Mathematics - 2014-04-19 (page 3 of 4)

Mathematicians these days mostly integrate increasingly bizarre functions. Nobody's proven things since a few decades ago, with the advent of formal proofs.

Sab

Advanced mathematicians can write a proof in 2 lines for advanced mathematicians to read

Balarka Sen

Read a lots of proof. That's all.

Pedro Tamaroff

@Sab How do you learn to write good essays? By reading other good essays, or books.

Sab

but a beginner in math won't understand

Mike

9:04 PM

(As in, computers that prove things for you)

Pedro Tamaroff

@Sab Give it a try.

Come back with results.

Sab

I should

Pedro Tamaroff

Yes.

Go now.

Sab

Well it makes sense

I just read about root 2 is irrational

Pedro Tamaroff

Fly.

Sab

9:05 PM

Seems easy

By the same principle we can say that root of 5 is irrational

and prove it by contradiction.

Wow. I'm going to prove it. Brb

Mike

Why would you bother? You can get a computer to prove that for you.

Sab

No you can't

Thomas Andrews

Ignore @Mike. He's trying to be funny, but it might be hard to tell, depending on your English skills.

Balarka Sen

You can.

Sab

You can never check to infinity even with a computer

infinity is not a number

Balarka Sen

9:07 PM

@Sab Why do you need infinity here?

Thomas Andrews

Sab, all proofs are finite - a computer can check any proof a human can write.

Sab

How can a computer check that root of 2 is irrational?

Balarka Sen

Root of x^2 - 2.

Rational root thm.

QED.

Fernando Martin

Proofs are (formally) finite strings of symbols

Computers can check that

Balarka Sen

(Besides, you can do well by diophantine approximations)

Thomas Andrews

9:08 PM

By providing the same proof that a human could provide, @Sab.

Balarka Sen

modern computers use that.

Bel

Hi, can anyone help me to answer my question here: http://math.stackexchange.com/questions/755241/set-geometry-and-inclusion
I have posted that since 4 days ago so I opened a bounty of 50 points

Sab

There too much being slapped on me right now.

Googling diophantine approximation

Balarka Sen

@Pedro Today, someone gave me primers on hyperbolic geometry and I learned how to prove independence of the 5th postulate of Euclid.

@Sab Mr. Google is a very bad person.

Sab

I know, Mrs. Wikipedia is worse.

I was trying to implement the L-system in Python today and Mrs. Wikipedia didn't have a clear explanation.

Balarka Sen

9:11 PM

You get to know mathematics very superficial by googling everything out.

Sab

That's why I asked for a book on proofs.

Balarka Sen

Don't do it.

@Sab I don't understand if proof-writing is what you want.

Sab

I want to understand how it's done.

Balarka Sen

You don't get a book of collection of all proofs in math you know.

Sab

I want to get the how to think part of it.

Balarka Sen

9:12 PM

@Sab First read on some solid topic.

Choose out one of two - geometry, algebra

Then learn.

Sab

Obviously a book can't have all the proofs. But a book can have the method of proving.

That's what I need.

Balarka Sen

@Sab There is no general method for all proofs.

Hilbert's problem is answered negatively.

Sab

The forward-backward method is the only method I know

Balarka Sen

(Of course I am talking about diophantine equations)

Sab

And how are graphs made?

Balarka Sen

9:14 PM

@Pedro Today, someone gave me primers on hyperbolic geometry and I learned how to prove the independence of 5th postulate of Euclidean geometry from the others.

Sab

Let's say I slap a parametric equation, can it's graph be done>

?

Balarka Sen

@Sab I don't understand that question.

Graphs from what?

Bel

Hey folks, I need help in algebric geometry and set inclusion

Sab

The shaped-graphs

Balarka Sen

@Sab Oh. Depends on what the shape is.

Sab

9:15 PM

How do you know equation X will be a heart?

Balarka Sen

Ellipse and circles.

Pedro Tamaroff

@Bel Those two terms are quite far from each other.

Balarka Sen

Or just circles.

Sab

Let's say you didn't know the equation and you decide to make an equation to draw a heart>

?

