Mathematics - 2014-12-13 (page 1 of 5)

Pedro Tamaroff

12:01 AM

@skullpatrol raises fist

skullpatrol

Mark of a bully^

Pedro Tamaroff

@skullpatrol raises eyebrows

skullpatrol

Mark of an intellectual^

Perhaps

;-)

evinda

12:17 AM

@TedShifrin The equation $a^3+1=0, a\in \{X,Y,Z\} $ has also the solution $e^{\frac{i \pi (2m+1)}{3}}, m=0,1,2$.

So does this mean that the inflection points of $ \mathbb{P}^2(\mathbb{C})$ are the following?

$ [0,1,-1], [0,-1,1], [1,0,-1], [-1,0,1], [1,-1,0], [-1,1,0], [e^{\frac{i \pi (2m+1)}{3}},1,0], [e^{\frac{i \pi (2m+1)}{3}},0,1], [0, e^{\frac{i \pi (2m+1)}{3}},1], [1, e^{\frac{i \pi (2m+1)}{3}},0], [0, 1, e^{\frac{i \pi (2m+1)}{3}}], [1, 0, e^{\frac{i \pi (2m+1)}{3}}], m=0,1,2$ ? Or am I wrong?

hi pal

hi pal @Twink

>D

:D

where were you_

?

skullpatrol

12:25 AM

Christmas shopping, like my new hat?

Twink

yes, it's lovely

skullpatrol

Come dec 15 everybody gets them

evinda

@TedShifrin Or isn't it like that? :/

Twink

I'm gonna postulate

I wanna be a moderator

Jorge Fernández

I wanna be moderate

Twink

12:34 AM

can I vote for myself?

skullpatrol

Yes, first you need to nominate yourself.

Tom Cruise

12:49 AM

Twink you cannot be a moderator

because you claim to hate math

skullpatrol

It could be a love-hate relationship.

evinda

Good night!!! :)

skullpatrol

1:04 AM

Later pal :)

Khallil Benyattou

1:35 AM

Night everybody!

Twink

lol

Mary Star

2:12 AM

@DanielFischer Instead of iterating until we get the desired result, could we also use the following to show that $k=gcd(n,m) ??

$$\mathbb{F}_{p^n} \leq \mathbb{F}_{p^m} \Leftrightarrow n \mid m$$

Integrator

@Behaviour I said It's nice that you started to access review queues.. Nothing more, nothing gauss.

@Behaviour And who said anything about elecetion?

Behaviour

Everything said about a nominee during election period is about election.

Do you think your remark would get two stars if it was not made during election? I don't think so.

quid

Why does every other answer on this site start with Hint? And why do so many answers not contain a word beyond Hint?

One could also give a not complete answer without this stylistic quirk.

usukidoll

@robjohn @anon where are ya?

Meelo

@quid I like to imagine that the answerer is winking suggestively at the reader when they write that. Maybe we could replace starting with "Hint" by ending with "If you know what I mean."

Pedro Tamaroff

2:25 AM

@Behaviour Hello there.

You're more knowledgeable in analysis, yes?

usukidoll

-_- anyone out there know pdes?

quid

Only rudiments.

usukidoll

@quid what?

quid

Only basic things about them.

robjohn

@usukidoll what's the matter?

usukidoll

2:29 AM

@robjohn I'm trying to figure out a solution that would satisfy the heat equation with the IC of u(x,0) =$ x^2+1$ hold on I'll upload the problem

quid

@Meelo yes, but first what is that good for. It is not as is part of the answer is highlithed or something.

Second I find this, I miss the right word, but not at all elegant.

usukidoll

i.stack.imgur.com/HDwOA.png @robjohn

quid

Recall that, Note that, Observe that...is what would be written in a proper text. Why not use this instead?

Behaviour

@quid I think the idea is to avoid a puzzled comment from OP... but this does not solve the problem?!

usukidoll

@robjohn I'm trying to use inspection so I can satisfy the I.C but the last time I did that I had two different equations that satisfied either $u_t$ or $u_{xx}$, but not the same equation that can satisfy both

Behaviour

2:32 AM

The word is an indication that one should not expect a complete answer in what follows; a part of it was intentionally omitted.

