Mathematics - 2013-03-24 (page 2 of 4)

5:04 AM

@GustavoBandeira how do you support yourself financially

My mother helps me. She wants to support me while I study, then I have freedom to make my unergrad, grad and Ph'D.

@Ethan Try Gazehawk.

gazehawk?

Search for it. Perhaps it me be useful.

Look:

is that you

@GustavoBandeira gazehawk, looks cool, but in a creapy way

@Ethan Yes.

5:10 AM

lol my computer setup is really lame, I just moved in with my mom, and she has all my stuff from when I was a child

@Ethan You can get 2 - 4 U$D for 5 minutes - it was this value when I used it some months ago.

2 - 4 U$D/5 minutes is a good money in Brazil.

ahh its to dark, its like 10:12 here

Yep.

I remember the time when I could use the computer in the dark.

Now I feel deeply disturbed.

lol listening to music in the dark feels awsome

sometimes

@

5:13 AM

why

they're a sywstem of control

@caveman why do you say that?

A system of a down.

check i tout en.wikipedia.org/wiki/Straight_edge

@caveman XD

5:15 AM

@caveman yes I know the tearm straight edge, I didn't know it refered to that tho lol

it's agreat philosphu

y

I thought it was just someone who never did any recreational drugs

If doing somthing makes you happy

then why not?

You only live one life

have you read Brave new world?

Sometimes there's a cost.

For happinnes.

Yes, agreed lol

There is a downside

usually

5:17 AM

►

the book is better

but this is the story

I would caracterize our age as an age where people desperately want to be happy, but are unable to measure the costs to achieve this happiness.

it's difficult to understand in a culture where everyonr drinks alchohol

What's more disturbing is the fact that happiness = entertainment.

@caveman lol Here in America your old enough to go to war and die, before your old enough to drink

yeah

5:19 AM

I havn't done any of those things yet lol, I wouldn't even know where to get them

Yep. I guess Ethan isn't a drunk guy.

But @JasperLoy drinks a lot!

user19161

@GustavoBandeira Yes, I drink tea.

I'm addict to coffee.

user19161

Tea is certainly superior to coffee, for me.

It's not about it's flavor, I like the brain overdrive it can provide me.

5:22 AM

I dont drink coffee

I tried to buy caffeine pills.

They would sell me.

user19161

I think I am going to go off coffee and stick to tea.

That's conspiracy.

I take vyvanse and adderall

Oh, I wanted to take aderall.

5:22 AM

just vyvanse

lolol

user19161

I take fluvoxamine now.

ah its the same stuff anyway

It seems to raise concentration.

amphetamines

it seems, lol it does

Yep.

Erdos took anphetamines.

user19161

5:23 AM

Guys, don't take amphetamines, tea will do.

user19161

Let Erdos do what he wants, we are not him.

If you take to much you just get high basicly

It doesn't help you concentrate if you take alot at once

you just get jiddery

We're not him, but we want to be.

Yep.

The role model is Erdos

LOL!

user19161

That was a sudden LOL.

5:25 AM

XD

LOL

yes

user19161

Looks like a drug addict to me.

Erdos dancing gangnam style.

user19161

5:26 AM

I want Ethan's (removed) style, LOL.

EHHHH (REMOVED) LADY!

user19161

Ethan, your spelling is terrible!

yes

I guess it depends on the person

How to say this in english.

Sleeping this way is called...?

$\color{grey}{\text{(removed)}}$

5:30 AM

spooning

In portuguese, it's called (Dormir de conchinha).

i suspose would be the informal term

I don't think youd find it in a dictionary

its more slang

Some days ago, my friend told me something, I heard something completelly different.

tell me what

I understood something like: "Let's sleep spooning at arisco".

Arisco is a corporation in Brazil.

Today I made a pictorial representation of what I understood.

5:32 AM

lollol

Get ready...

lol

I sent it to him.

