Mathematics - 2015-02-04 (page 3 of 6)

Ted Shifrin

03:00

@Pedro: You mean maximum principle in complex variables, right?

Alexander Gruber

@TedShifrin If I see a gay president in my lifetime I'll be as amazed by the times as I'm sure elderly people were when obama was elected

Pedro Tamaroff

@TedShifrin $$\frac{1}{2\pi}\int_0^{2\pi}|f(z+re^{it})|^2dt=\sum_{\nu\geqslant 0}|a_\nu|^2r^{2\nu}$$

Ted Shifrin

Well, California's elected Jerry Brown governor over several decades, and I've always been sure he is ... :P

Pedro Tamaroff

Where $a_\nu$ are the Taylor coefficients.

Ted Shifrin

Ah, sure, @Pedro. I didn't know a name.

Pedro Tamaroff

03:02

It basically Fourier, because the $r$s come from weighing the power functions to get them to be orthonormal.

Ted Shifrin

Sure, @Pedro

Pedro Tamaroff

OK. I'll stop telling you stuff you already know and go back to studying.

Kevin Driscoll

To be fair seeing a gay president would be amazing on several levels. First, its much more acceptable to be uncomfortable voting for a gay president than a black one. Second, the number of people who could be president is small. Third, we live in a heteronormative culture so most people identify as straight. So, you're like multiplying a bunch of small probabilities.

Ted Shifrin

LOL :)

Assuming everything's independent? @Kevin

Alexander Gruber

@TedShifrin Baldwin should run. vs Boehner. I would buy a TV.

Ted Shifrin

03:04

Ugh, Boehner is despicable ...

Kevin Driscoll

@Ted Ya, in fact I think being gay and being a politician are probably anti-correlated at this point because it was impossible to get elected 10-20 years ago unless you were closeted.

Alexander Gruber

@TedShifrin I'm sorry. He is my county's fault.

I voted against him.

Ted Shifrin

Well, my part of Georgia sends some of the worst neanderthals in the house ...

Kevin Driscoll

My congressman, Trey Gowdy, is far too conservative on social issues for my taste. But he's actually a fairly good representative.

Votes against the establishment when they're being idiots about military spending, privacy issues, etc.

Ted Shifrin

We had Paul Broun, supposedly with a BS in Chem from UGA and a MD from Medical College of GA, who does not believe in science, evolution, or research. He's been replaced by an even stupider preacher.

Alexander Gruber

03:07

@TedShifrin My high school chemistry teacher was the first guy to photograph the atom, has a PhD in electrochem, and staunchly advocates ID and denounces climate science

Ted Shifrin

rolls eyes

and we wonder why this country is going down the tubes ..

Alexander Gruber

my dad, btw, was a climate engineer for the EPA for 40 years

Ted Shifrin

was he fond of that chemistry teacher?

Kevin Driscoll

I can't speak for chemists, but I've found physicists are fond of knowing just enough to hang themselves when it comes to climate science. We have a tendency to speak outside our field of expertise.

Alexander Gruber

@TedShifrin I still, to this day, have managed to keep this from him. :P

Ted Shifrin

03:09

well, everyone else speaks with even less science expertise, @Kevin, so why not? :D

Alexander Gruber

Burn

Soft scientists

Get on my level Einstein, do you even Zorn's lemma?

Ted Shifrin

mr finite math person, surely you don't believe in Zorn :P

Alexander Gruber

Of course not.

Ted Shifrin

your own version of ID, I see :D

Kevin Driscoll

Suppose that Einstein had an infinitely large sock drawer, could he choose exactly the elft sock from each pair of socks......

Alexander Gruber

03:12

Exactly. I have designed my mathematical practice to avoid terrible things like cantor sets

@KevinDriscoll I think you'd have to break the light barrier to do it all at once. Einstein might argue that you couldn't.

Kevin Driscoll

@AlexanderGruber But.....then the socks would become point-like in your reference frame

Alexander Gruber

@KevinDriscoll which is finite

See I'm just obeying the laws of physics y'all.

Kevin Driscoll

Well, really they'd become disc-like I guess because they have some transverse components

Ted Shifrin

LOL, the panorama of conversation in here is quite amusing

and a hush falls over the room ...

Alexander Gruber

We wore ourselves out.

Ted Shifrin

03:19

LOL ... imagine how our students feel :D

Pedro Tamaroff

Hello.

