Mathematics - 2017-05-26 (page 5 of 6)

Fargle

18:00

@Ted, I wasn't saying you were. I just truly have no input besides that I like numbers and letters. :)

Daminark

Especially since the math for physical science courses do count as a sufficient prereq to ODEs and maybe complex analysis? So there's definitely a path to do some math classes without having to go through Rudin

Ted Shifrin

Demonark, I have to keep reminding you that if we ran math department major courses as UC does, we'd close down as well. You and Eric are in the top 1 percentile of math majors.

Semiclassical

Physics cares more about Bessel functions than of proving convergence

Daminark

Yeah, I mean, it's a model that only works here I guess

Ted Shifrin

And at UGA only 15-20 people max finished my multivariable math class. Hardly a huge number.

Daminark

18:00

Or maybe a few similar places

Wait really? Hmm

Dodsy

This chatroom is very niche as well...

Ted Shifrin

Princeton, Chicago, Harvard have very pie-in-the-sky major courses, but even they have students who can't survive them.

Fargle

@TedShifrin If only I had gone there instead! I would have loved that class, even as much of a procrastinator as I am.

Daminark

$\pi$ in the sky? :P

Fargle

@Dami lul

Ted Shifrin

18:01

Well, Nate, we have plenty of people who come in to get help on very elementary stuff, but you're right for the most part.

Daminark

@Fargle procrastinators unite!

Fargle

@Dami: we'll get around to it...

Ted Shifrin

@Fargle: Perhaps I would have motivated you to be more motivated. Perhaps not.

Zee

I once watched motivational videos on YouTube to get motivated, ended up watching them for hours

Ted Shifrin

Demonark: I've mentioned two students that I knew from GA whom UC chased out of math. Certainly Serge Lang chased my best friend from high school out of math at Princeton centuries ago. There are lots of stories like that.

Fargle

18:03

@TedShifrin Full disclosure, you have gotten me to be more fierce and focused on my self-study. Which reminds me, I should do notes for Artin chapter 4 and then work more on your chapter 3 exercises, while I've got a good day for it.

Dodsy

@Fargle Procrastination is all fun and games until it's not.

Balarka Sen

@Daminark Vodka for you comrade!

Fargle

@Dodsy I wrote that show tune.

Ted Shifrin

Well, I'm glad to help a bit, @Fargle.

Dodsy

@TedShifrin I find that disheartening.

Ted Shifrin

18:04

Which, Nate?

Daminark

@Dodsy See, the trick is, once you decide to work on not being procrastinated, you procrastinate on doing htat

Net result: DOOMED

Ted Shifrin

Chat is an addiction that abets procrastination.

3

Dodsy

@TedShifrin "I've mentioned two students that I knew from GA whom UC chased out of math."

Daminark

@Balarka Woo

Dodsy

I just hope I don't have a similar experience at whatever school I go to. Though I found on the UWO website that a teacher said "If you want to be one of my grad students because you're interested in my research, email me"

Ted Shifrin

18:05

How's the Jumble, everyone except Fargle?

Dodsy

which I haven't really seen before.

Mike Miller

this room is constant meta lately no matg

Ted Shifrin

You'll have to raise your game, Nate, for sure, to be successful in math.

It's the end of the school year and people are burnt out, @MikeM. But perhaps it'll be better when I'm gone for a month.

Dodsy

Yes :) I am hoping to do some studying in August and maybe complete a freshman calculus book.

Mike Miller

fair enough

Daminark

18:06

begins going so meta as to talk about how meta the room is becoming

Lol jk

Ted Shifrin

Oh, @Danu asked me for a resource. I don't have a great answer, but Springer's book on Riemann surfaces is a bit more concrete. But he does the usual Riemann-Roch stuff in the end.

Fargle

@MikeMiller Any question I can answer would be better answered by someone else, and any question I could ask here is something that I should probably come to understand on my own.

Ted Shifrin

@MikeM: I don't mean to get into all these philosophical discussions.

