Mathematics - 2015-08-01 (page 1 of 2)

Soham Chowdhury

12:19 AM

hahahaha

PVAL

12:35 AM

@SohamChowdhury What book is that? I'd like to be able to tell people to avoid it.

Paul Plummer

@PVAL Pretty sure it is Algebra Ch0

PVAL

Oh I already tell people to avoid that book.

Paul Plummer

Haha

Alec Teal

It's a weird book.I sort of love it and hate it.

I hate it because it's ... hatable, but it also covers a lot of ground, quickly and well.

pjs36

Care to elaborate, @PVAL? I have no opinion either way (actually I didn't mind the book), I'm just curious

Paul Plummer

12:41 AM

The past two answers I have written, I have ended up citing the same author. I sort of feel like a stalker.

PVAL

Well I haven't looked at it for a long long time. IIRC it takes a lot of time developing categorical stuff with no good examples of categories present. Looking at it now, group actions are in the last 10 pages of the chapter on group theory.

2

Also I dont like the title

Mike Miller

I agree.

Paul Plummer

Been doing much interesting @MikeMiller?

Mike Miller

The point of introducing category theory early, in my mind, is to try to teach functorial thinking early. But functorial/categorical thinking (to the average mathematician) is mostly useful in places like algebraic topology when you're transporting structure between completely different contexts. There's not much of it in algebra. I liked Hungerford's book for this: occasionally there are proofs that are basically "This is unique because initial objects are unique"...

precisely when something like that shortens the proof and provides intuition, rather than for its own sake.

Alec Teal

Oh it's useful to have, but it'll develop naturally anyway.

Mike Miller

12:53 AM

@PaulPlummer: Just reading. I start TAing probability here in the summer session next week, but until then I can read in exotic locales. (I'm camping out at a friend's in a state park now.)

Paul Plummer

I think that is basically the approach Algebra Ch0 takes. Its not all categories, it just isn't afraid to go there. It goes fairly slow, for example it does not introduce functors till ch8 (I think...), which can be considered a good a bad thing, probably good from an educational perspective

Sounds fun, the reading in exotic locales.

Mike Miller

Also why LA is nice. Can just go do work on the beach whenever.

Soham Chowdhury

@Mike, @PVAL: He does the usual $na = a + a + \cdots + a$ thing earlier on, though.

Paul Plummer

I have a tough time working in the heat, and the bright sun

Mike Miller

I read some of Aluffi and don't really agree, @Paul. But I don't feel strongly enough to fight about it, just strongly enough not to teach out of it or suggest it to beginners.

Paul Plummer

12:58 AM

Well I don't think I would recommend Hungerford to beginners either :)

Mike Miller

@SohamChowdhury: Sure, then this is inoffensive. Same proof, of course.

Paul Plummer

Oh, I guess he has an undergraduate book, never seen it, so not sure about that one.

Soham Chowdhury

But the initial object way shows that there is only one way to do it, as well, right? So there's that.

Mike Miller

Never seen it either.

No, the other way does too. It's the same proof. This is just a cute way of phrasing it.

Soham Chowdhury

Haha, okay.

Mike Miller

1:08 AM

@Paul: I tried to ask about you, but I guess the message didn't send. What are you up to?

Paul Plummer

@MikeMiller Not much, just moved, and will be starting graduate school soon. So I had to get ready for the move and do a bunch of stuff after the move (like fill out GA paper work etc). Attempting to study some algebra and topology, in hopes of passing a qual or 2 so that I don't have to take those classes. Today mostly procrastinated (did research for a math.se answer, listened to some podcasts, chatting...).

Mike Miller

Those are fun. Where did you move to?

Paul Plummer

Oklahoma, will be going to University of Oklahoma (moving from Idaho)

Mike Miller

Gotcha. What do you hope to study?

Fair warning: My computer claims to have 13 minutes of battery life left, so I'm going to vanish at some point.

