Mathematics - 2017-08-31 (page 1 of 3)

Ted put him on ignore.

1 hour ago, by Ted Shifrin

Now I can put Demonark on ignore for a few weeks. Whew.

12:46 AM

Y tho?

You lied.

I am not a demonnn.... cackles internally

O:-)

^angelic skully

Hello chat

Yo

12:57 AM

hi

So in our algebra class we don't really have a specified reference, but out prof told us to check out Artin, Herstein, or Dummit and Foote's algebra textbooks. Personally I like Artin's style, but my seniors tell me that Artin has way too much emphasis on the matrices and less on the algebra. Is it worth reading another textbook simultaneously?

D & F is the classic.

My class this fall is gonna use DF but I think it drags on way too much

Getting there is half the fun :-)

So is it worth reading D&F as well, at least for the theory?

1:07 AM

Will you have enough time?

perhaps

I'm already trying to read baby rudin in addition to our usual analysis text, but I think I can squeeze it in eventually.

I won't try both at the same time.

But, that's me.

Alright, I'll keep it in mind.

2:01 AM

hey guys what's up?

journals.sagepub.com/doi/10.1177/0956797617714580

hey secret

It is quite possible that these are one of those few things that does not obey maths

But the more interesting question is: How

that's a tough topic, the mathematics behind love. :P

hi @dodsy

2:03 AM

Hey man how have you been!?

well

remember how we'd talk about how much you had to struggle with uni bureaucracy?

Yes.

That was pretty bad.

my last month has been me on the receiving end of that

:(

What's been going on?

The law of unintended consequences.

2:04 AM

Hah, yes.

I'm finally out of the woodworks, thank god..

And I never have to deal with that distance education institution again.

i couldn't register for certain credits because of a requirement i hadn't fulfilled, and my advisor worked through channels to get a waiver for that. that took a while, but it's through

Hopefully you will be out of the woodworks soon as well :)

ooo that sucks.

okay, so advisor tells me i should register for those credits over the summer. it's mid-july at that point, so that has to be done via late registration. okay, do that

...oh, wait. because it was done in mid-july, i wasn't able to be a TA/RA over the summer. so no tuition benefit. hence: $8k bill on my student account.

woa, that's nuts....

okay, talk with the advisor, we figure out what happened, so I withdraw the credits again by a late exception...

...but the bill doesn't go away. people i ask say to wait a few days, but nothing happens. so i look around online, and there's a tuition refund appeal form that has to be filed

...okay, so i do that

2:08 AM

jesus.

"okay, well, the committee for that doesn't meet for the first time until two weeks into the semester." (it's made up of counselors in the student services office, and their schedules are tight right now)

that's monday

I come back at the day again to get more clarity on the process, and someone there tells me they'll email me tomorrow. I spent yesterday waiting for that; nothing

wow

oh, and because of the bill on my account i've got a "past due" hold so i can't actually register for my own courses this semester

that's how they always are "we'll email you tomorrow"

wtf dude

so i go back again today, and they route me to another office (just one floor down, so no big deal). and apparently there's a form to fill out for that (of course)

good news is, the committee for that meets once a week!

guess what the bad news is.

2:11 AM

they don't meet until the school year starts

actually, no.

but they meet on wednesdays.

o

oh haha

that sucks

and the deadline each week for filing that form is...Tuesday at noon.

so not until the 6th

now, this is not as big of a deal as it seems

2:12 AM

mannnn

for one, it's not a problem with my grad student status if I have to do it late

for another, i have enough in savings to cover the bill (though i would still want the refund)

but stiiilll

yeah

man that actually does suck

so that was my morning...and my day wasn't over.

This all happened today!?

3 mins ago, by Semiclassical

so i go back again today, and they route me to another office (just one floor down, so no big deal). and apparently there's a form to fill out for that (of course)

everything starting from there was today

so not all that much, really

2:14 AM

oh right

okay then what happened

but, day wasn't over. now we go back a few weeks

I knew that this fall I was going to be trying to write my thesis, so while I knew I'd be a TA I really wanted to have a role that was reasonable

So the plan was for me to be half-RA / half-TA (technically quarter each---it's complicated).

and i spoke with a prof i'd TA'd for before, and he agreed to request me (and did so) as his TA for an upper-division QM course. good stuff.

so fast forward to this morning, and TA assignments get sent out...and I'm assigned to 1201, intro physics.

lol

that's a big change.

yea really

i go speak with the prof about it, and he says that he had to switch from 3 sections of students to 4. so he needed a second full-time TA

but when he did so, he specifically asked the front office to try to get me a different upper-division course.

evidently they didn't manage that.