He's deeply "impressed" with my skill of doing bullshit. xD

@GustavoBandeira lol

Anyone know any good movies, I think im gona watch somthing soon

Do you know fermat's room?

5:35 AM

no whats that

It's a movie.

I don't wana watch any crapy movies that romanticise math lol, like good will hunting

Git Gud recommended me yesterday. Seems nice

XD

watch the one I linked

...

I jsut linked you a movie like 5 mins ago

@caveman What one?

5:36 AM

The Postman (film)

The Postman is an American post-apocalyptic film directed by and starring Kevin Costner, and based on the 1985 novel of the same name by David Brin. The film co-stars Will Patton, Larenz Tate, Olivia Williams, James Russo, and Tom Petty. It was filmed in Metaline Falls and Fidalgo Island, Washington, central Oregon, and Tucson, Arizona. The film is set after an unspecified apocalypse has left a huge impact on human civilization. A nomadic survivor flees a warlord's army while unwittingly inspiring hope of restoring peace. The film was released on Christmas Day 1997 by Warner Bros. Pl...

brave new wrld

no thats too old

Yes.

youre old

Brave new world is nice.

5:37 AM

I like watching post-apocalyptic movies

The idea was made by asimov, right?

it is post apocalyptic!

sorty of

Or like messed up movies

uhm

Brave New World has a nice content.

Really.

That was prolly the best one I have seen in a while

Here are some really horrible ones I have seen

the book of eli

was just horrible

uhm

uhh

this was horible

5:38 AM

This what?

ahh I cant find it

actors I hate are uhm

honestly ethan

there have been no good films made in the last 10 years

nicholass cage omg

everything great was made beofre it

He is soo bad

5:40 AM

@caveman True.

Cloud Atlas is kinda good.

@caveman There are two versions, one of 1980 and another from 1998, which one is better?

isn't that a book

I dont think ive seen the new one

but definitely the book is better

It is. But there are some adaptations.

@caveman How old are you?

According to your nickname, several thousands of years, right?

Yes caveman tell us

ohoh

5:43 AM

watch any television

no

I sometimes watch the colbert report or the dailyshow

funny

I don't watch television. XD

TV is just stuff to mak you stick around between advert breaks

well, I watch it on hulu

5:44 AM

we dont get those here

Q: For what mathematical fields it the use of computers wouldn't be useful?

It seems my questions was awful. =/

-3

I'm a Mathematica user and by reading the help, I've noticed that there's a lot of fields in which you can use a computer to obtain results$^1$ - at least into some degree or another. But I've read a lot of other fields that aren't included in the help, I supose using a computer to perform some k...

@GustavoBandeira , I like it

do you know Terry Tao uses

massive amounts of computer results on the riemann hypothesis to prove goldbach 5

@Ethan, did he give a talk?

oh

They are finishing up finals I suspose

in the math building

@Ethan, read the book I gave you

what book

5:50 AM

yo will be an expert programmer

mitpress.mit.edu/sicp/full-text/book/book.html

sorry

lol

new stuff is just watered down copies of old stuff

i don't know

python is like a version of scheme turned to crap

in all respects

i wouldn't know

@caveman Your 20+ atleast I think

5:53 AM

lol

@caveman SICP is great!

yeah

There are video lectures of it on MIT OCW

I should probably study more math before I start studying another field

Karl's students

5 months later...

►

5:55 AM

Look: youtube.com/…

@Ethan you' know more than me already

Karl's students

(removed)

a bit

mobius transforms that kind of thing?

A: how to prove the relation between the floor function and the number of divisors

es

@Ethan look at this

1

Consider first $$\sum_{k=1}^n \sum_{d|k} 1$$ Here is a table k | divisors of k -------------------- n | ..| ... 9 | 1 3 9 8 | 1 2 4 8 7 | 1 7 6 | 1 2 3 6 5 | 1 5 4 | 1 2 4 3 | 1 3 2 | 1 2 1 | 1 The sum is just going up the rows of this table countin...