Paul Plummer

Political science :) Nah, I am not 100% but they have some geometric group theorists, and what seems to be a good geometry and representation theory groups. So leaning towards GGT. @MikeMiller

Mike Miller

1:16 AM

Seems like that's what you've been generally interested in before, yeah?

Paul Plummer

Yes

Alec Teal

I've heard bad things about Oklahoma

Deep south :/

Paul Plummer

Its not deep south...

Mike Miller

Oklahoma is at the tip of the midwest, and culturally tends to be more like the midwest than, say, Alabama.

Paul Plummer

Culturally it is probably more south than north (geographically it is basically the middle of the US)

Alec Teal

1:19 AM

What I meant was: the more... nutty part of America.

Where they speak like Kletus

Mike Miller

Right, Oklahoma is not so bad in that respect. You could do much worse.

Paul Plummer

Yah, for example Ted managed to escape Georgia with his life

Alec Teal

Anyway good luck! I'm sure you'll be fine!

Mary Star

Hello!!

Kevin Driscoll

1:34 AM

I dunno I remain unconvinced about the cultural heritage of Oklahoma. To me it's more like Arkansas or Texas than Kansas. That outrageously racist chant that went viral was by an OU frat

Paul Plummer

Eh, maybe you're right, I didn't exactly do a cultural analysis of the place before moving. I am not sure how much you can base a place by its frats though.

Kevin Driscoll

its a good point. They represent a vocal but extreme minority even of young people

Paul Plummer

But football(ellipsoidishball) is pretty big here, so that is one indicator

pjs36

I don't know much about the "dust bowl" region; I'm a born-and-bred rust-belter :P

I don't know if Oklahoma even qualifies as dust bowl, quite frankly!

Soham Chowdhury

Wayback Machine seems down. :(

Paul Plummer

1:45 AM

Well it is definetly dust bowl, pretty sure that is where The Grapes of Wrath was set

What did you want to wayback? @SohamChowdhury

Soham Chowdhury

1:59 AM

A blog post on a website that seems down.

Mike Miller

rip

Kevin Driscoll

yup its down, been that way for less than an hour though

Mike Miller

I have two minutes left. How exciting.

Paul Plummer

It feels like it has been longer than 13 mins

Were you forced to have the picture taken @SohamChowdhury It sort of looks like you are scared

Soham Chowdhury

Which picture?

Oh, god.

Paul Plummer

2:14 AM

Just the one on your account

Soham Chowdhury

Oh, no.

:P

The Substitute

7:10 AM

hello - off topic. Why is it that when we want to check whether $S$ is a subring of $R$ the multiplicative property we have to check is that $ab\in S$ for $a,b\in S$ but with respect to the additive structure we check $a-b\in S$? Shouldn't the multiplicative property be $ab^{-1}\in S$ (for the same reason that showing $a+b\in S$ is not sufficient to show that $S$ is a subgroup of $R$?)

Balarka Sen

Rings do not nessesarily have multiplicative inverse. You're thinking of fields.

The Substitute

ah, of course, thanks

Huy

9:05 AM

@DanielFischer: Do you know why in $S^n$ we have $R_{ijkl} = g_{ik} g_{jl} - g_{il} g_{jk}$? I have a computation of sectional curvature and it starts with this formula, but I've never seen it before. Is this a special case of the more general formula for $R_{ijk}^l$ expressed by Christoffel symbols which simplifies on $S^n$?

Daniel Fischer

@Huy Sorry, but differential geometry is not something I'm comfortable with. Ted will probably know.

Huy

No problem, I'll ask him or Mike when they're around!

Chris's sis the artist

10:29 AM

@Gato I think you might like to show the power for complex analysis here

15

Q: About the integral $\int_{-1}^1 \frac{1}{\pi^2+(2 \operatorname{arctanh}(x))^2} \, dx=\frac{1}{6} $

Here is a question that naturally arose in the study of some specific integrals. I'm curious if for such integrals are known nice real analysis tools for calculating them (including here all possible sources in literature that are publicaly available). At some point I'll add my real analysis so...