(I dislike this practice in general, although some hints are pretty good.)

usukidoll

@robjohn I do know that $C^2$ is second partial order derivative... but hmm is there really a solution to this that will satisfy the I.C to begin with?

Meelo

@quid It notifies the reader that there's some subtext they ought to be paying attention to - i.e. the rest of the proof. There are plenty of incomplete answers that don't use "Hint", but it seems appropriate for shorter answers where explaining exactly what the hint is good for is too much.

Behaviour

The worst ones I downvote and flag NAA. "Hint: use induction" is certainly in this category.

quid

@Behaviour so why not "The key idea is [...] "

usukidoll

IF I just put $u(x,t ) = t + x^2-1$ and take $u_t$ that will work, but my $u_{xx} = t+2-1 = t+1$ what?!

quid

2:35 AM

@Meelo see my reply to Behaviour

robjohn

@usukidoll I have to get dinner. I may be able to get to this later tonight.

usukidoll

@robjohn ok..but can I have a hint on how to solve this? ^_^

Behaviour

Key Ideas

3.2k 2 17

Tom Cruise

how many students did you all fail this semester?

quid

On the other part of your comment @Behaviour it is not even only the amount of information or detail, the style is just really hard to get used to for me. "Hint: SomeMathJaxMonster" What happened to words?

Meelo

2:38 AM

@quid It's probably appropriate in many cases; looking through some of my answers, I certainly see cases where that'd be more appropriate, but I also see cases where "Hint" feels right (e.g. if someone asks if a property holds for all integers (and it doesn't), "Hint: check this case" seems appropriate).

Behaviour

Well, I don't use this syntax myself. Some people, like now-departed user17762, used it all the time. Others imitate what they see. My habit of inserting the heading Progress when adding OP's comment into the post also seems to have similar effect -- I see other users inserting it.

Studentmath

I personally imitated it in one or two answers that I posted. Didn't think too much about it.

Meelo

That is, I mean "The key idea" is probably more appropriate than "hint" in many cases.

quid

@Meelo in this example the "Hint" seems not necessary to me at all.

Pedro Tamaroff

@quid Yes, Bill's style was not my favourite either.

Behaviour

2:41 AM

I personally prefer a roadmap: a sequence of steps leading to solution, where not all the details of each step are spelled out. I tend to present those as a numbered list. But I don't put Roadmap on top of it...

quid

Yes the "imitating" part is a problem I assumed.

Studentmath

Yeah, I felt like these are the 'normas' of the community, so I copied them

Pedro Tamaroff

@Behaviour I noted that.

Studentmath

Coming to think about it 'The key idea would be..." or something like that would be just as good.

2

quid

Certainly I do not want to advocate spelling out everything. I just want somewhat full sentence. Like, in a research paper there are also steps missing but noone would write "Hint"

Or hardly anyone at least.

Okay some leave thing as execrcise to the reader but I also seriously dislike that.

Behaviour

2:43 AM

One way to avoid being irritated by answers is to filter out all the answered questions, as I do.

Studentmath

I have proofs left as exercise to the reader.. I dislike that very much.

usukidoll

@studentmath do you know pdes?

Studentmath

@Usu I looked at your problem, I don't know enough to help you sadly

Meelo

@quid Woah. You're right. I can't find a single answer of mine where the word "Hint" couldn't just be painlessly excised. (Though I don't seem to have contracted a severe case of using the word in the first place)

usukidoll

@studentmath I know it has to be one equation. I have done this problem before for the wave equation in my homework... I thought creating two separate equations would work, but I only got partial credit on it.

Tom Cruise

2:44 AM

I think that in the answer section we usually expect complete solutions. If you do not give a complete solution I think its ok to use "hint" - especially if there is still a significant amount of work to do.

Pedro Tamaroff

@quid I cannot recall who started the "Hint" thing, but slowly I am filtering it from my style.

quid

This is nice. I find some reassurance in this conversation.

Pedro Tamaroff

The use of "Hint", also, suggests to many users the idea that the answer(er) knows the solution but has decided to withhold information for the good of the OP.