6:02 AM

@caveman yes, if d(n) is the divisor function, then for any function f(k), $$\sum_{k=1}^n d(k)f(k)=\sum_{k=1}^n\sum_{j\leq n/k} f(jk)$$

this can be improved by the dirichlet hyperbola method

@caveman Are you from CS?

user19161

So sad, nobody wants to upvote my latest answer...

@GustavoBandeira, not really - I study both

though

to $$\sum_{k=1}^nd(k)=2\sum_{k=1}^{[\sqrt{n}]}[\frac{n}{k}]-[\sqrt{n}]^2$$

@JasperLoy Yes. The question also has low visibility.

@caveman Both what? Math and CS?

6:04 AM

yes

user19161

@GustavoBandeira The problem with some of the hints is that they are too skinny. For example, if the asker cannot prove that, do you think throwing the definition of a rational number at him will help?

I want to study math, CS and philosophy. XD

@JasperLoy what question

user19161

@Ethan math.stackexchange.com/questions/339372/… this

@Ethan last one.

@JasperLoy Yes. I would make no sense.

user19161

6:06 AM

@GustavoBandeira And then the people on meta would say "downvote the complete solutions", LOL. Ridiculous!

Wait.

@Ethan, I only saw dirichlet hyperbola to get a big O, not exact

If $f_n$ is the set of all rationals between 0 and 1 with denominators less then n, then $$M(n)=\sum_{k=1}^n\mu(k)=\sum_{q\in f_n}e^{2\pi i q}$$

where $\mu(n)$ is the mobius function

user19161

In fact, the hint wasn't even correct until someone edited it, LOL.

user19161

And my so called solution still leaves gaps for the asker to fill in.

6:09 AM

how?

user19161

@caveman Are you talking to me?

user19161

Well, the asker has to work out the fraction himself!

user19161

I could have added more steps in computing the fraction.

user19161

Hey @anon I realised you grew a little older.

ell me how to make that sum

6:13 AM

anon knows alot

@caveman I messed up it should be

the rationals bettween 0 and 1 with denominator less then or equal to n

man there's so many htings you can sum

user19161

@caveman So you weren't talking to me.

I need to go through apostol again

For example the rationals between 0 and 1 with denominators less then or equal to 5 are

user19161

Oh man, I feel so cheated now...

6:14 AM

@JasperLoy Are you talking to me?

0/1,1/5,1/4,1/3,2/5,1/2,3/5,2/3,3/4,4/5,1/1

are the rationals between 0 and 1 with denominator less then or equal to 5

if you take those rationals q

and sum

$$\sum_{q}e^{2\pi i q}$$

it should be equal to

$$\sum_{k=1}^5\mu(k)$$

tha'ts sick

ok I think see why its true

How about this one\

MaoYiyi

having trouble with Maple. I want to graph these polar equations and fill in the area inbetween: r = 2+2 sin theta and r = 2. Anyone know how to do that.

$$\phi(n)=\sum_{k=1}^n\gcd(k,n)e^{2\pi i k/n}$$

6:17 AM

in fact $\sum_{(k,d)=1} e(k/d) = \mu(k)$?

@caveman yes haha, its a root of unity sum

the sum of the primitive qth roots of unity is mobius(q)

I have just summed over q

thats neat

eulerstotient function

@caveman ramanujan sums are also very nice

if you sum $$\sum_{(k,n)=1} e(sk/n)=c_s(n)$$

@Ethan, I palyed with it a bit did the first couple pages of his paper but I am not sure what they get used for

@JasperLoy yes, you are quick on the uptake

6:19 AM

actually one did come up in one my classes but I forgot

@caveman look

@caveman you know the divisor function

oh yes

$$\sum_{d\mid n} d^x=\sigma_x(n)$$

user19161

@anon I did not want to wish you because I did not check every day, so I did not know the exact day!