Balarka Sen

24 secs ago, by Balarka Sen

Ellipse and circles.

Sab

9:16 PM

What would you do with elipses and circles?

Bel

@PedroTamaroff Yes I know but this is how I can discribe my problem

Balarka Sen

You just need to know the shape of well-known geometric objects.

Bel

I would say it's more set inclusion problem

Sab

Aha.

But with a circle and an ellipse, how would I turn it to a heart?

Bel

@PedroTamaroff: I have posted my problem here: math.stackexchange.com/questions/755241/…

Balarka Sen

9:17 PM

@Sab Uh... superimpose? By clever piecewising?

Sab

I don't have the knowledge to make this. I need to learn it S:

It's so interesting but I don't know where to go after circles and ellipses

Balarka Sen

@Sab See examples.

Sab

ok

Balarka Sen

OK, gotta goes.

Bye.

Pedro Tamaroff

That's not algebraic geometry.

Balarka Sen

9:19 PM

I'll come back moday next week.

Sab

Bye

I won't be trolling when you come back next Monday.

I got a dissertation to prepare.

Balarka Sen

@Sab On?

Sab

Ellipses

Balarka Sen

Ah.

Good luck with that!

Sab

It's a basic assignment for 10 marks.

Balarka Sen

9:21 PM

@PedroTamaroff In right mood to try out a nice elementary math excercise?

Sab

Oh it's not a university dissertation(if you were thinking so)

Just high school stuff.

Balarka Sen

@Sab I know that. You're just 13.

Sab

I realized I used the wrong word.

Bel

@PedroTamaroff I know that algebraic geometry is about polynomial equations but when I say set of matrices I think it is about algebra and I said geometry because a set of matrices could have some shape

Balarka Sen

@Bel It's not.

Who told you so?

Bel

9:23 PM

it's just a personal interpretation of the problem

Mike

@Bel This is not algebraic geometry. :) "Polynomial equations" is a vast simplification.

Balarka Sen

Algebraic geometry is not about polynomials.

what @Mike said.

Reading first lines of wikipedia articles only gives one a superficial idea.

Bel

@all: sorry guys my last class in algebra was in 2008 but at least I can still fully understand when I read about it :)

Chris's sis

Prove elementarily that $$\int_0^{\pi/2} \log(\sin(x)) \ dx $$ is convergent. (I've found a funny way of proving that)

Enjoys Math

What's the word for all points of $X$ are within distance $d$ from subset $A$?

Denseness or no?

lol @BalarkaSen

Pedro Tamaroff

9:32 PM

@EnjoysMath No.

saadtaame

Can the linearity of integration be used to find closed forms for some sums?

For finite sums $$\int \sum = \sum \int$$

Pedro Tamaroff

You can call it $B(d,A)=\{x\in X:d(x,A)<d\}$.

Fernando Martin

I call that a $d$-neighborhood of $A$

Mike

I wouldn't call it much anything.

Pedro Tamaroff

@Mike Yes, we know you're not a name caller.

Mike

9:36 PM

@Pedro "...fuckface"

Fernando Martin

this is awesome

Pedro Tamaroff

@FernandoMartin why?

Fernando Martin

I find it amusing that the fact that $\emptyset$ has 2 covers is actually relevant for something non-trivial

Pedro Tamaroff

Ah, true. I don't understand all that comes after "This comes up when using the Grothendieck ..." =P

Enjoys Math

Thanks @PedroTamaroff

Fernando Martin

9:45 PM

I don't either

Grothendieck stuff scares me

Pedro Tamaroff

@EnjoysMath What for?

►

YouTUBE was making me watch it.

Chris's sis

I didn't see @robjohn active in the last "many"hours ...

Mike

@Fernado I like the thing in the comments. "An integral domain is one in which the $0$ ideal is prime. But the definition of prime forbids the $0$ ring from having any."

Pedro Tamaroff

@Mike Death to the zero ring.

Fernando Martin

everyone knows the zero ring is not a ring

Pedro Tamaroff

9:56 PM

@FernandoMartin DIS

Gabriel R.