@Gato specifically, the supplementary question.

Gato

@Chris'ssistheartist nice question

Chris's sis the artist

@Gato This is the way my book will look like. :-)

Gato

@Chris'ssistheartist very interesting, I am excited to read it :D

Mats Granvik

Click away the Wolfram message at the "x" next to the word sniply. The fluid flow animation graphics is amazing: haxiomic.github.io/GPU-Fluid-Experiments/html5

Vrouvrou

Hello, please when we have $\int_{\Omega}v_n(x)v(x) dx\rightarrow 0, \forall v\in W^{1,p}_0$ can we say that $v_n\rightarrow 0$ in $(W^{1,p}_0)^*$ ? please

Chris's sis the artist

10:32 AM

@Gato My opinion, it's just my opinion, the real analysis used very wisely is more powerful than complex analysis and offers far nicer and easier solutions.

Gato

@Chris'ssistheartist perhaps, but I will said that complex analysis doesn't require much knowledge, but real analysis tools, one needs lot of known facts.

Chris's sis the artist

I took all problems from Nahin's book, the ones considered the worst as difficulty and solved them all in very easy ways (from the complex analysis chapter).

Gato

@Chris'ssistheartist you second integral is much more difficult that the first one ^^

Chris's sis the artist

@Gato Yeap. :-) Both are created by me and many others like that far more complex.

What you see on MSE is a piece of cake (referring to my question on main) conpared to the hard stuff I have.

Vrouvrou

@robjohn Hello, please when we have $\int_{\Omega}v_n(x)v(x) dx\rightarrow 0, \forall v\in W^{1,p}_0$ can we say that $v_n\rightarrow 0$ in $(W^{1,p}_0)^*$ ? please

Chris's sis the artist

10:39 AM

compared

Gato

@Chris'ssistheartist there is lot of questions very hard here aout integrals

But to create it, it's very impressive :)

r9m

@Chris'ssistheartist Hello! How are you? :-)

Chris's sis the artist

10:56 AM

@Gato like, say, $$\int_{-\infty }^{\infty } \frac{e^{\pi x} \left(4 e^{\pi x} x+2 e^{\pi/2 x}\right)-\sqrt{e^{\pi x}} \left(\pi x^2+2 x+\pi \right) x}{\left(e^{\pi x}+1\right)^3 \left(x^2+1\right)^2} \, dx=\frac{5 }{32}\zeta (2)$$

@r9m hey! Not too bad. You? :-)

r9m

@Chris'ssistheartist alive :)

Chris's sis the artist

@r9m Good! Pretty silent in the last period of time though.

r9m

@Chris'ssistheartist ya! I was semi-depressed about a bunch of stuff .. that's all

Chris's sis the artist

@r9m Take some chocolate when depressed. :-)

(It works!!!)

r9m

@Chris'ssistheartist hehe! I do .. :) that's why I added the semi- ..

Chris's sis the artist

11:01 AM

@r9m I only hope you're not depressed with my stuff. I would feel guilty then. :D

r9m

@Chris'ssistheartist I usually get the depression from stuff external to mathematics .. :P math never depressed me :P

Chris's sis the artist

@r9m Is it about something bad?

r9m

@Chris'ssistheartist nah .. nothing bad.

Chris's sis the artist

@r9m You have too many positive qualities to ever let you caught by any kind of despression. Really.

Be honest with yourself and put the right price on you, those like you are very rare. ;)

r9m

@Chris'ssistheartist I'll keep that in mind, thanks!

Alec Teal

12:30 PM

@EricStucky

2

I think that's brilliant.

:D

Also I replied BTW

yeah I noticed :)

Glad your smiling now.

Eric Stucky

When you say you're running multiple computers, do you mean like hundreds?

Alec Teal

12:35 PM

No, 6.

But they're rarely restarted so LOADS of tabs build up. So I'm in this chat from probably >20 different tabs.

