonkey

$a^0+a+a^2...+a^n=\frac{a^{n+1}-1}{a-1}$

user19161

@Khromonkey That is not what you wrote there.

Orange Harvester

@Ethereal I am not arguing against you, just wanted an opinion. It is perfectly fine to like apostol too. (Your opinions matter.) :-)

Akram Hassan

:8247682

user58512

16:31

just get spivak its better

user19161

I prefer Apostol.

Khromonkey

ok, is it correct now

?

Jonas Teuwen

I have too many books.

No more storage.

user58512

@JacobBlack, why?

Khromonkey

I have too many books, I don't understand 1/4 of the books I own

My grandfather buys me math books

Orange Harvester

16:33

@JonasTeuwen Does your VPS provider give you ArchLinux for hosting?

Jonas Teuwen

You can chose or provide your own image.

Orange Harvester

Ahh cool.

Jonas Teuwen

But I took their pure Debian image.

It is a good choice for a server.

Orange Harvester

I see. Yes. I would prefer Debian too.

robjohn

@AkramHassan hello

user19161

16:34

@Khromonkey No, because the ratio can be positive or negative.

Khromonkey

what ratio?

Jonas Teuwen

There is also CentOS.

user19161

@user58512 Well, at least one gets more multivariable calculus and also differential equations and probability thrown in as well. =)

Argon

@robjohn Yes, $(3)$. I differentiated the denominator and plugged $z^\pm_k$, but it didn't simplify well for me.

user58512

I see

Khromonkey

16:35

oh, I only need it for positive a's

user19161

@JonasTeuwen CentOS does not even have TeXworks now.

Jonas Teuwen

That's perfect, I don't need it on a server.

It is a server OS.

Otherwise take Fedora.

user19161

@Khromonkey Why can't the ratio be negative?

Khromonkey

he said that the sum was positive and a was also

robjohn

@Argon Note that on the lines $\mathrm{Re}(z)=\pm\mathrm{Im}(z)$, that $\cos(z)=\overline{\cosh(z)}$

Charlie

16:38

@jacob hello, Jaspito

user19161

@Khromonkey The first term can be postivie and the ratio can be negative and the sum still can be positive.

Khromonkey

good point

user19161

Also, why use a for the ratio when the common notation is r?

user19161

Bad notation, wrong ratio, and originally wrong first line, QED.

Peter Tamaroff

@JacobBlack And there you go again.

Using QED unnecessarily. You should burn, man.

Charlie

16:40

If I want to use :) as ratio, I do

user19161

@PeterTamaroff Hehe, with you.

Khromonkey

using QED when critizising other people is sort of like having sex in front of your ex

7

Argon

@Charlie My math teacher sometimes uses smileyfaces as variables

user19161

WTF?

user19161

Well, if you ask me, be prepared for my strict criticism.

Peter Tamaroff

16:42

@Khromonkey I fail to see the paralellism.

Khromonkey

I'm only gonna break your heart.

user19161

See, after Peter asks me sth he will say bleh, then he might as well not ask me.

Peter Tamaroff

@Argon Is the teacher a he or a she?

Khromonkey

what is sth?

Charlie

@Argon yay!

Argon

16:42

@PeterTamaroff She

user19161

sth is something

user19161

sb is somebody

user58512

help

Orange Harvester

somebody is me

Peter Tamaroff

@Argon She's lonely.

Khromonkey

16:43

oh

Peter Tamaroff

@user58512 Here, have a candy.

user58512

how to find hte minimum of a function f(1),f(2) to f(1000) in pari gp??

Argon

@PeterTamaroff She is married

Orange Harvester

@PeterTamaroff and he would be?

@Argon all the more the reason to be lonely. :P

Peter Tamaroff

@Argon That doesn't mean anytinhg.

Argon

16:43

This is so unfounded :)

Charlie

I'M not understanding anything!

Peter Tamaroff

@OrangeHarvester He would be probably a pederast. But who knows...

Khromonkey

Oh, so then the question might have two solutions

Peter Tamaroff

@Charlie Good.

user19161

I suggest you study AP, GP again @khr.

robjohn

16:44

@Argon or using $(1)$ is even easier

Khromonkey

AP?