@chris'ssis Asymptotics

Fernando Martin

I have that answer upvoted already

haha

praise be to Bourbaki

Chris's sis

@GabrielR. $$\left|\int_0^{\pi/2} \log(\sin(x)) \ dx\right|=\left|\int_0^{\pi/2} \log\left(\frac{\sin(x)}{x}\right) \ dx +\int_0^{\pi/2} \log(x) \ dx \right|<\infty \rightarrow \text{Q.E.D.}$$

Pedro Tamaroff

@FernandoMartin We should ask FCEYN to open a Bourbaki prayer room.

Fernando Martin

The deposit works as one

Pedro Tamaroff

10:00 PM

Oh, wonderful place.

Fernando Martin

That's where people go if they've been good in their lifetimes

Poli Tolstov

Hey guys...

Pedro Tamaroff

Gabriel R.

@chris'ssis it's an overkill

Fernando Martin

I have a weakness for hardcover GTM books

dat yellow

Pedro Tamaroff

10:02 PM

@PoliTolstov Comrade.

@FernandoMartin I think that section should have half a dozen armored guards.

One day I might lose it and steal 'em all.

Jack M

hey

Pedro Tamaroff

PREEEEEEEEEEEEEEEEEEEEEECIOUS.

r9m

@PedroTamaroff golum

Chris's sis

@GabrielR. what do you mean by an "overkill" here?

Mike

Bourbaki is as dead as God.

Pedro Tamaroff

10:06 PM

you break a' ma' heart, son.

Fernando Martin

shun the non-believer

Poli Tolstov

:)

5space

@Mike: Maybe that's because you don't read it in French?

Mike

@Pedro do you know why Bourbaki stopped writing books?

Gabriel R.

@chris'ssis there's simpler

Pedro Tamaroff

10:06 PM

@Mike he wrote enough?

usukidoll

hi hi

Mike

Hello @5space

5space

Oh man. Best joke ever coming up...

Gabriel R.

They ?

Jack M

@PedroTamaroff Surely Bourbaki books aren't that valuable?

Mike

10:07 PM

@5space Is that sarcasm? :P

5space

@Mike no I love this joke.

Jack M

they have a shelf like that in my local math library too

Chris's sis

@GabrielR. Well, it's just a way that came to mind suddenly .... It requires no effort. I know what you mean, but this is just another way.

Mike

@Pedro They found out Lang was one person.

Pedro Tamaroff

Lang deserves all the respect in the world.

Mike

10:08 PM

Maybe not all the respect.

5space

To be fair, at least the bourbaki books are better written than Lang's. :-P

At least what I've read.

Pedro Tamaroff

@Mike Why?

Jack M

I've tried reading Algebra and Calculus of Several Variables by Lang

I found Algebra to be impenetrable and only good for reference

Mike

@Pedro He was a bit of a braggart.

Jack M

CSV was alright

Pedro Tamaroff

10:09 PM

@JackM His Algebra is nice, it just take time.

@Mike I approve.

Mike

And not the best writer.

5space

I've heard is complex analysis text is decent.

*his

Mike

I don't see why one wouldn't just use Ahlfors.

5space

But surely there are betters in any subject :-P

Jack M

@PedroTamaroff I'm not sure why I should give time to a book that introduces the definitions for normal subgroups, quotient groups, and short exact sequences within about two pages, all without the slightest attempt at giving any intuition or motivation

Gabriel R.

10:10 PM

@chris'ssis it does : well-definedness of sin(x)/x at 0 and convergence of the integral of log at0. But well this is "elementary" ;)

Jack M

I didn't give it much of a chance, though

Pedro Tamaroff

@JackM It's not supposed to be a book for a first read.

Jack M

That's what I mean - it's probably good for reference

Pedro Tamaroff

@JackM Well, or for a second read. =D

Mike

Or perhaps to be read at all.

What's up @5space?

Chris's sis

10:12 PM

@GabrielR. :-)

5space

@Mike No mucho. Doing homework.

Mike

What for?

5space

Galois theory and topology

usukidoll

http://math.stackexchange.com/questions/751410/prove-f-infty-a-infty-rightarrow-b-infty-is-a-bijection

there updated

Mike

Fun stuff, @5space

Gabriel R.