Studentmath

I used it once it seems, and it was a terrible choice to use it there, it seems.

Pedro Tamaroff

Many users use "Hint" when it just means "Hey, this is the first thing that popped to mind, see if it works.

Studentmath

2:46 AM

@Usu did he give you any hint regarding why, the grading lad?

Pedro Tamaroff

Ron Gordon is an advocate of the "Hint" use, but he always checks his hint will work, for example.

Tom Cruise

yes but the student should work through the details on their own, otherwise they won't learn as much

usukidoll

@studentmath I had two different equations and when she took derivatives of it, they weren't equal or something

Meelo

@PedroTamaroff What precisely is the problem with that? I should hope that people aren't posting answers without knowing if they're correct, regardless of the use of "hint"

Tom Cruise

Brian M Scott is my favorite user and he uses "hint" a lot

Studentmath

2:47 AM

Huh, well, I have no idea really @Usu, sorry - don't know PDEs well enough

usukidoll

wait a sec @Behaviour didn't I saw you answer a pde question not too long ago?

Pedro Tamaroff

@Meelo I didn't say there is a problem with it. 4

Studentmath

Don't know PDEs besides the very basic things would be a better description..

Pedro Tamaroff

Actually, I was going to say that that's why some "Hint" answers draw up many upvotes.

Tom Cruise

I want to be as good as Brian M Scott someday <3

Studentmath

2:48 AM

@Pedro that's true, but that might be because they are often done on lhf

Such as when I used it

usukidoll

@studentmath at least I know two of the proof problems so ... that's good ^_^...you can't differentiate term by term for Fourier Series.. so I can disprove that...

quid

@usukidoll math.stackexchange.com/search?q=user:147263+[pde]

seems plausible

usukidoll

ooooooooooh!!! he's in the chat

now if he could be not afk that would be coolies

Pedro Tamaroff

@Behaviour I think a mildly serious problem is the lack of use of the search engine by users.

Studentmath

I've got a question.

Mike Miller

2:50 AM

Mildly?

Pedro Tamaroff

OK. Horrendous.

Tom Cruise

new users dont care, they just want their question answered

Pedro Tamaroff

This creates a ton of duplicates or near duplicates. It might be good, as it has been done before, to keep maintaining the site's popular or FAQs so that people consult them.

Behaviour

Yes, it is. Especially among those with experience, who could have voted to close as a duplicate instead of posting yer another HINT.

Studentmath

It's really ineffective. Sometimes I write down key-words in 'ask a question', add tags and a title - just to get suggestions instead of trying to search through the engine.

That's how bad my experience with the engine is.

Pedro Tamaroff

2:51 AM

It is true, for example, that many people want "personal treatment" and are quite stubborn in reading another person's post. But they should learn.

Behaviour

@Studentmath Use Google with site:math.stackexchange.com

Tom Cruise

whats your question @Studentmath

usukidoll

me too why does Pedro eat bunnies?

@Behaviour hiiiiiii

Studentmath

@Behaviour didn't think about that

Pedro Tamaroff

In fact, I think the tour to the site must include a "how to find questions" and "how to effectively use the search engine" tutorials, or something.

Behaviour

2:51 AM

@Studentmath I even have a bookmarklet for this.

Heh. As if anyone actually reads the tour.

usukidoll

:/

Behaviour

The only button a user sees is Ask Question.

Meelo

Experienced users read the tour. It gives you a free badge. :)

usukidoll

@Behaviour is there an unique equation of u(x,t) that can satisfy the heat equation with the I.C of $u(x,0) =x^2+1$?

Studentmath

@Behaviour how would I run the 'interesting question' thingy?

Behaviour

2:53 AM

Just open any page of the site (not chat), and hit it. Either question list, or a question, or user profile -- does not matter.

As long as the URL in your browser says math.stackexchange.com/... Has to do with cross-domain access etc.

usukidoll

hmmmmm *gives @studentmath a cookie... * trying to get some hints and help here >:/

Studentmath

Oh, this is great. Gives me few out-of-league questions, but really nice!