I've advanced pretty decently in my preparation for the exam.

Ted Shifrin

good to hear, @Pedro. :) After your exam, you can tell me about that problem on my exam :)

Alexander Gruber

@TedShifrin This must be why they include us in geneds. So that students have to encounter mathematicians in a safe environment, in case they run into one in the wild

Pedro Tamaroff

@TedShifrin Oh. I have to get back to Remmert's second volume. Such a nice book. Beautiful results!

Kevin Driscoll

A wild Mathematician appears!

Ted Shifrin

03:21

unkempt mathematicians abound !

@Pedro: The exam's in another 10 days, right? Don't forget some computational applications will probably show up ...

Kevin Driscoll

I choose you, Feynman Path integral!

Feynman Path Integral used renormalization group! It's Super Effective!

Pedro Tamaroff

@TedShifrin Nope. It's all theory.

Ted Shifrin

I guess Mathematica slayed @Axoren

Kevin Driscoll

Mathematician fainted....

Ted Shifrin

ah, cool, @Pedro

Axoren

03:22

I can't get it working @_@

I just want to execute 2+2

As a hello world

Kevin Driscoll

@Axoren whats not working?

Axoren

I'm reading your primer now, @TedShifrin

Pedro Tamaroff

@TedShifrin We've done enough computation in midterms, and I don't think my professor likes analysis's computations.

Alexander Gruber

@Axoren So you can't run the program?

Ted Shifrin

aha @Pedro

Axoren

03:23

I can run the program, but when I type 2+2, all it does it go to the next line

Alexander Gruber

@Axoren Shift enter

Ted Shifrin

Hit enter or shift return

Pedro Tamaroff

@TedShifrin I've pinged you in Facebook.

Ted Shifrin

I'll get there later, Pedro

Alexander Gruber

Or you can go to "Evaluation -> Evaluate Cells" with your cursor in the 2+2 cell

Axoren

03:25

Okay, it's shift enter, not CTRL enter

I hadn't seen the edit yet

I thought the blue box it made was a plot loading

Alexander Gruber

@Axoren Yeah, sorry, I rebinded my key to ctrl-enter and sometimes forget it isn't that by default

Pedro Tamaroff

@TedShifrin Oh, OK.

Alexander Gruber

I don't have a left shift anymore. Y'all don't know what I've got to go through to capitalize this stuff for you.

Ted Shifrin

it went in that accident, too, Alex?

Alexander Gruber

@TedShifrin i think this laptop turned 10 this year.

Axoren

03:28

@AlexanderGruber Where does it put gifs?

Alexander Gruber

@Axoren Run Directory[]

and it will show you where Mathematica is read/writing

Axoren

Are all notebooks on the same thread?

How do I prematurely cancel an execution?

Alexander Gruber

@Axoren I have never used more than one at a time honestly. They're on the same kernel but I think there is a way you can make them run on different kernels, I'd have to look into that.

@Axoren Control .

@Axoren And in the case that Control . doesn't work you'll want to go to Evaluation -> Quit Kernel -> Local

Axoren

It's taking a really long time to process 2+2.

Alexander Gruber

Maybe it is Alt . by default

@Axoren Sounds like the kernel is having a problem starting.

Axoren

03:32

Alt .

Kevin Driscoll

@Axoren Evaluation -> Abort Evaluation

also works

Alexander Gruber

Two things to note:

1. I am pretty sure Alt . (or Abort Evaluation) is done cell by cell.

Axoren

Oh my god... how do I ask for an approximation instead of an exact answer?

Alexander Gruber

So if you're queueing evaluations you'll have to do it a couple times

Axoren

The exact answer is 1 million decimal points in both numerator and denominator.

Alexander Gruber

03:35

2. Quit kernel loses all stored values

Axoren

Given in fractional form.

Alexander Gruber

@Axoren Use N

Axoren

N?

Alexander Gruber

So, N[your number]

or yournumber // N also works

Axoren

Thank you.

Alexander Gruber

03:36

(and is often convenient cause you'll forget to use numerical evaluation and want to tack on the //N at the last second)

Kevin Driscoll

@Axoren N[functon, number] specifies number of digits of precision

Alexander Gruber

@Axoren There is one very important thing I must tell you before I forget, it is the most important thing to tell a new mathematica user

? command

Kevin Driscoll

uuuuuuuuuuugh this episode of Stargate is a clip show.... DAMNIT

Alexander Gruber

will tell you about command

it is very good

Kevin Driscoll

@Alexander I did not know this.....