10:17 PM

@chris'ssis are you interested in series of functions?

5space

@Mike, I agree. But I'm not so into Galois theory this quarter. I'm drowning in topology :-P

usukidoll

I'm drowning on my own stuff D:

5space

I like topology a lot more.

Mike

Who's teaching it?

Chris's sis

@GabrielR. limits, series, integrals ...

Gabriel R.

10:19 PM

@chris'ssis is that a yes?

Chris's sis

@GabrielR. Sure.

5space

Haesemeyer is teaching algebra. Gilmore is teaching topology. And Liu is teaching algebraic topology.

Bel

@SamiBenRomdhane Est ce que vous pouvez m'aider à résoudre un problème en Algèbre. Au fait j'ai étudié à l'IPEIT 2006-2008 MP mais je me rappelle plus des noms des profs qui m'ont enseigné :)

Mike

I dunno which courses you mean by the latter two. But fun. What's AT covering now?

5space

The latter two are (respectively) introductory topology (ugrad) and algebraic topology is the graduate one.

Mike

10:21 PM

Ah, gotcha.

5space

We are starting to talk about complex projective plane.

And recently we were talking about CW complexes.

Mike

What year are you?

5space

Technically junior. I transferred here this year. But I'm taking two more years after this.

Mike

Yeesh.

5space

??

Mike

10:24 PM

I wish I was as well-prepared as you my junior year.

5space

Well, before this year I had only taken lower-divs. So I don't have that many upper-division units.

This is my first grad class.

Sami Ben Romdhane

@Bel Salut @Bel oui je ferais mon mieux sinon tu peux bien sûr poser la question à math.SE

Mike

You are, nonetheless, taking a grad class in your junior year. :)

5space

Truth.

I want to do their bachelors/masters concurrent degree, so I have to take 8 grad classes before I graduate.

Bel

@SamiBenRomdhane Merci bien pour m'avoir répondu. Au fait j'ai posé ma question sur ce lien: math.stackexchange.com/questions/755241/…

Mike

10:28 PM

Nice.

5space

Are you taking any cool classes your last term?

Most of my friends who are graduating are taking only GE's!

usukidoll

ge's? general education?!

5space

@usukidoll Yes.

usukidoll

XD liberal arts stuff

5space

Mostly, yes.

usukidoll

10:31 PM

like where in the help wanted job listings does it say need a BA in liberal arts XDDDDDDDDDD

useless degree x)

5space

That's the only good thing about transferring. I got all of my GEs done in advance!

Mike

I'm only taking two math classes. One is C* algebras, the other is more algebraic to

topology. Cohomology and some hodge theory.

5space

$C^\ast$ algebras sounds cool.

usukidoll

have you done your ges through community college @5space

5space

@usukidoll Yes

usukidoll

10:31 PM

same here

Mike

It's work.

usukidoll

boy that saves a lot of $$$$$

one of my classmates just went straight uni after high school..now he has over $25,000 in student loans

5space

Yeah. And I am low income, so community college was free anyways!

usukidoll

same

but you didn't use all of your pell grant eligibility did you?

5space

I did.

Mike

10:33 PM

Enjoyable, but some of the proofs come out of nowhere.

usukidoll

damn what happens afterwards @5space?

like if you used all of your pell grants, then...is it just loans afterwards?

5space

The cool thing about my community college was that I could take math classes at a local university for the same as community college tuition (for me free)

Oh, I got a merit scholarship when I transferred.

usukidoll

my community college was too dirt cheap to have calc 3 and 4 so I transferred

and I'm still stuck on that damn bijection question. how the heck does each hint take 2 lines a piece?

Sami Ben Romdhane

@Bel C'est une très belle question et je pense qu'elle mérite un bon temps de réflexion. Est-ce que je peux savoir qu'est ce que tu fais (étude) maintenant?

5space

@usukidoll You might explain the notation in your question. I'm not sure what $f_\infty$ and $f_+$ mean, for instance.

@Mike, I'd like to take functional analysis.