Daminark

Along somewhat similar-ish lines, I wonder if anything is ever proven via induction on how many times you're inducting

Ted Shifrin

But I do have opinions.

Dodsy

18:07

@TedShifrin I've got time, the main thing is that I need to do very well in my courses, and do some supplemental learning on the side to broaden my knowledge base.

Balarka Sen

@TedShifrin Do you agree with the theory of existence as uttered forth in the public works of Puncher and Wattman?

Ted Shifrin

LOL, huh? @Balarka

Fargle

@BalarkaSen In spite of the tennis I resume.

Balarka Sen

How can you conclude that? They are refuted beyond all doubt by the works unfinished by Cunard et al.

Ted Shifrin

Nate: I had many students at UGA who loved math but who just had never had to be so self-motivated and disciplined in order to succeed in classes like mine.

Dodsy

18:08

@BalarkaSen That we all live in the matrix?

Daminark

OH WAIT THE JUMBLE CHECKS OUT

caps lock engaged

Fargle

@Daminark: that took you a good minute.

Daminark

Better than a bad minute @Fargle emirite?

Balarka Sen

@Fargle Of all sorts, of course.

Fargle

ehehehehehehehe

Dodsy

18:09

@TedShifrin Yes, I am hoping that I can buckle up my socks. I've never done well in a classroom setting, however I really want to succeed and I think I'll do whatever necessary to get to the point of having a good routine down.

One of the major distractors will be that in the math building there is also a bar.

Eric Silva

@Ted a lot of pretty cool geometry questions posed by neves to me this morning

Daminark

Good rid-dents

Balarka Sen

Ugh

Dodsy

I am not going anywhere Daminark.

Daminark

Lel @Dodsy

Dodsy

18:12

The idea of the hole puncher exists before the hole puncher exists.

Hey Sha.

Sha Vuklia

hey Dodsy

Dodsy

What are you working on today?

Daminark

Hey @Sha!

Sha Vuklia

@Semi, can I ask you something real quick about waves? (the physics chat is dead once again:P) It's a tiny question!

Ted Shifrin

hi @Sha.

Sha Vuklia

18:13

hey @Dami

hi @Ted

Ted Shifrin

Cool, @EricSilva. Like what?

LOL @"it's a tiny question"

Sha Vuklia

@Dodsy I'm about to read about the free particle (quantum mechanics), but I haven't had waves yet, so I have to review that:l

Dodsy

:|

Balarka Sen

Ok, I gotta leave for dinner now.

I didn't get any work done today. Go me.

user314159

cu

Zee

18:14

Good job

Ted Shifrin

Good dinner, @Balarka.

Sha Vuklia

maybe Walter Lewin can help me

I think he can

Ted Shifrin

Now there's a controversial name. MIT actually took down his videos.

Sha Vuklia

oh really?

Ted Shifrin

Yup.

Sha Vuklia

18:17

I was about to watch his lectures on the wave equation

user314159

Well, he was convicted

Ted Shifrin

I'm sure they're up there on YouTube somewhere.

Sha Vuklia

yea they are

Astyx

Rehi

Ted Shifrin

It's sad. I'm not saying I disagree with MIT's actions. Not at all.

That was fast, @Astyx.

Astyx

18:18

Was it ?

Ted Shifrin

Well, now that you're back, I should depart.

user314159

Sad, but true.

Zee

Wow talk about super hysterical reaction

Sha Vuklia

sexual harassment online?

user314159

Yup.

Zee

18:19

If that's what they did to him, I should be in prison for half the stuff I say online

Astyx

Sexual harassement is no joke

Fargle

pinches bridge of nose

Astyx

See ya @Ted !

Ted Shifrin

If you do any of this as a person in a position of power (grad student, faculty), you should be canned, @Zee.

Zee

Sure

Ted Shifrin

18:20

Now the world thinks they can get away with crap just because our idiot president does.

But I'm leaving before I get angry.

user314159

cu

Fargle

See you, @Ted.