@Usu I really don't know, sorry - if you won't solve it in like 3 months I may already be able to help you :P

Behaviour

@PedroTamaroff I'd rather see more questions closed as dupes than OT. But don't know how to make this happen. Sometimes, by the time I vote as dupe, there are already 3 votes to close for another reason. So the dupe-mark does not take effect.

usukidoll

@studentmath I'm trying to get @Behaviour to notice what my issue with finding an equation that can satisfy the D.E and the I.C...it's like I can get the equation if I split the cases up in two parts, but I can't do that!!!!

Mike Miller

In some sense, I prefer them closed as off-topic to encourage the askers to not ask again. If they get closed as a dupe, they get their answer.

Meelo

2:57 AM

@Behaviour It'd be nice if there was some separate mechanism to prevent dupe votes from getting eaten by OT votes

Studentmath

@Tom Well, every rational positive number can be expressed uniquely as $n/m$, where $n,m$ are coprime. So, I am looking at a function $f:Q\to R$, where $f(m/n)=m+n$. I want to show it is nowhere continuous.

Behaviour

@Meelo There is one, it's called gold badge. :) But I don't have any. :(

Studentmath

The metric is the usual one. Anyhow, I went ahead and tried to show that $f(B(m/n,\delta))$ for any $\delta$ is not a subset of $B(f(m/n),1/2)$, for every $m/n$.

As this should probably work. Problem is, when I try to find the other item in $f(B(m/n,\delta))$ besides $m+n$, I have no gurantee that the function won't send it to $m+n$ too - for example $2/3$, $3/2$, $1/4$, $4/1$ all map to the same place.

I have no clue how to gurantee that.

Mike Miller

@Behaviour Spend less time in chat and more on main :)

2

usukidoll

..

quid

3:04 AM

@Behaviour or...a diamond

Behaviour

@MikeMiller I don't spend that much time here... and save more of it by perm-ignoring many of the chat regulars. (Yes, usukidoll, you too). I would probably have real- and complex- analysis gold badges by now, were it not for the account deletions/abandonment.

Mike Miller

Yeah, I know. You waste your time far more productively than I.

Studentmath

Ah, think I got it. If $a,b$ are coprime, $ak+1$ and $bk$ are coprime too, right?

@Mike if my time-wasting would've been as useful as yours

I way too often go to places I don't really want to and spend money I don't really have for no real reason, that's time-wasting.

Behaviour

Here's a question where I voted OT instead of spending five more seconds and locating a duplicate. Shame on me. Go close it as a duplicate. (Link is there in a comment)

Pedro Tamaroff

3:29 AM

@Behaviour MUAHAHAHA.

quid

With the Golden hammer

Behaviour

That's what I'm talking about!

quid

was surprise it was closed already when I was there but that explained it.

robjohn

4:44 AM

@usukidoll what does $u(0,0)$ need to be?

usukidoll

@robjohn u(0,0)? that would mean that x = 0 and t = 0 right?

robjohn

@usukidoll that would be what that would mean.

usukidoll

hmm suppose if I do have u(0,0) on the IC I would have a -1 @robjohn

robjohn

@usukidoll what about the BC?

usukidoll

so I need an equation where it not only satisfies the B.V's but also the I.C
B.C u(0,0) = 0, u(1,0) = 0?

robjohn

4:47 AM

that would be what solving the equation implies

usukidoll

@robjohn but what would be the almighty equation to satisfy the D.E unless we make all 0's with a -1?

robjohn

@usukidoll so $u(0,0)=0$ and $u(0,0)=-1$

usukidoll

but wait that would mean that we won't have a $c^2$ solution then

robjohn

@usukidoll we can't even have a solution with an error less than $.01$

usukidoll

Suppose we have $u(0,0)$. Then our B.C and I.C would be
$u(0,0) = 0, u(1,0) =0$
$u(0,0) = -1$

omg this is was a simple one........... as in if we have (0,0) all around... our solution is -1 which is smaller than .01.. so would that mean that we won't have a $C^2$ solution as well? @robjohn

Swapnil Tripathi

4:53 AM

I don't know if it is the right way to do things, but can 3 more people upvote the question "https://math.stackexchange.com/questions/1065836/taking-a-putnam-general-questi‌ons". The guy needs to reach 20 rep to participate in chat.

usukidoll

@robjohn so there isn't a $C^2$ solution isn't it... because wouldn't that just mean second order partial derivative?