Orange Harvester

@Argon do you mean confounded?

Khromonkey

come on don't insult me

I haven't even studied gp yet

Argon

@OrangeHarvester That too haha

user19161

I am serious, it does not hurt to study again.

Khromonkey

16:44

I just took that result out of a book

user19161

One cannot fly before running.

user19161

One cannot run before walking.

Charlie

@PeterTamaroff estás borracho, Pedro?

Orange Harvester

@Charlie habla espanol, amigos?

user19161

As I always say, if you go too fast, it will all fall apart.

Orange Harvester

16:46

and if you go too slow.....

user19161

There is no such thing.

Khromonkey

but the ratio still works @JacobBlack

It's not wrong

Charlie

Slowly you go far

Khromonkey

unless a=1

Peter Tamaroff

@OrangeHarvester No estaba esperando eso.

@Charlie Not at all.

user19161

16:48

@Khromonkey What do you mean by still works?

Khromonkey

is still true

user19161

Anyway, the rest is your homework.

user19161

What is true?

Charlie

@PeterTamaroff are you sure?

user19161

If the first step is wrong, there is no need to see the second.

Khromonkey

16:49

uhm, chat.stackexchange.com/transcript/message/8247683#8247683

Orange Harvester

@PeterTamaroff I do not know anything else. :P

user19161

However, if one can reduce it to the case where the ratio is positive, then one must explain why.

Peter Tamaroff

@Charlie How can't I be sure. Listen to yourself!

user19161

But I am not saying that is the case here.

Khromonkey

what is the case?

I don't understand anything

user19161

16:51

I already told you the ratio can be positive or negative.

Khromonkey

what ratio?

user19161

The ratio of the GP.

Charlie

@PeterTamaroff some drunks claim not to be drunk, it.happens

Khromonkey

ok, i assumed it was positive

but I can check for the negative case

Peter Tamaroff

@Charlie Oh, man. When will you upload a picture of you to your facebook?

Khromonkey

16:52

but I think the answer asked for positive

you guys are friends on facebook?

Peter Tamaroff

@Charlie Hey, you're not that much older than me. Barely a year.

user19161

I have no facebook.

Charlie

@PeterTamaroff when is your birthday?

user19161

I also have no face.

Peter Tamaroff

@Charlie July the 6$^{th}$

Charlie

16:54

@Khromonkey yes

Argon

@JacobBlack But you have books!

Khromonkey

nice

user19161

@Argon There can be miracles when you believe.

Argon

@JacobBlack Hehehe

Charlie

@PeterTamaroff less than a year then

Peter Tamaroff

16:55

@Charlie When is your birthday?

Charlie

@PeterTamaroff may 22nd

user19161

Some time this year.

Khromonkey

september 2

user19161

Just announce it when your BD comes. I will be here to smash a cake into your face.

Khromonkey

@anon how is the hangover going?

user19161

16:58

@Khromonkey How do you write dates there, month or day first?

Khromonkey

day, I think its better

go from shorter to longer

user58512

why can't dates be written Jan, Feb, etc. instead of numbers - then it doesn't matter what order you write it

user19161

I like writing in this format: 03 Jun 1452

Orange Harvester

I like writing it like this:
1361725232

Charlie

@OrangeHarvester stardate...

Orange Harvester

17:02

@Charlie Hmm, mine is the number of seconds since 01/01/1970 00:00:00 UTC

stardate is cool too.

Argon

Hmm... 1361725405015
:)

Orange Harvester

@Argon cool. That is even better I think. :P

Argon

@OrangeHarvester This is Java's "System.currentTimeMillis()"

Charlie

I write 24/02/13

Orange Harvester

I write 24/02/2013 actually.

Khromonkey

17:04

I like writing in days after megan fox was born

Orange Harvester

@Khromonkey you win the contest I suppose.

Argon

I use dates from the Seleucid Era

:)

user58512

what's good about megan fox

Argon

I think "find" should be able to handle regex

Khromonkey

@user58512 everything

i can see

Orange Harvester

17:12

@Argon it does.