Zee

But this is not similar

Sha Vuklia

@Semi never mind btw, I think I've found a good resource.

user314159

Walter?

Sha Vuklia

18:23

well yea, academically speaking he's still good

user314159

Indeed.

Eric Silva

@Ted finding a sequence of simple closed geodesics on $S^{2} \times S^{2}$ whose length blows up

estimating the Laplacian of distance functions

Astyx

People are more than their academic achievements

Eric Silva

finding eigenfunctions on einstein manifolds

and there's one about studying conformal changes of metric and what it does to scalar curvature

Balarka Sen

@EricSilva Is the picture somehow analogous to (p, q)-curves on S^1 x S^1 with larger and larger p, say?

user193319

18:30

Let $x,y,g$ be elements in some group $G$. Is is true that $g \langle x,y, \rangle = \langle gx,gy \rangle$? Clearly $\langle gx,gy \rangle \le \g \langle x,y \rangle$, since the latter contains the former's generators. However, I am having a little trouble with the other inclusion I could use a hint, or a link to a solution.

Balarka Sen

I guess it's harder than that because that has a simple description in terms of lines in R^2.

Eric Silva

@Balarka I haven't thought about these questions at all

well, except the Laplacian estimates :P

Balarka Sen

Oh ok

user314159

True @Astyx but, there's "information" and there's "too much information" :P

Eric Silva

$S^{2} \times S^{2}$ is weird

Balarka Sen

18:32

I wonder what the totally geodesic spheres in S^2 x S^2 are.

S^2 x S^1 in S^2 x S^2 are totally geodesic, right? Where S^1 is the equator of S^2 say. Because there's a reflection along it which is an isometry.

Vrouvrou

@Astyx then $A$ is closed ?

Astyx

No

Vrouvrou

not closed sorry

Balarka Sen

It should be easier to understand geodesics in S^2 x S^1; lift to S^2 x R.

Astyx

Yes

Balarka Sen

18:35

Yeah I'm pretty sure you can produce geodesics like that which "twists around" a lot.

Eric Silva

@Balarka I was thinking along these lines when I glanced at it

Balarka Sen

But I really have to go now.

@EricSilva Yeah I think sthing like this should do it.

user314159

Wow! nice artsy discussion in the hbar @BalarkaSen :P

Studentmath

Blah. I think I should give up, it's impossible to study once in two weekends or so only.

Dodsy

@TedShifrin Called UWO and they said two weeks before a decision, so you may never find out!

Mike Miller

18:45

wha r we doing?

Dodsy

Hey Mikey.

user314159

Ya, why so long? @Studentmath

Studentmath

@user314159 Just can't the rest of the time. Not for the next half a year or so, at least.

Eric Silva

@Mike I'm trying to think about conformal changes of scalar curvature

Studentmath

All I have to finish up in this two months is some advanced functional analysis course, then I can start my graduate in half a year. But I get stuck on some basic issues/questions and every little bit of delay means I just can't make it.

Mike Miller

18:48

ah good good, that's one of my favorite equations

Eric Silva

I worked out the formula for the change in sc under conformal change in metric, now trying to work out that you can't take nsc and find a conformal metric where's it's nonnegative

Abdullah UYU

where can i find @Semiclassical?

Mike Miller

ehhhhhh I'm mixing two problems

Eric Silva

is constant nsc rigid? I think Neves was saying something about this

kind of a vague question I guess

Akiva Weinberger

Can someone help me with [number 27](http://people.cs.uchicago.edu/~laci/REU12/puzzles.pdf)? I have no idea how to do this.

27. (Irreducibility over finite fields) Let $p$ be a prime and $n$ a natural number.
(a) Prove that there is an irreducible polynomial over $\Bbb F_p$ of degree $n$.
(b) Prove that if $p^n$ is large then roughly a $1/n$ fraction of all monic polynomials of degree $n$ over $\Bbb F_p$ are irreducible.

(Ted said to use the sieve of Eratosthenes, but I'm not sure how.)