Behaviour

@SwapnilTripathi I don't think this is a right way to do thing. If those users were in chat, they'd be able to invite the OP to a separate room, despite the reputation. As it is, they are not in chat. Also, I don't think that at this stage the OP really needs someone who took the exam recently. The basic background research consists of looking at the problems of past exams and reading the description on Putnam page

Swapnil Tripathi

@Behaviour: I didn't know that. Thanks. And sorry. :)

usukidoll

hmm I think @robjohn is afk?!

skullpatrol

He does that sometimes ...

usukidoll

5:02 AM

@skullpatrol just need to know if I'm doing these wave equations right...
4. I chose to do it with D'Alemberts
5. I used harmonics solution...
I wonder if that's a great idea. I think so since the problems looked similar to what I've done already.

I swear #4 really looks like a D'Alemberts... so I'm just hoping that 0 is a typo because D'Alemberts can be used for a $-\infty <x< \infty$

#5 I used harmonics solutions via separation of variables...I'm almost done (it's in my notebook in draft mode)

blah I'm hungry

I should go afk for a bit...and then study some Number Theory ...then Japanese and finish these pdes later....cuz I'm planning to stay up late!!!!!!!!!!!!

skullpatrol

I think the guys in the physics chat room can help you.

Swapnil Tripathi

And here is @Integrator. Good at differential too? Hi!

Integrator

@SwapnilTripathi Hi!

usukidoll

@skullpatrol physics chat room?

skullpatrol

It is called the h bar

Tom Cruise

5:10 AM

iiiiiiiiiiiiiii

Swapnil Tripathi

iiiiiiiii :D @TomCruise

Oh. I fell short of i's

Tom Cruise

are you a topologist?

Swapnil Tripathi

Not yet. :) Course next semester.

Tom Cruise

oh then we can talk topology

Integrator

I'm outta this!

Tom Cruise

5:12 AM

you are a masters student at 21?

most masters students here start at 23 or later

Swapnil Tripathi

Its a totally different scenario here in India. We have a 3 years bachelor's program in which our span of knowledge is really really small.

Ironically they start teaching us "äctual" maths after we enroll for Masters. Oh, all the fun I had before this.

Tom Cruise

I pretty much started math with my masters as well

but that is because I had a different undergraduate major

Swapnil Tripathi

Sweet! Which subject?

Tom Cruise

it is not important ;)

math is all that matters

Swapnil Tripathi

lol. Yes, now it is.

Sawarnik

5:30 AM

@SwapnilTripathi What did you study in bachelors?

Swapnil Tripathi

Mathematics. :D @Sawarnik

Sawarnik

I mean, what in maths? :P

Tom Cruise

and poetry

Swapnil Tripathi

poetry? @TomCruise

Tom Cruise

yes medieval spanish poetry

I can write a haiku about math now

Swapnil Tripathi

5:32 AM

Oh, analysis stuff, abstract algebra..differential, though I didn't like it.

@Sawarnik

Tom Cruise

multitalented I am

Swapnil Tripathi

@TomCruise: Wow. Haha. Yes, indeed.

Sawarnik

@SwapnilTripathi Eww... though can you tutor me algebra? :D

Swapnil Tripathi

Abstract?

Tom Cruise

Analysis is just too studied and stale for my taste

Sawarnik

5:33 AM

@SwapnilTripathi And linear..

Swapnil Tripathi

@Sawarnik: I haven't been good at linear. I am up for abstract!

Tom Cruise

same with me

Sawarnik

Fine, how much would you charge?

:P

Tom Cruise

one billion dollars

Swapnil Tripathi

lol. @Sawarnik

@TomCruise: Nobody likes linear? What's up with that. I thought I was the only one.

Tom Cruise

5:35 AM

I dont like matrices

Sawarnik

@SwapnilTripathi tell me something reasonable :D

Swapnil Tripathi

@Sawarnik: Still thinking...............

Tom Cruise

in abstract algebra you just follow the definitions

Swapnil Tripathi

@TomCruise: You started with topology? It sounds like some pretty tough stuff.