Eric Stucky

But you can press the "leave room" button and that should just work?

per computer of course

Alec Teal

Only in one chat. I'd have to leave it in everything I opened after the first time I joined

Eric Stucky

I'm not sure what you're saying

Alec Teal

But ignorance may be bliss for you. I'm still going to be checking up on the chat even if I'm not there all the time.

Eric Stucky

There's a "leave that room" button to leave rooms remotely

Alec Teal

12:37 PM

I'd have go to every tab I opened after the first time I joined and leave - the ones from before wont matter.

Eric Stucky

hmm that's interesting

Anyway I gotta get to teaching. I'll see you around.

Alec Teal

Yes. Yes you will.

Soham Chowdhury

12:57 PM

@Balarka, of course I'm not learning tensor products now! I'm learning about linear maps. :)

Remember me

@AlecTeal Nice one

Soham Chowdhury

Hello, @Rem.

Remember me

Hello@Soham

Hey@Bal

Soham Chowdhury

I was outside all day.

Alec Teal

Hey @Rememberme

Remember me

12:59 PM

Hi

Balarka Sen

@Soham Sure, but you're a bit jumpy anyway. :P

Remember me

Why@Soham .. In that rain what on earth are you doing outside

Balarka Sen

hi @Rememberme

Soham Chowdhury

Of course I am. I'm a hormonal 16-year-old, what do you expect? :P

Remember me

haha

Alec Teal

1:01 PM

You to be doing what the other 16 year olds do: fall in love with girls because they touched a part of you.

skill patrol

@AlecTeal did you take any codiene pal?

Soham Chowdhury

I only became amenable to learning lin alg when I learned that a module is just a vector space over any arbitrary ring. :)

Remember me

@SohamChowdhury Isnt that the reason why modules were introduced

Alec Teal

@skillpatrol why do you ask?

Remember me

hi@EricStucky

Balarka Sen

1:02 PM

Being jumpy has grave consequences in mathematics. You'll turn into google.

skill patrol

@AlecTeal just wondering if you feel better.

Balarka Sen

Trust me, I know.

Alec Teal

I went swimming yesterday and it has made my balls angry @skillpatrol - thanks for asking.

skill patrol

np

Soham Chowdhury

Personal experience?

Alec Teal

1:04 PM

No, swimming.

Balarka Sen

yep

Hey, when are you going to meet up with SB? D'you have any idea?

Soham Chowdhury

Nope.

I should email him. Actually, I will, after I get groups down perfectly. :P

Remember me

Can you guys secretly tell me who is SB?

Soham Chowdhury

My mentor.

Remember me

Ah .. full name

Balarka Sen

1:06 PM

You wouldn't know him.

Remember me

Where does he teach ISI?

skill patrol

is he a mathematician?

Remember me

Okay dropping the topic

Balarka Sen

Algebraic topologist. And he doesn't teach in ISI, no.

Alec Teal

Sometimes I don't know why I bother doing maths, my dream job is an Emerald Guard on Takeshi's castle.

Soham Chowdhury

1:07 PM

"Star farmer spotted!"

Alec Teal

?

Balarka Sen

@Soham I am going to meet with a motivic guy after the exams. evilgrin

Alec Teal

Should we be worried for his safety @BalarkaSen ?

skill patrol

what's a "motivic"?

Alec Teal

You know that mod picture that Richard linked? It's a hammer with the word "mod" written on it

skill patrol

1:10 PM

motivation?

Alec Teal

Did anyone else see it like this:

skill patrol

@AlecTeal yes

Soham Chowdhury

@BalarkaSen You mean all that AG stuff?

Sheesh, I am turning into Google. :'(

Chris's sis the artist

Today is one of those days when I think I'll leave mathematics after publishing my book. I don't know if I wanna reach a peak where to feel myself completely alone although being alone is not a problem to me, but it's about a certain math level that major part of math people would probably never enjoy. Then you share your stuff with yourself.