Eric Silva

18:58

hmm ok

Mike Miller

i mean, are you willing to think of surfaces?

oh, i'm reading things so wrong toda

remind me the formula for a conformal change of the scalar curvature (in dim > 2)?

s(e^{2f}g) = e^{-2f}(s(g) + \Delta_g f + (n-1)(n-2)|df|/2)$ or something like that up to a sign, but there's a better formula

it's in Besse

Eric Silva

The one Neves is having me consider for this problem is on a $3$-manifold, if $u^{4}g = g'$ then, $s(g') = -8u^{-5}\Delta_{g}u + u^{-4}s(g)$

which is kind of a weird one

@Mike isn't the one you gave the one in Besse

I have it open in the other tabh and they look basically the same

Mike Miller

19:14

look further down the page

they have one in terms of a different (but obviously equivalent) conformal change that gives a more useful eqn

Eric Silva

ah yeah ok

this is what I wrote

Mike Miller

what's their formula for general n?

but yes, once you fiddle with coefficients a bit this becomes almost precisely the Kazdan-Warner equation

Eric Silva

If $g' = u^{4/(n - 2)}g$ then $u^{(n + 2)/(n - 2)}s' = 4 \frac{n-1}{n-2}\Delta_{g}u + su$.

Mike Miller

perfect, thanks

now check Salomon Appendix D to see what I'm calling the Kazdan-Warner equation

Eric Silva

$\Delta u + e^{u}h = f$

Mike Miller

19:27

aw fuck I'm doing the wrong one :x

Eric Silva

ahahhaa

Mike Miller

this is not my day, man

Eric Silva

don't worry about it lol

btw have you ever read moore's notes on SW stuff

Mike Miller

yeah they're good

Eric Silva

Neves recommended it to me this morning

Mike Miller

19:28

I walked away with the best undersanding when I finally worked through a lot of Salamon

But Moore was probably the first thing I read

Eric Silva

right, Salamon is long and extensive

Mike Miller

i think its a very easy read tbh

Eric Silva

it looks that way at a glance

I guess I could read both at once

that usually helps me

Mike Miller

the other canonical text is Morgan

lectures on

Eric Silva

do you have a source of exercises?

or are the ones in Salamon enough

Mike Miller

19:38

are there some in salamon?

Eric Silva

yeah

I think at the end of every section

maybe that's just for preliminaries though

Mike Miller

i dont at all remember them

you're reaching the point where you start to make your own exercises, or reading the next section is the exercise that requires you to know the previous

you probably want some basic exercises for the spin geometry though to get a feel for it

Eric Silva

hmm ok I see

yeah actually looking through it it might just be prelim stuff that has exercises

Mike Miller

that should be fine

prelim includes spin geometry?

Eric Silva

spin stuff is in part 2 i believe

Mike Miller

19:41

darn

Eric Silva

starting around page 100

I think I could maybe get through the first hundred pages before my summer vacation starts

Mike Miller

the fuck's in the first 100?

Eric Silva

well i know the stuff in the first 50 pages basically, the 50 after that is complex stuff I don't know that well

and spin geometry is after that

Mike Miller

gotcha

the kahler stuff is nice and important because it drastically simplifies the SW eqns

Eric Silva

cool cool

man summer cannot come fast enough

user314159

19:55

Are you in high school?

Eric Silva

Nah

Dodsy

Summer will come too fast for me.

And in an instant be gone.

Eric Silva

I just wanna do cool math man

Mike Miller

i don't taech this summer which will be nice

but i also don't teach right now

i basically need to write like crazy for 2 months

Balarka Sen

Summer surprised us, coming over the Starnbergersee / with a shower of rain; we stopped in the colonnade / and went on in sunlight into the Hofgarten / and drank coffee, and talked for an hour.

Semiclassical

19:57

In the mountains, there you feel free.

Dodsy

Once I'm done my schooling I can study math for fun guilt free.

Balarka Sen

I read, much of the night, and go south in the winter.

Dodsy

Right now even talking to you guys makes me feel guilty.