2:18 AM

hm, that actually blows

My way to deal with administration stuff: 1. Send them email, 2. if no email or no reply after reasonable wait, find them directly at the office. People tend to be a lot more responsive when you do it face to face

and, to quote that prof: "A half-time assignment of an intro physics course is more work than a full-time assignment of his upper division course"

So basically my workload for the upcoming semester just jumped by a substantial amount

and it didnt get fixed?

oh, and classes start next Tuesday.

yeah I can imagine

2:20 AM

I found that out today

class size would be much larger for introductory class

plus, intro physics courses have a lab attached

wow man.

That will literally be a shitty year.

BUT, you can now help me with my intro physics course

And when I talked to the Associate Head about it the answer was basically "well, you're not taking classes anymore, so your schedule is open"

since you'll be all refreshed :D

man that's actually brutal...

2:22 AM

I had to walk around for half an hour as soon as I confirmed that, partly trying to track down the first prof

but also just to settle myself down because i was pissed

yeah I don't blame you.

and because this is so last minute, the chance of this actually being able to be resolved is low

Yeah :/

(to clarify what I mean by "your schedule is open" it's not "oh, you've got a lot of time to work on stuff". it's "you don't have class conflicts that have to be taken into account")

Oh I see.

2:25 AM

scheduling it all is a hard task, and I don't begrudge them it

but that doesn't make me any happier to be on the short end of the stick

plus, if the reason this all happened was because "oh, you're a half-time TA"

...well, I would much rather be a full-time TA doing the easier job than a half-time TA doing the hard one.

Yeah that's really lame of the school.

and, moreover, they didn't even bother to check on that

just "oh, he can't be in that position anymore? well, we'll just slot him wherever then"

Hey maybe something good will come of that though.

I can see at least one good thing: clear motivation to get the f*** out of this school

Maybe you meet your future wife in intro physics.

haha yea true.

2:28 AM

so my morning was asinine and the rest of the day was infuriating.

sooo yeah

:/

Sounds like you're going to be spending a lot less time in here :-(

if all else fails, maybe I can convince them to at least give me a second-semester course rather than first-semester

main reason being that I appreciate the labs in the second semester so much more than first semester

What's the difference?

just better experiments?

Physics is the class I'm most worried about atm.

well, part of it is that in first semester it's mostly about motion

and the thing with motion experiments here is that that mostly means "take video of it"

2:31 AM

ugh

why

specifically: take a video, then go frame by frame and mark the position of the moving object

also, the software for that? it was designed in-house

that's very strange

so you can imagine the level of quality assurance

main thing with the program is that it is seemingly designed to be as tedious as possible

which means those first few labs just suck

That's been my experience with them, at any rate.

I hate when assignments are made to purposely be tedious...

yeah

especially when you've got 90 minutes of time with 18 students in lab (5 groups)

so the longer it takes to do stuff, the less they're able to do

the other thing is that, in second semester, you actually get to use stuff like power supplies

2:35 AM

"power supplies"?

current/voltage source

ah nice.

yeah

so second semester is in general just way more interesting than first

more interesting for sure

well, I hope it all works out man

keep me updated

I should be back on on the 8th after my first class :D

nice

2:37 AM

but maybe I'll check in earlier

if you could spring for second semester that'd certainly be better than your current situation.

yeah

we'll see, i guess

I'm sure your advisor will have some words of wisdom :-)

maybe.

what i'm paranoid about now is

if I were to say "I'm okay with being a full-time TA if it means I can do an upper-division course"

that they'll just ignore the condition there and say "oh, okay, so now you're a full-time TA with intro courses"

and that's even worse

hard to trust them when that seems to have backfired already

Yeah, I see your point.

@Semiclassical I'm sorry that you have to go through all this mess

2:43 AM

i think i know what song I should listen to now, at least

What's the worst possible case scenario?

i try to adjust my TA/RA balance to make this work, and they use that to make me a full-time TA with intro course responsibilities

oh, and my tuition refund could be denied for absurd reasons. so then i'd owe the university $8k

(i already do owe them that much, but i wouldn't get it back)

That's horrible. What do you think will likely happen?

How about take a year off?