Alec Teal

I shall find that mod pic and put them side by side "claim" and "reality"

Balarka Sen

1:11 PM

it's not exactly correct to say that motives are algebraic geometry, but whatever

skill patrol

@AlecTeal that's just the way some mods are pal

Balarka Sen

he's an A^1-homotopy theorist, in fact :)

Soham Chowdhury

Nooooooooo

I dunno what that is, but it sounds cool.

:P

Who turns you on to these people?

Balarka Sen

prof.

Soham Chowdhury

ofc.

Balarka Sen

1:13 PM

he's in the faculty in the uni.

Soham Chowdhury

"Balarka, shon, tor khub htpy theory bhalo lage tai na? . . . " :P

Anyway, good luck.

Balarka Sen

i won't learn A^1-htpy theory from him. i just need a person i can pick up some etale-ish stuff.

hopefully, i would be able to exploit him rightly so as to know what a motive is too :P

skill patrol

@Chris'ssistheartist you'd be surprised how many smart people are out there...

Alec Teal

Just wanna test something quickly:

Didn't work :/

skill patrol

@Chris'ssistheartist ...don't feel alone, yet.

Chris's sis the artist

1:17 PM

@skillpatrol It's not about smartness, it's more about much experience combined with crazy passion in a certain corner of math.

skill patrol

@Chris'ssistheartist that's what I meant too.

Chris's sis the artist

@skillpatrol ah, OK.

N3buchadnezzar

Mmm

skill patrol

OMG! @N3buchadnezzar

Chris's sis the artist

Ramanujan would have never been what is known to be today without a crazy amount of work, driven by a burning passion.

skill patrol

1:21 PM

@N3buchadnezzar Look who's back :D

Alec Teal

Yeah you compare yourself a lot to him @Chris'ssistheartist - don't others have to do that?

I've always said "It's not arrogance if your right" but you're just farming integrals right?

skill patrol

Party!!!

N3buchadnezzar

Looking for a sequence of functions such that $\lim_{n \to \infty} \int_0^1 f_n(x) \,\mathrm{d}x = 0$ but $f_n(x)$ is almost nowhere zero, eg $f_n(x) \to 0$ as $n\to \zero$ does not occur. any ideas?

Alec Teal

Those hamsters are living my secondary dream.

N3buchadnezzar

Any ideas?

Alec Teal

1:24 PM

@N3buchadnezzar

N3buchadnezzar

I think I got it, thanks!

Chris's sis the artist

@AlecTeal I can compare to anyone I want to, but that's not the point. Ramanujan is a referrence to me as performance, one that I wanna reach and exceed in the area of integrals, series and limits.

Alec Teal

Good.

Chris's sis the artist

Maybe it's not the case if I leave mathematics after publishing my book.

Alec Teal

Also that gif is brilliant, it could be the codeine talking but LOL so much

I mean it's a STOP sign!!

N3buchadnezzar

1:25 PM

x^n seems to work

Alec Teal

In future @N3buchadnezzar post a question

N3buchadnezzar

Nah

skill patrol

he's too cool for that ;-)

N3buchadnezzar

@AlecTeal Random bits and bobs about mathematics is for the chat ;-) Also I have supreme seniority

2

Daniel Fischer

@N3buchadnezzar Characteristic functions of intervals of length $2^{-k}$. Sweep the whole interval.

skill patrol

1:27 PM

Konig of coolness^

Alec Teal

skill patrol

*König

@AlecTeal is that Pippi Longstocking?

Alec Teal

No idea

Huy

1:46 PM

@N3buchadnezzar: What do you mean by almost nowhere zero? That it is almost everywhere nonzero?

That the set of points where it is zero has measure zero?

N3buchadnezzar

@Huy Look at the image i posted =)

Huy

There's a $^2$ in that image, but not in your original question.

Also, why is your image's quality so bad? :(

N3buchadnezzar

2:10 PM

@Huy Sorry about the image and the missprint... =(

Seems like a characheristic function might work as Daniel said.

Huy

@N3buchadnezzar: That was what I thought of first too, but you need to adjust it somehow.