Sawarnik

@SwapnilTripathi Are you following the match? :D

Tom Cruise

5:38 AM

no it is actually similar to abstract algebra in that way... lots of definitions but it's pretty easy to connect everything together

at least in the early stages

Swapnil Tripathi

@Sawarnik: No. Stopped following it back in 10th standard. Much into FIFA.

Tom Cruise

I started with Analysis and then I decided to go more abstract, into topology

Sawarnik

@SwapnilTripathi :< India are towards a miraculous win :D

Swapnil Tripathi

@TomCruise Self study?

Tom Cruise

because there are lots of amazing spaces to play with

no this is when I started my masters

Swapnil Tripathi

5:42 AM

@TomCruise: Oh oh. Transition! Poetry to maths! Doesn't it seem like an alien language?

@Sawarnik: Haha. Ok..

Sawarnik

Oh gawd .. what bad omen .. two wickets in 1 over :O

Towards a loss now. Vijay out on 99 :< :<

Tom Cruise

I guess I self-studied some as an underaduate

I had some math background because I was initially an engineering major

Swapnil Tripathi

@Sawarnik: lol. I don't know what to say :P

Tom Cruise

the reason I prefer math to engineering is that nothing I do can be used to hurt people

one reason

Swapnil Tripathi

@TomCruise: lol. That's an overstatement.

Tom Cruise

5:45 AM

because nothing in abstract topology will ever be of practical use to anyone

:)

Sawarnik

@SwapnilTripathi It can be sure.

Tom Cruise

this is cricket?

Sawarnik

@TomCruise Yup!

Tom Cruise

it is funny I have no idea how cricket is played

Sawarnik

Both Rahane and Dhawan got bad decisions at crucial stages :<

Swapnil Tripathi

5:47 AM

I couldn't stop laughing on this one.

Sawarnik

@SwapnilTripathi 9GAG?

Swapnil Tripathi

I don't know. :D

Tom Cruise

that is funny

Sawarnik

@TomCruise Its a very interesting game :D

Tom Cruise

because she did not study she had to marry a fat rich man

I think it is like baseball with a flat bat and a tiny ball

Sawarnik

5:49 AM

@TomCruise Tiny ball .. no way.

Tom Cruise

thats all I can tell you

Sawarnik

A very recent case:

dailymail.co.uk/news/article-2848230/…

Swapnil Tripathi

Continue. :) I'm leaving @TomCruise @Sawarnik. See you.

Sawarnik

@SwapnilTripathi ta-ta :D

Swapnil Tripathi

:D

Tom Cruise

5:52 AM

ok come back again

dailymail has some crazy stories

Sawarnik

This is exactly the time Dhoni was required @Swapnil :((

@TomCruise It happened around a week ago. The first test match of the 4 match series was abandoned due to this.

@Tom Are you somewhere from America?

Balarka Sen

I'm up earlier than I planned. Grumph.

Sawarnik

Ooops Balarka .. silently slips away.

@BalarkaSen Me too btw.

Balarka Sen

Hello @Sawarnik

Tom Cruise

I am so tired

I'm gonna watch a movie and leave chat running

so ping me if you need me!

Balarka Sen

5:59 AM

@TomCruise Isn't it a dead of a night there?

@anon

You there?

Tom Cruise

yes it is night

Balarka Sen

@anon Consider the inverse limit of the system $\cdots \to \mathcal{M}_2 \to \mathcal{M}_1 \to \mathcal{M_0}$ where $\mathcal{M}_n$ is the Riemann surface of$w^{p^n} = z$ over $\mathbb{C}$ and the maps $\mathcal{M}_n \to \mathcal{M}_{n-1}$ are $(w, z) \mapsto (w, z^p)$. $\mathbb{Z}/p^n\mathbb{Z}$ are monodromy groups of $\mathcal{M}_n$ so $\mathbf{Z}_p$ acts on the inverse limit ("solenoid Riemann surface") $\mathcal{M}$.

Tom Cruise

whoa

Balarka Sen

But if you chuck out the branched locus, which is $0$, the whole thing deformation retracts to just inverse limit of circle, so it's just the same homotopy type as the solenoid.