Axoren

03:37

Syntax::tsntxi: "N?" is incomplete; more input is needed.

Alexander Gruber

@Axoren ?N

@KevinDriscoll Oh my gosh. How did you get so far without their help? :)

Axoren

Like Spanish!

Kevin Driscoll

@Alexander Help -> type in command

Alexander Gruber

@KevinDriscoll Ohhhhhhh. :P

Kevin Driscoll

@axoren ¿ N

Axoren

03:39

ÞN

Alexander Gruber

When you ?thing it'll give you the basic outline, then you can click on the >> if you want more and it will take you to the full documentation for that command, which for most non-obscure commands is VERY detailed

Axoren

@AlexanderGruber Thank you, it's very helpful.

Kevin Driscoll

@Axoren GTFO with your thorn

Axoren

I'm already picking apart your code to see what you were doing.

@KevinDriscoll :Þ

Kevin Driscoll

@Axoren don't MAKE me Chinese you

Axoren

03:41

Do it, you're bluffing.

Kevin Driscoll

明白了？

Axoren

はい。

Pedro Tamaroff

Holy. Moley.

Kevin Driscoll

My characters are cooler than yours

Mathy Person

I don't understand what the answer is hinting at. Can anyone help? math.stackexchange.com/questions/1132786/…

Axoren

03:43

@KevinDriscoll 最高のことをあなたが持っているのですか？

Я могу также использовать Google Translate для русских , тоже.

Alexander Gruber

@KevinDriscoll 有两太子

Axoren

Still, it's funny how the Chinese font is larger than the Japanese equivalent characters.

Or at least it looks that way.

Maybe it has to do with the fact that they think we have bad eye sight.

Kevin Driscoll

@AlexanderGruber 有两太子？？？ Have 2 somethings....

Axoren

I feel insulted.

Alexander Gruber

@KevinDriscoll it means you are a person who has many talents

Julian Rachman

03:45

I just wanted to get this out there because it is funny: Why did the chicken cross the Mobius strip?

Kevin Driscoll

@AlexanderGruber Oh is it a chengyu?

Axoren

@JulianRachman To stay on the same side.

Julian Rachman

Yep.

Alexander Gruber

@KevinDriscoll It's just slang.

Axoren

This one's always a good one that pisses off some of my friends:

Kevin Driscoll

03:46

@AlexanderGruber Ah okay

Julian Rachman

But it is to get to the same side. Sorry this was stupid......

Axoren

Why did the chicken cross the road?

Julian Rachman

To get to the gay guys house

knock knock

Axoren

So you've heard a version of it.

Alexander Gruber

@Axoren Who wants to know? Am I being detained?

Axoren

03:47

Either that, or you've met the chicken.

Julian Rachman

@Axoren

yep

Yep. so you say "who's there" and I say "the chicken"

Axoren

Yup.

Julian Rachman

then the person thinks about it for a second and then starts to chase after you :)

Axoren

It took me 20 years to get the original joke.

"Why does the chicken cross the road?"

Julian Rachman

lol. What was the original? To get to the other side?

Axoren

03:48

Yeah.

Why was it ever funny?

At some point, it had to be.

The real meaning behind it is the obvious.

The chicken will die trying to cross the road, and it will end up on the "other side".

Julian Rachman

Idk. It would jsut make the other person go "huh" with that awkward face

Axoren

The afterlife.

Julian Rachman

Math version: There exists a chicken $C$ for all possibilities $p$.

Axoren

It was an epiphany like no other. I don't think you understand.

Alexander Gruber

did you guys see the chicken joke on mathoverflow?

Axoren

03:51

Like a lifetime of humorless jokes suddenly cackled madly.

Julian Rachman

No i did not

Axoren

Link it?

Julian Rachman

Did you hear the joke with the man that has a topological coffee cup

?

Alexander Gruber

95

A: Do good math jokes exist?

Here's one I came up with a few years ago that I'm quite proud of. Q: What do you get when you cross a chicken with an elephant? A: The trivial elephant bundle on a chicken.

Julian Rachman

Wow. I assume the terminology is very humerous

Since I am working on topology right now, here is one:
"Klein bottle for rent -- inquire within."