Ah, what Daniel said should work actually.

Chris's sis the artist

@M.N.C.E. hey! Good approaches so far! :-)

N3buchadnezzar

@Huy Yeah. I get the idea, having small rectangles with width 1/2^k. Silly question is there a simple way to write that mathematically?

Something like $\Xi_{[0,2^-n]}(x) = 1$ ?

Huy

@N3buchadnezzar: I'm not sure what exactly you're trying to express with your equation.

Can you put into words what your aim is?

N3buchadnezzar

Express the characeristic function Danial described as an explicit formula

Huy

2:20 PM

@N3buchadnezzar: Can you express in words the exact properties you want that function to satisfy?

Or do you not know in general how to denote characteristic functions?

Daniel Fischer

$$f_{2^k+r} = \chi_{[r\cdot 2^{-k}, (r+1)\cdot 2^{-k}]}$$

M.N.C.E.

@Chris'ssistheartist Thanks. Unfortunately I haven't exactly figured out a solution to your other integral, but I will try again when I have the time.

Huy

dl.dropboxusercontent.com/u/19940612/bunnygroup.png LOL.

Chris's sis the artist

@M.N.C.E. OK, no hurry with that, They are amongst the most beautiful integrals I managed to create this year, and I have versions far more complex but I only posted those $2$ versions. It's fascinating to see that the real analysis has a lot to say in this area :-)

robjohn

2:36 PM

@Chris'ssistheartist: I finally decided to take a stab at your last integral. Just summing the residues in the upper half-plane works nicely.

Chris's sis the artist

@robjohn Back. Which one? The supplementary one in the last post?

robjohn

@Chris'ssistheartist I think it was just the main one. I will look at the supplementary one.

Chris's sis the artist

@robjohn that was a fast one. :-)

robjohn

@Chris'ssistheartist The answer involves a constant $A$. I am not sure what that is, but I probably haven't encountered it before. I will take a look later. I have a lot to do today, so I may not get back to stuff until tonight.

Chris's sis the artist

@robjohn Glaisher-Kinkelin constant

@robjohn OK

robjohn

2:42 PM

@Chris'ssistheartist The long, but mechanical, part was computing the residues.

Chris's sis the artist

@robjohn Yeah.

Guess who it is.

Something I did a while ago. Good thing I was able to borrow a computer. :)

robjohn

3:19 PM

@Guesswhoitis. I would go crazy without my computer.

Main is down >8( well, at least in read-only mode

Clayton

Yes :-/ some server maintenance it appears.

Might I ask what happened with amWhy? I just noticed her reputation was set back to 1. I'm usually lurking on Math.SE without posting much

robjohn

StackExchange Status

@StackStatus

Status updates for the Stack Exchange network, including http://t.co/VY1vdMiR. You can also find more detailed updates on http://t.co/uCcZjNx5.

489 tweets, 2.6k followers, following 1 users

@Clayton anyone who is suspended has their reputation reset to 1 temporarily.

Clayton

That is what I thought; is it too much to ask what happened?

robjohn

@Clayton The proper reputation is restored once the suspension is over.

@Clayton I can't say beyond what is publicly visible.

Clayton

She always seemed really positive in all of the interactions I had with her (of course, the last year or so has had me very busy with research, so I haven't been on much)

Got it. Thanks!

robjohn

3:26 PM

> This account is temporarily suspended for voting irregularities. The suspension period ends on Mar 21 '16 at 5:30.

Clayton

Are you a professor @robjohn?

robjohn

@Clayton I was, many years ago. Been doing some programming since then.

Clayton

@robjohn Industrial/full-time programming or more for a hobby nowadays?

@robjohn I've been trying to get a grasp of Python, but I haven't had much luck. Project Euler has helped in forcing me to learn new techniques in programming.

robjohn

@Clayton I worked at Apple for 8 years and now at UCLA for 18.