But you have to take the grad analysis sequence here as prerequisite.

usukidoll

10:36 PM

what the ?! I've put the def for infinity

$f_\infty$ is the restriction of f with the codomain and domain restricted @5space

5space

Oh, I see it at the bottom.

usukidoll

ok that just means that I'm in a certain area

Mike

@5space To say things that aren't just real analysis again, you need a lot of background.

5space

You might put the definitions at the beginning. Otherwise, people might stop reading because they don't know what's happening.

@Mike Yeah. And I'm weak in analysis :-(

Mike

Not to mention one calls back to results from Rudin 2 all the damn time.

@5space Become strong in analysis, then! :D

usukidoll

10:38 PM

bangs head

Bel

@SamiBenRomdhane Je fais un master en automatique et conception des systèms

5space

That's my plan over summer. Tons of analysis. So I can attempt the grad analysis next year and take functional analysis my third year!

Mike

Good luck! I think one doesn't need too much to be ready for grad analysis... just a good background. Baby Rudin totally suffices.

But that stuff hits like a tank.

5space

I was going to work through Pugh's book. My friend did that and killed grad analysis.

usukidoll

done I've put the def on top

5space

10:40 PM

Lots of Berkeley prelim problems in the book supposedly.

Mike

I don't know Pugh.

5space

It looks a lot like Rudin, with more topology, more explanations, and more pictures (and way too many exercises lol)

I read about 5 chapters of Rudin while I was at community college, but I haven't done any analysis in about a year.

Chris's sis

lol, I just received a very nice problem, that is actually a tricky problem. In fact, it's a question well-packed in another one that is not really straightforward. (I laught a bit when I saw it)

$$\lim_{n\to\infty} \int_0^{\infty} \frac{\sin((2n+1)x)}{\sin(x)} \frac{dx}{1+x^2} \ dx=\frac{\pi}{2} \coth(1)$$

This is good for fun. Really!

Mike

@5space Well, you seem like a smart fellow. I have the utmost faith in you. :D

5space

Thanks :-P

I might be doing some analysis related research project over the summer, so that will help too.

Mike

10:49 PM

What on?

5space

Not sure yet.

Hopefully something related to topology or diff. geometry.

Mike

That's barely analysis!

5space

Supposed to get it sorted this coming week.

I know, but it's going to be something more analytic.

Mike

I'd love to hear about it. You've got me email, so hit me up when you know.

My typos make me sound like a pirate.

5space

Aaargh.

Are you doing the prelim/basic exam preparatory class over the summer?

Mike

10:51 PM

Yeah, they pay me to.

5space

Cool. I am doing it too!

Mike

Most of it shouldn't be too new... but review isn't bad, and neither is money.

5space

Exactly! It will definitely help my analysis.

And then hopefully I can pass the basic exam in the fall.

Mike

You have to take that because you're a masters student, I assume?

5space

Well, because I want to get a masters with my bachelors.

Mike

10:54 PM

Right.

5space

Not technically a masters student. But yeah, basically :-P

Mike

I'll be working on an analysis project this summer, too.

5space

Oh, crazy!

With someone from here or your current school?

Mike

All the research I've done is analysis. Which is funny. Because I don't intend to do analysis. :P

My current school.

5space

You're into alg # theory right?

Mike

10:57 PM

I'm into disparate shit.

5space

That's okay. It's early!

Mike

It's been a while since I've studied any number theory so I'ge lost a bit of the starry-eyed feel.

I'm interested somewhere on the geometry-algeraic geometry-arithmetic geometry continuum. But there's the one word in common, regardless of where I end up.

5space

The grad algebra sequence here next year will be good for that. The prof who is teaching it is into algebraic geometry, algebraic number theory, and K-theory.

Mike

Haesemeyer, yes? To be honest, I'm hoping to pass the qual.

5space

Yes.

Pedro Tamaroff

10:59 PM

@seaturtles

I meant to say the group $\Bbb Q/\Bbb Z$ is torsion, and it is infinite. Hence, it cannot be finitely generated.

5space

Passing the qual would be great.

Transcript for

$Mathematics$ Mathematics