Tom Cruise

do you prefer group theory or field theory?

Balarka Sen

6:09 AM

Field.

Question of apparent interest : Every Galois group over $\mathbb{C}(z)$ can be realized as monodromy group of some Riemann surface over $\mathbb{P^1}$. Can we construct a solenoid Riemann surface on which $Gal(\overline{\mathbb{C}(z)}/\Bbb C(z))$ acts?

@anon ^^

Tom Cruise

I guess field theory is sort of like super group theory

more complex

Balarka Sen

@TomCruise Field/Galois theory is the most geometric part of algebra.

And I disagree with the "more complex" part

Tom Cruise

yes I enjoyed that

Balarka Sen

Fields have a lot of structure, making a lot of things less pain in the neck.

Tom Cruise

yeah you're right

sort of like normed linear spaces vs metric spaces

Balarka Sen

6:12 AM

yeah.

indeed.

@TomCruise for example you could try to do galois theory on groups (same definitions, same proof) but the action you'd get there wouldn't give you the galois group short exact sequence, but a left exact sequence.

that's why, say, groups have a cohomological aspect and fields do not.

Tom Cruise

I am losing some of my knowledge in algebra because I don't use it really

Balarka Sen

General topologists rarely ever use algebra. But they come in handy.

Tom Cruise

but I was very good at it a couple years ago

Balarka Sen

I am learning topology to set it against some problems in algebra :P

@TomCruise Maybe you could sort of restudy it.

Tom Cruise

yes I should

but I need to study graph theory now for my graduate program

I need to cover the first semester over the winter break

IN 3-4 WEEKS

ugh

but once I am done with it, I can focus 100% on research, and study whatever I like

Balarka Sen

6:19 AM

I've never formally studied graphs

@TomCruise And your research work I guess would consist of a lot of pathological spaces? :P

Tom Cruise

probably, lol

oops

I want to solve some of these problems

Balarka Sen

I dunno what a widely connected space is.

Tom Cruise

problem 14 is the one we were talking about earlier

I just phrased it a little differently

Balarka Sen

ah

oh you can just make up widely connected space from any indecomposable continua using your method.

Tom Cruise

yes

well not any

it has to have at least as many composants as closed sets which disconnect the space

Balarka Sen

6:25 AM

right, indeed

Tom Cruise

some indecomposable continua have very few (finitely many in fact) composants

Balarka Sen

maybe the first goal should be to find an exotic example of a widely connected space

Tom Cruise

yeah one problem is we dont have many examples

Balarka Sen

yeah having enough examples is always good for working with them

Tom Cruise

have you ever heard of an explosion point?

Balarka Sen

6:27 AM

@TomCruise nope

Tom Cruise

there exist connected spaces such that when you remove a particular point, the remainder is totally disconnected

Balarka Sen

yeah, that i know

Tom Cruise

ok that point is called an explosion point

Balarka Sen

ah ok

i think such a space is called Kurakowtski fan or something like that

Tom Cruise

yes

that is the only one I know of

Balarka Sen

6:30 AM

what about the hawaiian earring, @TomCruise?

Tom Cruise

that does not have an explosion point

Balarka Sen

oh totally disconnected

Tom Cruise

yeah

Balarka Sen

if it's just disconnected then a interval would do.

hehehe.

Tom Cruise

I was surprised that such a space exists

Balarka Sen

6:34 AM

@TomCruise Maybe you could do something like this : Cantor set is totally disconnected. Now add something like long strings with the points in the space and join them together at some point. removal of that meeting points leaves everything disconnected.

oh no that doesn't work. the strings are connected.

Tom Cruise

yeah

Balarka Sen

looks like some wild fractal type structure is needed.

Tom Cruise

I wonder if there could exist a widely connected space with an explosion point

Balarka Sen

make the strings homeomorphic to the cantor set and then join their comoponents too with a cantor set and ad infinitum but make sure the strings meet at some point.

this sounds intimidating. hehe.

Tom Cruise

I think you are describing the kuratowski fan

Balarka Sen

6:36 AM

oh?