I'm fairly optimistic on the tuition front, since there's various admin people who are on my side with that

so I'm not really expecting that to be an issue

for the context re: my song reference, see the bit starting at 2min of this: cc.com/video-clips/yz886x/the-colbert-report-john-darnielle

culminating in Colbert's description at 3:05

user84215

2:57 AM

Is it necessary to post the math workshops announcement here everyday?

I won't say "necessary."

In fact I think it's better you don't

Like at some point people not showing isn't gonna be that they didn't see it as much as lack of interest

If people are interested they will look for it.

user84215

My idea is very bad. Right?

I don't know if it's very bad but I think MSE isn't the right place for this sort of thing

I think Reddit University and r/math are probably somewhat better contexts

Like this idea will get more traction there, and traction makes/breaks this sort of thing

3:06 AM

^

Trying to push it too hard in the wrong setting is a very bad idea, because they'll start to take it as trolling or crankhood.

3

And once people think you're one of those, it'll be hell to ever make them take you seriously again

3:25 AM

Wow Semi, thats rough.

DaneJoe

3:48 AM

Found it

you said there wasn't a way to turn any product into the gamma function semi

or "not just any product"

but I guess you'll have to find out in the next research paper on it

4:20 AM

I slept for 10 hours :D

11 hours ago, by ÍgjøgnumMeg

Why might $\langle a^2, b \rangle$ be the unique subgroup of index $2$ in the group $\langle a, b \mid a^4 = b^{17} = 1, aba^{-1} = b^{-1}\rangle$?

10 hours ago, by Kasmir Khaan

@KasmirKhaan change the question to "Suppose that for every $x,y \in G$, $(xy)^2 = x^2y^2$. Prove that $G$ is abelian."

4:47 AM

bab=a, ab=b16a, ab^n = b^(16n)a, a^m b^n a^p b^q = b^(256q+16n) a^(m+p)

= b^(q-n) a^(m+p)

[Random]

it is a finite group of order 68 @ÍgjøgnumMeg

The collection of all alephs indexed with the naturals are in bijection with the naturals

@Secret axiom schema of replacement

this is how aleph_omega is constructed

But thinking closely, it sounds a bit strange:

ah wait, let me think...

4:56 AM

@ÍgjøgnumMeg it is Z4 x Z17. This is why it has a unique subgroup of order 2.

$\aleph_{\omega} =\{\alpha|\alpha < \omega_{\omega}\}$ while $|\Bbb{N}|=\aleph_0=\omega =\{\alpha | \alpha < \omega\}$ (Assuming GCH)

that has nothing to do with GCH

So while $\sup (\aleph_n|n\in\Bbb{N}) =\aleph_{\omega}, \aleph_{\omega} \neq \{\aleph_n|n\in\Bbb{N}\}$

of course, the last thing isn't even an ordinal

So, $\omega$ is quite an unusual limit ordinal in that its supremum is given by the elements it contains. I.e. $\sup (n|n\in \Bbb{N})=\omega=\{n|n\in\Bbb{N}\}$

5:01 AM

that is true for aleph_omega also

But $\aleph_{\omega} =\{\alpha|\alpha < \omega_{\omega}\}$, thus it must contains ordinals that are not alephs

that is true for omega also

$\omega = \{0,1,2,3,....\} = \sup (\{0,1,2,3,....\})$
but
$\aleph_{\omega} = \{\alpha|\alpha < \omega_{\omega}\} = \sup (\{\alpha|\alpha < \omega_{\omega}\}) \neq \{\aleph_{n}|n\in\Bbb{N}\}$

Ok, you are right, in that case I have no idea what I am trying to show here

Or whatever I tried to show here, I don't know of the correct terminology to describe

do you mean that omega contains only cardinals but aleph_omega contains non-cardinals?

I guess yes

I think, what I might want to say is that $\omega$ is the only ordinal such that given some ordered set $S=\{a_n|n\in \Bbb{N}\}$ there exists $a$ such that $\sup(S)$ and $S$ is the ordinal itself

That is, for a countable increasing sequence, only for $\omega$ will its supremum is the same as the sequence itself

5:36 AM

hmm, nice

bwDraco

5:46 AM

Cut it out with those flags. There was nothing offensive about those messages.

chat.stackexchange.com/transcript/36?m=39738235#39738235, chat.stackexchange.com/transcript/36?m=39738237#39738237

6:56 AM

Hello!! I have to compute the double integral $\int_0^{\sqrt{\frac{\pi}{2}}}\int_x^{\sqrt{\frac{\pi}{2}}} 2\sin(y^2)dydx$.