Argon

@OrangeHarvester Not on Windows

Orange Harvester

@Argon Windows has "find"!

Argon

Not with regex!

Orange Harvester

I mean I am surprised that windows has find.

Gigili

Hello @robjohn, I believe the linked question here is not an exact duplicate. Don't you agree?

Argon

17:14

@OrangeHarvester Of course! Ctrl-F :)

Orange Harvester

@Argon Eh, I thought you were talking about the find command on command line.

Argon

@OrangeHarvester No, no. I mean find in general, on pages and stuff

Orange Harvester

ahh I see

Argon

:)

robjohn

@Gigili They look pretty identical. They both ask for a bijection from $2^A$ and $\mathcal{P}(A)$

Gigili

17:18

@robjohn Umm, not really.

Charlie

@Argon i wanted to have ctrl+f everywhere...

Argon

@Charlie It would be handy for notes :)

Gigili

@robjohn Pfft, you're right. I was looking at another page!

Charlie

@Argon YES

Gigili

Sorry.

Argon

17:21

Hmm... It's snowing!

Charlie

@Argon cool!

user58512

17:34

I feel sleepy now

user58512

17:50

wait is it? math.stackexchange.com/questions/313114/…

Is (2) a Liouville number?

Theorem

can someone tell me if i am right ?

in the following taylor expansion .

$\phi (t)=u(tx+(1-t)y)$

i want to expand $\phi$ around $1$ .

$\sum _{j=0}^{m-1} \frac{1}{j!} \phi^j(t)$

Arkamis

18:08

Halp

anon

18:26

@Khromonkey good. woke up still drunk, chugged water, back to sleep, wake up craving french toast.

Khromonkey

what did you drink?

@arkamis how?

Arkamis

I have a complex analysis question.

anon

jagermeister, russian standard, white russian, some wine I don't remember

Khromonkey

why did you get drunk?

Arkamis

Suppose an entire function maps two horizontal lines onto two other horizontal lines. Prove that its derivative is periodic.

Khromonkey

18:29

I think robjohn is good at complex analyisis

Arkamis

There is a hint given, assume f = u+iv maps y=y1 and y=y2 to v=v1 and v=v2 with y2-y1 = c and v2-v1 = d. Show that f(z+2ci) + f(z)+2di.

anon

24 hours ago, by anon

ladyfriend's bday party tonight. otherwise, math and nostalgia.

Khromonkey

oh

Arkamis

I've got no idea where even to begin, aside from using schwartz reflection principle

anon

:-)

Waqas Ali Azhar

18:35

Is there any non real solution of cosz=1/2 ?

anon

@WaqasAliAzhar yes, if you write it using complex exponentials, multiply through you can obtain a quadratic equation

Waqas Ali Azhar

yes, by my calculations, i get only real

is that true?

anon

oh, right, 1/2 is in the range of cos. then only reals sounds right.

Waqas Ali Azhar

what about sinz=1/2?

anon

same thing no?

Waqas Ali Azhar

18:39

I am solving this, please wait for a sec

anon

the solutions to sin(z)=a and cos(z)=a are in bijection to each other according to the transformation x->pi/2-x, which preserves reals and nonreals.

Waqas Ali Azhar

exp(iz)-exp(-iz)=i

oh great

but how to do it for sin, using exponentials

again by quadratic formula?

anon

yeah

Waqas Ali Azhar

ok thank you, can i ask one more thing?

anon

yeah

Waqas Ali Azhar

18:44

what is the image of a unit circle and an open unit disc under the transformation z--> 1/z

anon

unit circle stays (since reciprocation is just conjugation on it). the image of the open unit disk is its complement (0 and the point at infinity notwithstanding)

Waqas Ali Azhar

oh so the open disc becomes the remaining part of the plane

with zero as well

anon

z->1/z is a standard way to do inversive geometry using the complex plane, in fact

Waqas Ali Azhar

i know that the exponential map is the covering of unit circle

so what i get if i apply this to only x between -1/2 and 1/2(end points also included) and y greater equals to 1

anon

I'm not doing your homework for you am I?