Tom Cruise

you take rationals or irrationals as the "strings"

Balarka Sen

ah, indeed

usukidoll

yo

Balarka Sen

we are such pathetic pathological topologists, @TomCruise

Tom Cruise

lol

it is difficult to think of these spaces

Balarka Sen

6:41 AM

but fun nevertheless

Tom Cruise

they wouldn't be pathological if they were easy to think of

Balarka Sen

when you "see" them finally, it feels like you have overcome a great mental obstacle or something.

Tom Cruise

yeah

but when dealing with nonmetric spaces it is even more difficult

Balarka Sen

yeesh, tell me about it

Tom Cruise

I've got to get some sleep

Balarka Sen

6:45 AM

yeah, bu-byes.

Tom Cruise

see you tomorrow

Balarka Sen

don't let the pathological spaces bite

Tom Cruise

no worries :)

Daniel Fischer

10:22 AM

@MaryStar Yes, if you know that, using it shortens the argument.

r9m

@DanielFischer is there any way of determining asymptotics of a quadratic recursion relation like $x_{n+1} = x_n^2 + c$, where, $c = \frac{1}{4}$ and $x_1 = x$ ?

Daniel Fischer

@r9m Not sure. For real $x$ with $\lvert x\rvert \leqslant \frac{1}{2}$, I think one can work something out. For real $x$ with $\lvert x\rvert > \frac{1}{2}$, maybe the approximation $x_n \approx a\cdot b^{2^n}$ works, but it's possible that the addition of $c$ makes that a too bad approximation, even asymptotically wrong. For complex $x$, uuh, looks difficult.

@Behaviour Get a few gold tag badges. The dupe-hammer overrules.

Mary Star

10:47 AM

@DanielFischer $$x^{p^n-1} = x^{p^m-1} = 1 \Rightarrow x^{p^n-1} = x^{p^m-1} \Rightarrow x^{p^n-1-p^m+1}=1 \Rightarrow x^{p^n-p^m}=1 \Rightarrow \left ( x^{p^{n-m}-1} \right )^{p^m}=1 \overset{ \text{ Frobenious homomorphism }}{\Longrightarrow} x^{p^{n-m}-1}=1 \Rightarrow x \in \mathbb{F}_{p^{n-m}} \Rightarrow \mathbb{F}_{p^n} \cap \mathbb{F}_{p^m} \subseteq \mathbb{F}_{p^{n-m}} \Rightarrow \mathbb{F}_k \subseteq \mathbb{F}_{p^{n-m}} \\ \Rightarrow k \mid n-m$$

$$\mathbb{F}_k \subseteq \mathbb{F}_{p^m} \Rightarrow k \mid m$$

r9m

@DanielFischer i see ! so I want to find asymptotics of the this sequence with $a(0) < 1$ I see the behavior changes completely ! :o

Daniel Fischer

@MaryStar You typo'ed $\mathbb{F}_k$ where it should be $\mathbb{F}_{p^k}$ twice. If you already (officially) know that $\mathbb{F}_{p^k} \subset \mathbb{F}_{p^r} \iff k \mid r$, then we don't even need the first step, we directly know that $\mathbb{F}_{p^n} \cap \mathbb{F}_{p^m}=\mathbb{F}_{p^k}$ with $k\mid \gcd(n,m)$. For the reverse inclusion, let $g=\gcd(n,m)$, and note that $\mathbb{F}_{p^g} \subset \mathbb{F}_{p^n}$ and $\mathbb{F}_{p^g}\subset \mathbb{F}_{p^m}$ by the equivalence above.

r9m

seems I'm interrupting a conversation ! sorry :) after you @Mary kun :-)

Daniel Fischer

@r9m For this?

r9m

@DanielFischer hee (busted) :) yes !! :D

Swapnil Tripathi

10:56 AM

@DanielFischer: If there are 3 vacancies for moderators. Exactly 3 would be selected? Not less?

Daniel Fischer

@r9m I've also spent some time thinking about it. No problem getting an answer by letting the computer iterate, but I haven't yet seen how to get good enough bounds for $x_{2015}$ in an elementary way.

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$Mathematics$ Mathematics