ramanujan showed how to express pretty much everything in terms of his sums

6:20 AM

yes lol

$$\sigma_x(n)=\frac{n^{x}}{\zeta(x+1)}\sum_{q=1}^\infty\frac{c_q(n)}{q^{x+1}}$$

I havn't seen any real uses for them though

They are nice looking though

@JasperLoy the exact day was 2 hours ago in my timezone

happy birthday anon

user19161

@anon Wow, happy birthday!

lolol

thanks

6:24 AM

why do peope celebrate birthdays

user19161

Wait @anon is it 23rd or 24th?

user19161

@Ethan Just like you!

lol

@GustavoBandeira You ask a lot of vague questions.

user19161

Oh I think it is the 23rd @anon. I am also born on the 23rd, but in Aug, LOL.

6:27 AM

@anon Happy birthday @anon

@伟轩 It's manily due to lack of intelligence.

@GustavoBandeira I would delete your latest question on math.se

For one geometry itself is so broad

I am studying two subjects now that could be considered as "geometry"

Yes. This is obvious.

@GustavoBandeira It is not clear to me why this is obvious. In any case your question is impossible to answer.

user19161

Wow, that makes me and anon special bros, LOL.

6:29 AM

@benjalim you're very humble

a good thing

atleast I think

@Ethan It's "you're"

@Ethan Was this sentence here "your very humble" meant to be sarcastic?

no

If i want to find zeros of a function at infinity do i have to consider the zeros of f(1/z) at 0?

I didn't need to study maths. Just needed to know that mankind is arround for a lot of years, the first idea that comes to mind when it comes to old geometry is euclidean geometry (which is very old), so they were developing this in greece, of course people kept developing this after greece.

@Ethan And why do you say so?

user19161

6:31 AM

The best book on Euclidean geometry is by Agricola and Friedrich: Elementary Geometry.

@Mathematician yes

@anon Quick question: do you know of a topology which is not hausdorff and not first countable?

@Ethan

@benjalim you are hesitant to say things are obvious

@anon and the order of zeros is the same of f at infintiy and f(1/z) at 0?

yes

6:32 AM

ty

@Ethan Because from experience many things which I think are obviuos

upon taking a second look are not so clear

@anon Should mercio delete his answer [here]( math.stackexchange.com/a/338641/38268)?

@Ethan And how do you know I am BenjaLim?

because I read your profile info

ok

@伟轩 can't say

user19161

I had a strange dream just now.

6:39 AM

@anon can you help me in finding order of zeros of 2/(2z+1)-1/(2z^2)-1/(z+1), i considered f(1/z) and got in the numerator a polynomial of degree 4 with no constant and a linear term, does this means the zero at infinity is of multiplicity 1?

user19161

In my dream, I was reading a story. The words were so clear, though I can't recall them now.

f(z)=2/(2z+1)-1/(2z^2)-1/(z+1), finding order of zeros at infinity

@伟轩 take the cofinite topology $\tau$ on an uncountable set X, pick two distinct points a,b in X, delete from $\tau$ any cofinite set containing one of a or b but not the other

@JasperLoy Any idea on what were the words about?

@Mathematician $\sim-\frac3{4z^3}$

user19161

6:45 AM

@GustavoBandeira Can't recall, but it's a story.

@robjohn can you please explain i am confused

For large $z$, $2/(2z+1)=\frac1z-\frac1{2z^2}+\frac1{4z^3}+O\left(\frac1{z^4
}\right)$

$-1/(z+1)=-\frac1z+\frac1{z^2}-\frac1{z^3}+O\left(\frac1{z^4}\right)$

Martin Sleziak

A user asked about a problem with posting questions in tagging chatroom. I thought that if some mods are in this chatroom, it might be good to mention this to them @robjohn. Although I am not sure that much can be said from his description of the problem.

(And you had the bad luck that you're the only mod here...)

@MartinSleziak It would be nice to see if there was a response

Martin Sleziak

His priofile says he was online 3 minutes ago, so maybe he will write something.