I drawed the region $0\leq x\leq \sqrt{\frac{\pi}{2}}$ and $x\leq y\leq \sqrt{\frac{\pi}{2}}$. This is a triangle with height and base equal to $\sqrt{\frac{\pi}{2}}$, right?

The double integral is equal to the are of the triangle, or not?

So, is the double integral equal to $\frac{1}{2}\cdot \sqrt{\frac{\pi}{2}}\cdot \sqrt{\frac{\pi}{2}}=\frac{\pi}{4}$ ?

7:08 AM

No it is not. If you integrated $1$ over the triangle that would be the area

The trick is to reparameterize the triangle with $0 \leq y \leq \sqrt{\pi/2}$ and $y \leq x \leq \sqrt{\pi/2}$

That corresponds to changing the order of the double integral

Why does the change of the order help us? Where is the difference?

Write it out and you'll see it.

We get $$\int_{x=0}^{\sqrt{\frac{\pi}{2}}}\int_{y=x}^{\sqrt{\frac{\pi}{2}}} 2\sin(y^2)dydx=\int_{y=0}^{\sqrt{\frac{\pi}{2}}}\int_{x=0}^{y} 2\sin(y^2)dxdy=\int_{y=0}^{\sqrt{\frac{\pi}{2}}} 2y\sin(y^2)dy$$

How can we continue from here?

Do we change the variable $u=y^2$ so that computing the integral is easier? Or is there an other way maybe by the area?

Or do we do something else? @BalarkaSen

7:27 AM

What you wrote is not correct. If you integrate with limits $0 \leq y \leq \sqrt{\pi/2}$ and $y \leq x \leq \sqrt{\pi/2}$ you get $\displaystyle \int_0^{\sqrt{\pi/2}} \int_y^{\sqrt{\pi/2}} 2\sin(y^2) dx dy$ which you can simply integrate because the innermost iterated integral is in variable $x$ and the function $2 \sin(y^2)$ is "$x$-free"

hi chat

unfortunately @BalarkaSen I had two exams the previous two days, so I didn''t think on you problem (shame on me)

Hi @mago. Oh, no problem at all.

I worked a bit but I had some problems computing the fundamental group of $\mathbb{R^3} \setminus K$, where $K$ is the Hopf link

but I'm confident I'll a solution somehow... anyway, how's going on?

It's kind of tricky.

@mago Learning a thing or two about mapping class groups (do you know what those are?)

ehm, sure ahahahh
no ide what you're talking about, let me wiki it

7:35 AM

@BalarkaSen Those are tricky beasts

For example, all finite groups occur as quotients of finite index subgroups of the mapping class group corresponding to any genus $\geq1$

@mago If $S$ is a closed surface, the mapping class group of $S$ is the group of self-homeomorphisms $f : S \to S$ "upto isotopy", that is, you identify two homeomorphisms $f, g$ if there is a homotopy $H : S \times I \to S$ between $f$ and $g$ with $H(-, t) : S \to S$ being a homeomorphism for every $t$.

So isotopy just means homotopy through homeomorphisms.

@TobiasKildetoft Oh wow, that's a cute fact

@BalarkaSen It is a result from 2012 msp.org/gt/2012/16-3/gt-v16-n3-p04-p.pdf

I remember it because Masbaum was visiting Aarhus around that time and gave a talk about it

ahh

pretty interesting ,and pretty difficult indeed ahahhahaah

@mago I have only started to learn them so I don't know much

7:46 AM

@BalarkaSen Unfortunately, I don't think the user fuglede is very active any longer. As far as I recall, he worked a lot with MCGs in his PhD

I don't think I know that user

Hi @Alessandro

hi @AlessandroCodenotti

Alessandro Codenotti

Hi chat

SteamyRoot

morning

@BalarkaSen I don't think he was ever very active, and not sure if he ever used chat

7:55 AM

@TobiasKildetoft hmm

I know Huy worked on MCGs

Alessandro Codenotti

Must every automorphism of a field fix the prime subfield pointwise? I'm pretty sure that's true, since 1 maps to 1 and I can get the rest of the field from there

@AlessandroCodenotti Yep

Alessandro Codenotti

So $\text{Gal}(\bar{\Bbb Q}/\Bbb Q)=\text{Aut}(\bar{\Bbb Q})$, while in general $\text{Gal}(E/F)$ is smaller than $\text{Aut}(E)$, if $F$ isn't $\Bbb Q$ or a field of prime order, right?