Alexander Gruber

03:53

@JulianRachman Yeah it's one of those jokes you can only tell to mathematicians and i usually don't like those but that one really gets me for some reason

Julian Rachman

Ya. It is like an inside joke but for mathematicians

Axoren

The topologist ass joke is hilarious.

Julian Rachman

In the topologic hell the beer is packed in Klein's bottles.

Axoren

I took a plastic cup and turned it inside out before going to the bubbler.

Julian Rachman

ANd that is for all who drink beer

Axoren

03:55

A professor said "What's wrong with your cup" and I said "Nothing's wrong with my cup."

Julian Rachman

ok, not trying to be inapropriate but: Moebius strippers only show you their back side.

I can keep going....

@Axoren lol. love it

Axoren

One of my friends likes to use the empty threat "I'll change your topology."

Julian Rachman

lol

did that friend use it on non mathematicians?

What does a topologist call a vergin?

Axoren

What?

Julian Rachman

Simply connected

A student was doing miserably on his oral final exam in General Toplogy (yes, this guy _really_ did give oral finals in topology). Exasperated by the student's abysmal performance up to that point, the professor asked the student "So, what _do_ you know about topology?" The student replied, "I know the definition of a topologist." The professor asked him to state the definition, expecting to get the old saw about someone who can't tell the difference between a coffee cup and a doughnut. Instead, the student replied: "A topologist is someone who can't tell the difference between his ass and …

here is you topologist ass one. took me a while to write it

Axoren

04:08

Wait...

Oh no... @AlexanderGruber

How do I know that the function converges for those points in that range?

What if it just takes 9 million operations for them to get even smaller?

I can't just throw 9 million operations at it.

And it might take arbitrarily more.

Alexander Gruber

@Axoren You don't know for sure, for that you would have to use actual mathematics.

Axoren

So this was all fruitless...

Kevin Driscoll

Is there some region where $\sqrt{z}$ has a negative real part?

Alexander Gruber

But Mathematica is good for giving you a good idea of what should happen in non-pathological situations

Axoren

The worst part is that I need the fourier transform of this function.

Alexander Gruber

04:11

Hmm

Kevin Driscoll

@Axoren You can use mathematica to take the fast fourier transform of a subset of the function

Axoren

@KevinDriscoll I'm explaining right now that that's pointless.

Kevin Driscoll

@Axoren Why?

Axoren

A subset of the function could be drastically different from the actual function.

Kevin Driscoll

I mean such a thing is possible

BUT if you take the log of your function then you have a sum

Axoren

04:13

We're not doing this again...

Alexander Gruber

@Axoren Think about this, what exactly do you want to output?

Axoren

The sum gets even worse.

Kevin Driscoll

$\log{(1 + \frac{x^2}{p^2})}$ and so for any fixed $x$ as you add more $p$'s the thing does indeed converge

Axoren

The fourier transform of a function that is periodic on the primes.

Alexander Gruber

@Axoren Right. But what do you want- a closed form for the terms? A function that outputs the value?

A graph of it?

Axoren

04:14

@AlexanderGruber a function that outputs the values.

Kevin Driscoll

@Axoren Do you need ot know the function analytically or is arbitrary numerical precison enough?

Axoren

Arbitrary numerical precision is enough, I guess.

But I don't know how I'd even get that.

Kevin Driscoll

@Axoren Then the terms in your product clearly do converge to $1$ for $p$ large enough, so what I would do is find an asymptotic expansion for your function analytically and then take the FFT numerically of that function

Axoren

Could I use the fact that $f(1) = \zeta(2)^{-1}$?

Kevin Driscoll

This should allow you to get arbitrary precision

Axoren

04:17

Like, would I iterate the function until $f_i(1) \approx \zeta(2)^{-1}$?

GBeau

should I indicate a cartesian cross product with \times ?

Kevin Driscoll

You might be able to analytically taek teh fourier transform of the asymptotic expansion, but I doubt it

@gbeau usually, ya

@Axoren I am not sure what you mean

Axoren

$\zeta$ is the Riemann-Zeta function.

$f(1)$ is the only known point for my function.

The only exactly known point.

$f(1) = \frac 6 {\pi^2}$

Alexander Gruber

So you're trying to get exact values for other points of the function

Axoren

Well, I want the fourier transform more than anything.