Semiclassical

(insert german here that I can't remember)

Balarka Sen

lol

Dodsy

19:58

Guten Tag

Du bist Schlau

Balarka Sen

i only remember "echt Deutsch"

Dodsy

I figured out "du bist"

and now everytime I learn a new word I just slap it on the end

Semiclassical

I think the quote means "Not Russian, but German"?

I forget, though.

Dodsy

I figured out the german word for guard the other day

"Bewatchen"

Balarka Sen

yeah I don't know

Dodsy

19:59

"du bist" just means "you are"

Semiclassical

And I'm annoyed to say I don't remember what the next line is, leading into the desert part.

Balarka Sen

What are the roots that clutch, what branches grow out of this stony rubbish?

Semiclassical

(there we go)

Son of man, you cannot say or guess

Balarka Sen

Son of man, you cannot say, or guess, for you know only a heap of broken images where the sun beats

This is my favorite part

well, all of the poem is literally my favorite

Semiclassical

Yeah, I dig that part of it

eh.

I have a harder time appreciating sections 2-4

Dodsy

20:01

Oh T.S Elliot.

Semiclassical

there are a bits I like, sure, but

user314159

You guys are poets.

Dodsy

My favourite of his is "The love song of J.alfred prufrock"

Semiclassical

the first and last sections are my fav bits.

Balarka Sen

Come in under the shadow of this red rock, and I'll show you something different / from either your shadow at morning, striding behind you / or your shadow at evening, rising to meet you

I will show you fear in a handful of dust

brilliant

Dodsy

20:02

Wow you guys are my kind of people, I'll tell you that much.

Balarka Sen

@Dodsy That's very good too.

@Semiclassical you don't like a game of chess?

Dodsy

We have lingered in the chambers of the sea
By sea-girls wreathed with seaweed red and brown
Till human voices wake us, and we drown.

Semiclassical

Friesch veit der vint der heimahtzu/ mein irisch kinde woe veilest du? (that's a guess and partially phonetic, mind)

@BalarkaSen Eh, it just doesn't jump out at me as much.

user314159

e. e. cummings was my fav

Dodsy

@BalarkaSen Is that another poem?

Semiclassical

20:03

Same with the Fire Sermon (though the last few lines are great)

All part of The Waste Land @dodsy

Dodsy

Ah, I have not read it myself

Balarka Sen

@Dodsy The Waste Land is like an epic divided into chapters

Dodsy

Only the love song and another one

Balarka Sen

you should def read it

Semiclassical

And the fourth bit isn't as long.

Balarka Sen

20:04

or listen to Jeremy Irons (and another person I don't recall) reading it.

Semiclassical

I've read pretty much all of his poetic works (including a few of his plays)

Dodsy

Oh the Hollow Men.

The hollow men is one of my all time favourite poems

Balarka Sen

fantastic, that one

Dodsy

I'll check out the waste land one.

Semiclassical

The Hollow Men is one of those poems I can't say I love, mostly because it makes me shudder a bit

Dodsy

20:05

Yes!

Me aswell

Semiclassical

Which I guess makes it very effective.

Balarka Sen

This is the way the world ends
This is the way the world ends
This is the way the world ends
Not with a bang, but with a whimper

Dodsy

My english teacher read poetry like the most amazing thing I've ever heard.

That ending is so amazing :)

Semiclassical

Next big one after that is Ash Wednesday

Dodsy

He sadly had a heart attack :C (my english teacher)

he did smoke like a fiend though.

Semiclassical

20:06

at which point you're getting a different sort of poetry from Eliot.

Balarka Sen

yup

Eric Silva

@Mike it's looking like the summer project I do under Neves might be some kind of geometric flow thing

bc other people involved seem to be interested

Dodsy

The eyes are not here
There are no eyes here

What other poets do you guys like?

Balarka Sen

@Semiclassical re the middle parts of The Waste Land, although I can't recite it to you, I think I quite like A Game of Chess.

Dodsy

I like Keats too.