Random Variable

@robjohn I was going to post that answer, but I decided not to because the question was about real analysis techniques. I mention it in the comments under the question. But I still ended up using some complex analysis in my answer.

robjohn

3:31 PM

@RandomVariable Ah, someone had said in a comment that the residue method didn't bear fruit, so I tried it and it turned out to be pretty low hanging.

Random Variable

@robjohn He was referring to the supplementary problem.

robjohn

@RandomVariable Okay, so I misread.

Random Variable

3:44 PM

The site is back to normal.

Chris's sis the artist

@RandomVariable did you refer above in the comment to robjohn to a solution to the supplementary question from my post?

robjohn

@Chris'ssistheartist yes

Chris's sis the artist

@robjohn Interesting.

robjohn

@Chris'ssistheartist a comment about the supplementary problem.

Chris's sis the artist

@robjohn I was just curious to know if any did the supplementary one by any mean.

robjohn

3:56 PM

@Chris'ssistheartist Oh, I don't know about that.

@Chris'ssistheartist I am working on it.

Chris's sis the artist

@robjohn My solution would shock you, btw (positively)! :D

robjohn

@Chris'ssistheartist I have an interesting idea. Let me see if it works.

Chris's sis the artist

@robjohn OK :-)

Random Variable

@Chris'ssistheartist I haven't attempted the supplementary problem.

Chris's sis the artist

@RandomVariable OK

Guess who it is.

4:13 PM

@rob, consider yourself lucky that you're never without one. :)

Chris's sis the artist

Viewed 452 times in 2 days. :-)

(I could have had more upvotes in these circumstances :D)

Balarka Sen

I wonder if @anon is around.

anon

why?

Balarka Sen

Oh, there you are. D'you know the Serre conjecture? It says that every projective module over polynomial ring is free.

anon

nope

Balarka Sen

4:24 PM

What's the motivation behind this?

darn. thanks anyway.

I see words like "algebraic fiber bundles" flying around in google, thus the question.

Mike Miller

4:37 PM

Projective modules are vector bundles. Every topological vector bundle over $\mathbb C^n$ is certainly trivial. Maybe every algebraic vector bundle over $\mathbb C^n$ is trivial, too.

Whence the question, which to my understanding is more fairly called a question than a conjecture.

Balarka Sen

Why is a projective module analogous to a vector bundle?

Mike Miller

Serre-Swan

Balarka Sen

The defn is similar, I agree, but not every fiber bundle has the lifting property. (do vector bundles have those? I have no idea)

I have to google that.

Mike Miller

What do you mean not every fiber bundle has the lifting property? A fiber bundle is a fibration. In any case, that's not the point being made.

Balarka Sen

The last time I heard, one can't lift maps in the base space to the total space in fiber bundles in general. I guess I am wrong?

Balarka Sen

4:51 PM

@MikeMiller How do you define an algebraic vector bundle?

robjohn

@Chris'ssistheartist: do you mind if I add the Wikipedia link to your question?

Chris's sis the artist

@robjohn No, not at all. It's OK to me. :-)

Mike Miller

@Balarka: Second result, dude.

robjohn

@Chris'ssistheartist okay, done. I won't have time to look at the second question until much later.

Chris's sis the artist

@robjohn I don't see any change on wiki.

@robjohn I misunderstood your point. OK.

@robjohn btw, the second integral should proudly stay both on wiki and mathworld at Glaisher-Kinkelin constant description. :-)

Remember me

5:19 PM

@Semiclassical Can we continue our discussion on quantum numbers?.. My exams are over so we can do the discussion if you are free.

Semiclassical

you'll have to remind me what exactly we were discussing

Remember me

How to derive n,l,m from SWE

Semiclassical

ah, right

i'm not sure how far we got when we last discussed it, but the bottom line is that the 3D schroedinger equation is separable, first into radial v. angular parts and then the angular part into azimuthal and polar

Remember me

okay

Semiclassical

for a summary, take a look at this bit of wikipedia's page on the hydrogen atom: link

Remember me

5:27 PM

okay lemme go through it

Semiclassical

it's not explicitly stated in terms of separation of variables of a PDE, but that is the underlying math

for the explicit math, check out this part of Wiki's page on the Schrodinger equation, particularly the subsection on the hydrogen atom

Remember me

I guess to understand it it would take me a few hours ....