Kevin Driscoll

04:19

@Axoren yes these things I know, but I mean I'm not sure how you are going to use that. Yes, you could use that value as a sanity check on your approximation to check that your approximation indeed gets very close to the value you know it must take at $x=1$

Axoren

@KevinDriscoll But how would error in that measurement affect the error in the transform's measurement?

Alexander Gruber

@Axoren But you said you wanted something that outputs the value of the function to arbitrary precision, right?

how does the fourier transform help you gain that? I mean it is still the function, just in a different form.

Kevin Driscoll

@Axoren if you wanted to know exactly, you'd have to do some hard work and keep track of the error term in your approximation

Axoren

@AlexanderGruber I want arbitrary precision in the transform, not the function itself.

For example, I want to find the value at 1 Hz.

So, $\hat f(1)$.

Kevin Driscoll

@Axoren Do you know anything about $\sum_{p \text{is prime}} e^{-p}$?

Axoren

04:24

@KevinDriscoll I think it's equal to the number of primes.

Actually, no.

It's $\frac{\sum_{p\text{ is prime}} e^p}{\prod_{p\text{ is prime}} e^p}$

Kevin Driscoll

@Axoren Just food for though, if one takes the log of your function, then does the Fourier transform, you get such an infinite sum $$\frac{- \sqrt{2 \pi}}{\lvert k \rvert} \sum_{\text{primes}} e^{-p \lvert k \rvert}$$

Axoren

So, the denominator becomes the "last" primoreal.

No, it's not. I forgot about e.

Which makes it so much bigger.

Kevin Driscoll

Well, smaller in this case cuz theres a minus sign

Alexander Gruber

it is an interesting problem

I'm working on it

Hey how complex do you want this

@Axoren

Axoren

What do you mean by complex?

Like, $i$?

Alexander Gruber

04:36

Right

Axoren

I don't care.

Alexander Gruber

Are you interested in knowing the imaginary part or not

Axoren

That's the point, isn't it?

OH

Yeah

Alexander Gruber

k

Axoren

Both parts

I could settle for $|z|$ though

Mathy Person

04:43

How would I Find the real part of $(\sqrt{3} - i)^{2011}$?

GBeau

for limits on \cup and \cap in sum-type notation is \bigcup and \bigcap what I should use?

Axoren

@MathyPerson Use the binomial theorem.

$$\sum_{x=0}^{2011} \binom{2011}{x} \sqrt{3^x} i^{2011-x}$$

Alexander Gruber

@MathyPerson Rewrite it as $2e^{i\frac{5\pi}{6}}$

Axoren

@AlexanderGruber How'd you get that? I was going to suggest taking only the sum across real terms.

Alexander Gruber

@Axoren Just rewriting it as $|z|e^{\operatorname{Arg}(z)}$

Axoren

04:54

My post above is also missing a $(-1)^x$, but I didn't finish editing it fast enough.

Clarinetist

Has anyone here ever had a mathematical industry job?

Alexander Gruber

@Clarinetist You mean programming? Yeah.

Axoren

There's lots of professors on here.

Clarinetist

@Alexander - Any suggestions for programming languages? I'm not sure what my options are with a B.S. in Mathematics (Statistics emphasis). I have a feeling I won't be doing much until I pursue a M.S. at the very least.

... anything except actuarial science is fine (I'm trying to leave this field).

Alexander Gruber

@Clarinetist Well in general the best languages for getting a job are Java and C++ and maybe Python

Axoren

04:57

^

Alexander Gruber

Also R if you're going to do something stats-y, whether it's actuarial or not

Axoren

Python's also a very good utility language.

Alexander Gruber

Python is very good if you want to work in computational science, or in some kind of hardware-heavy field like robotics.

Clarinetist

I'm glad I know some Python, but I'll have to do some review. It looks like I've been right on target so far - I bought a Java and a C++ book yesterday, and have about 3 books on Python. This will be interesting.

Axoren

It's quick and dirty, but can be clean and structured.

Java can't really be dirty. The language is designed to require structure.

C++ is dangerous but powerful.

I've seen people write entire programs entirely in C++ Templates.

Alexander Gruber

04:59

My favorite cool language is Julia, but it's bleeding edge and will not help with the job thing probably.

Transcript for

$Mathematics$ Mathematics