Balarka Sen

20:10

I think we are in rats’ alley
Where the dead men lost their bones.

@Dodsy I like Eliot a lot but he's not my favorite poet.

Fargle

Whoever linked those puzzles from Laci, thanks, those are really neat.

Semiclassical

I guess I'd go 5>1>2>4>3?

Dodsy

Who's your favourite?

Fargle

I think I solved the Erdos-de Bruijn one.

Balarka Sen

my all time favorite is hands down Arseni Tarkovsky

note that "favorite" doesn't have much to do with how good he is, or how well-recognized, or seminal his works are

Dodsy

20:11

I forgot that you loved russian writers (even more so than I)

user314159

Russian work in general

Balarka Sen

yeah that

Dodsy

:)

Can you speak any russian.

Balarka Sen

nope :P

Dodsy

I'm trying to think what language I should learn in school next year.

I'm between Chinese, German, or Russian.

Balarka Sen

20:13

@Semiclassical Not a bad selection

go for Russian :P

Dodsy

:D

Balarka Sen

oh here's the recitation i was speaking of earlier by the way. i didn't hear all of it but i felt it was very good

Abdullah UYU

@Semiclassical $\binom{23}{0}-\binom{23}{1}+\binom{23}{2}-\binom{23}{3}+\dots -\binom{23}{23}=0$ How can i prove this?

Eric Silva

That's equal to $(1 + (-1))^{23}$.

Dodsy

I'm dumb.

Ignore whatever I say.

Abdullah UYU

20:20

@EricSilva is there a formula for this?

Balarka Sen

binomial formula

Abdullah UYU

where $1, -1$ comes from?

Eric Silva

that's like the point of the binomial formula

Abdullah UYU

oh, i got it

Semiclassical

There's probably an inclusion-exclusion interpretation as well.

Eric Silva

20:22

$(x + y)^{n} = \sum_{k = 0}^{n} x^{n - k}y^{k} \binom{n}{k}$

probably

Abdullah UYU

i tried an inclusion-exclusion but don't know if it is same with your's @Semiclassical

@EricSilva exactly.

Eric Silva

yup yup

Balarka Sen

binom(23,k) = binom(23,23-k). If k is even 23-k is odd, you get opposite signs and stuff cancels out

Mike Miller

@EricSilva cool

find a geometric flow for me that optimizes that inequality in that paper i liked

Abdullah UYU

@BalarkaSen oh, this is the simplest one i think :)

arctic tern

20:28

@Semiclassical that is inclusion-exclusion for $A_1=A_2=\cdots=A_n$ all of size $1$.

Balarka Sen

@AbdullahUYU They're all the same proof in the end.

Abdullah UYU

yeah, but observing it from different points of view is so impressive

@BalarkaSen binom(6,k) = binom(6,6-k) doesn't work for (6,0)-...+(6,6)

Balarka Sen

Yeah I know. It was specific to 23 being odd.

Abdullah UYU

@Semiclassical A circle that have equation $x^2+y^2-4x+2y+n=0$ intersects with $y$ axis at points $A,B$. Find $||\vec{OA}+\vec{OB}||$.

Semiclassical

$O$ is the origin?

Abdullah UYU

20:38

oh, sorry $O$ is the center of the circle

Semiclassical

Ah.

Do you know how to find O,A,B?

Abdullah UYU

$O=(2,-1)$

$A=-1+\sqrt{1-n}, B=-1-\sqrt{1-n}$

right? @Semiclassical

Semiclassical

Well, not quite. But presumably you mean $A,B=(0,-1\pm \sqrt{1-n})$.

So what's $\vec{OA}$?

Abdullah UYU

$\vec{OA}=(-2,\sqrt{1-n})$

similarly

$\vec{OB}=(-2,-\sqrt{1-n})$

Semiclassical

Right. So what's their sum, and what's the length?

Abdullah UYU

20:49

$(-4,0)\rightarrow lenght=4$

thanks

Semiclassical

right-o

Transcript for

$Mathematics$ Mathematics