Waqas Ali Azhar

18:49

no

It's an exercise in the book that i am reading on complex analysis

anon

look at where each segment of the rectancle's perimeter would be sent under exponentiating, then fill in accordingly

user58512

hello

I feel lazy :(

does anyon want talk

pourjour

19:09

hi

user58512

hello

pourjour

@user58512 how are u?

user58512

I'm ok a bit confused

how are you

pourjour

@user58512 feel bad

user58512

what's wrong?

pourjour

19:11

@user58512 math's exam is coming and I still have a lot of things to do

user58512

it'll be ok

pourjour

$z^2-2sin(\alpha)z+2(1+cos(\alpha))=0$ like solving this equation in $\mathbb{C}$

user58512

19:22

I need to do some work :(

I am too lazy

@gnometorule, hello

pourjour

19:35

@user58512 me too

Khromonkey

I have tried to upvote my own answers like a thousand times

Arkamis

0

Q: Schwartz Reflection Principle -- Mapping across horizontal lines

I am stuck on the following problem: Suppose an entire function maps two horizontal lines onto two other horizontal lines. Prove that its derivative is periodic. The author supplies a hint: Assume $f = u+iv$ maps the lines $y=y_1$ and $y=y_2$ onto $v=v_1$ and $v=v_2$ with $y_2-y_1 = c$ and ...

If I could get a couple eyes on that, I'd love you all.

Khromonkey

only to have my heart broken when it tells me I can't. Allthough for a second I feel great because the number does change and everything seems well.

pourjour

0

Q: Solving complex equations

Suppose the equation $(E):z^2-2sin(\alpha)z+2(1+cos(\alpha))=0$ / $z\in \mathbb{C}$. I tried to calculate the discriminant but I could determinate it's sign(there is a hint $\Im (z_{1})\ge \Im(z_{2})$ / $z_{2}$ and $z_{1}$ are the two solution of the equation. In a second case we suppose $(E_{2...

complex-analysis complex-numbers

user58512

19:56

@pourjour, are you an undergrad?

pourjour

@user58512 yes

user58512

how many years left?

pourjour

@user58512 this the last year

user58512

will you be glad when its over?

pourjour

@user58512 yeah I'm tired of studying

user58512

20:05

I am tired of my work too, it will be nice to move on

pourjour

@user58512 so you've got a job?

user58512

I mean the school work

pourjour

@user58512 hmm

user58512

20:37

hi

I finished my work today!

pourjour

@user58512 great!

user58512

I'm very pleased

Peter Tamaroff

@user58512 What did you do?

user58512

I went over my group theory notes

Gustavo Marra

20:53

hi

user58512

hello

Gustavo Marra

My first time on chat ^^

user58512

welcome

skullpatrol

hi

Peter Tamaroff

@GustavoMarra Run while you can!

skullpatrol

20:59

... and don't look back...

user58512

how do I put verbatim text in a footnote?

anon

in a latex document?

user58512

yes

anon

and what's the difference between text and verbatim text?

user58512

it's for source code

anon

21:07

blah blah\footnote{stuff}. blah

so the entire footnote you write will go inline in the middle of your paragraph (in the source code)

user58512

I can't use verbatim inside footnote that way

anon

google gives me http://tex.stackexchange.com/questions/203/how-to-obtain-verbatim-text-in-a-footnote

user58512

thanks

Charlie

@skull hi!

skullpatrol

@Charlie $\Huge\text{Hi! :-D}$

Charlie

21:18

@skullpatrol how are you??

skullpatrol

@Charlie Fine thanks, how are you?

Charlie

@skullpatrol Fine

skullpatrol

@Charlie How did you like the songs I posted in the party zone?

Charlie

I liked @skull :)

skullpatrol

@Charlie I found another classic...

23 mins ago, by skullpatrol

... and don't look back...

user58512

21:23

@anon, do you know Circle Method?

Charlie

@skullpatrol nice!

anon

nope

user58512

I want to learn it

Transcript for

$Mathematics$ Mathematics