@AlessandroCodenotti Exactly

ÍgjøgnumMeg

8:52 AM

@LeakyNun It isn't quite the direct product, it's semidirect, also I was asking about the uniqueness of an index 2 subgroup rather than order 2, the problem has resolved itself now though, thanks for your input!

$\oiiint testing$

does not work

[Random]

$$\int_0^{\int \sum_{i=1}^{x}i^i dx} y^y \ln y dy$$

Q: Are there exact analytical solutions to the electronic states of the hydrogen molecular ion $\mathrm H_2^+$?

9:12 AM

A more interesting question: Prove or find counterexample that there exists no analytical solution to the following separable PDE

39

The hydrogen molecular ion (a.k.a. dihydrogen cation) $\mathrm H_2^+$ is the simplest possible molecular system, and as such you'd hope to be able to make some leeway in solving it, but it turns out that it's much harder than you'd hope. As it turns out, if you phrase it in spheroidal coordinates...

Bubaya

9:56 AM

Every right exact functor F (commuting with direct sums) between module categories is tensoring with a bimodule M. How should I call the relation of M and F? I flinch from saying "M represents F". Better suggestions?

10:35 AM

Mar 26 '15 at 23:14, by Chris's sis

Here is a question I consider it interesting. Find $f_n(x)$ such that the integral converges $$\int_0^1 \frac{1}{\log(x)}+ \frac{1}{\log^2(x)}+\cdots + \frac{1}{\log^n(x)}- f_n(x) \ dx$$

Extension:

I want to compute the integral $\iint_D x \ dxdy$ where $D=\{(x,y): y\geq x^2, \ y\leq x+2\}$.

I thought to find the intersection points of the curves $y= x^2$ and $y=x+2$. The intersection points are $-1$ and $2$.

Therefore, $$\iint_D x \ dxdy=\int_{-1}^2 \int_{x^2}^{x+2}x \ dydx=\frac{9}{4}$$

Is this correct?

10:56 AM

(cont.)

$$\lim_{R\to\infty}\int_0^1 \sum_{n=1}^{R} \frac{1}{\log^n(x)} \ dx$$

11:07 AM

@MaryStar yes, wolframalpha.com/input/?i=integrate+x%3D-1+to+2+x(x%2B2-x%5E2) and also checked by hand

They have wifi on the train?

11:24 AM

@Secret Great!! Thanks a lot!!

11:34 AM

@skullpatrol O I forgot, the moment when I replied, I am already back home

@ÍgjøgnumMeg alright

cool @Secret

I have also an other question @Secret :

I want to compute the integral $\oint_C \cos \left (x^{2017}\right )dx+\left (\frac{x^2}{2}+\sin y^{2018}\right )dy$, where $C$ is the boundary of the bounded field that is defined by the curves $y=2-x^2$ and $y=x$, with positive orientation.

We have to apply Green's Theorem, or not?

So, we get the following: $$\oint_C \cos \left (x^{2017}\right )dx+\left (\frac{x^2}{2}+\sin y^{2018}\right )dy=\iint_D \left ( \frac{\partial}{\partial{x}}\left[\frac{x^2}{2}+\sin y^{2018}\right ]-\frac{\partial}{\partial{y}}\left [\cos \left (x^{2017}\right )\right…

11:53 AM

I am not very sure, it seemed to be a correct application of Green's theorem, but the workings will suggest the line integral is independent of what the trig function will be, which I found strange. I am not very certain about this one

how did you all find out SE?

@Secret

12:22 PM

Let me check...

I remember I found PSE first before finding MSE and then CSE and finally WSE and others

But I need to double check what brings me to PSE in the first place

12:52 PM

Actually, I am wrong, I actually found MSE first

Simply Beautiful Art

@Secret o.o

Q: Any weird 'modular like mathematical space' that behaves like as if it is infinite until a threshold is reached?

5

(Using the advice from Mathoverflow, I have rephrased and splitted up the question) (Might be a bit layman because I don't have rigorous math term to describe the concept) Generalize it to mathematical spaces, are there spaces which are sort of like a. Having multiple $\mathbb{R}^2$ spaces th...

calculus geometry

This is my first ever SE question

I just happened to have screenie that moment into my facebook

This is my first site visited:

tea.mathoverflow.net/categories