Since I am not one of the brilliant ones

Semiclassical

in essence, it's just separation of variables for PDEs. so i'd read up on that

Remember me

I have done only till diffs .. I have never touched PDEs.. I will read up on that a bit I guess

r9m

5:54 PM

@mixedmath did you get my mail? :-)

wythagoras

@r9m It seems that mixedmath is not in the room. In general it is better to ask such things at Math Mods Office.

r9m

6:11 PM

@wythagoras thanks! :) :)

Chris's sis the artist

@r9m Maybe the best euphemism I read in the last period of time. :-)

r9m

@Chris'ssistheartist ???

Remember me

Okay I have been asked to prove that Every compact subspace of a metric space is closed and bounded.

The proof that it is closed is very easy as every metric space is a hausdorff space ,and using definitions we can show that it is closed (Which I have done)

For bounded ,what I am thinking is that ,Since Y(lets us call the compact subspace as Y) is compact , there will be an open cover for the following subspace consisting of open sets from that metric space . In a metric space the open sets are open balls of given radius . Since the balls are of a given radius,the union of all these balls…

Chris's sis the artist

@r9m Well, you did nothing wrong, but I felt some kind of smell for that "thanks! :) :)" above. :D

r9m

6:27 PM

@Chris'ssistheartist it was a genuine thanks -_-

Chris's sis the artist

@r9m OK :D

Out for a bit of jogging.

Moses

Hi @DanielFischer

Daniel Fischer

Hi

Moses

6:45 PM

@DanielFischer This is simple, but would I be right in stating that the sets $S_{1} : \{ (x,y) \in \mathbb{N} \times \mathbb{N}: x \leq 2y \}$ and $S_{2} := \{ (x,y) \in \mathbb{N} \times \mathbb{N}: \frac{x}{y} \leq 2$ where $y \neq 0$ \} are not equivalent? Since $(0,0) \in S_{1}$ but not in $S_{2}$.

Tobias Kildetoft

@Moses How do you define equivalence of sets in this context?

Moses

@TobiasKildetoft $S_{1} \subset S_{2}$ and $S_{2} \subset S_{1}$ iff $S_{1} = S_{2}$.

Remember me

Hello@Tobias How are you?

Hey@Soham

Tobias Kildetoft

@Moses Ahh, that is usually just called equality, not equivalence

@Rememberme Hi

@Moses And your reasoning is correct then

Remember me

@Tobias Mind checking up a proof of mine .. ?

Moses

6:49 PM

@TobiasKildetoft Okay kewl, thanks.

Tobias Kildetoft

@Rememberme sure

Remember me

Here chat.stackexchange.com/transcript/message/23157606#23157606

Soham Chowdhury

good night, @Rem.

Remember me

good night @Soham

Tobias Kildetoft

@Rememberme The idea is right, but the formulation is very messy

Remember me

6:51 PM

Yes I guess I have to bring it into mathematical language

@Tobias I also had one more thing to ask you ...
Since you were not there all these days ... Do you know what homological algebra is all about . As in what do we do in that subject

I want to study it . It seems fun for some reason

Though I dont know anything about it

Tobias Kildetoft

@Rememberme Yeah, I have a decent idea of the subject

Remember me

Can you give me some briefing what it is about?

Tobias Kildetoft

@Rememberme Originally, it started as a generalization of some concepts that emerges in algebraic topology, and then it took a life of its own

Remember me

As in homology

Tobias Kildetoft

right

the general idea if to start with something you want to study and then in a systematic way attach a chain complex to this object, which you can then take homology or cohomology of

Remember me

6:56 PM

Oh.

Tobias Kildetoft

usually one wants the 0'th (co)homology to be the original object (when this makes sense)

Transcript for

$Mathematics$ Mathematics