10:00 PM
(@CareBear I have to admit I only asked that question so I could use that response, which made me chuckle)

I guarantee that you'll love them, or your money back.

It doesn't take a genius to deduce that Petersen and I have different teaching styles and views of geometry. But my style displeases plenty of people, too.

We also have three tensors named R now, one named $\mathcal R$, and two named Ric

LOL, yes, that is Riemannian geometry ... Of course, I veered more to the complex projective stuff in my career. :P

I also need to learn some of the stuff from Milnor's books...

10:01 PM
But Cartan thought of torsion as coming from the infinitesimal displacement of the basepoint of vectors (affine, as opposed to linear) when you parallel translate.

I'm trying the calculate the distance from a point to a line, and I'm doing something dumb, and I don't know what.

@Mike, I think you're doing remarkably given that you didn't go to a big university ... enjoy learning and don't stress ..

My line is y=-995003 * x + 13233077

Thanks, and I am, and I'm not :)

@CareBear what money ?

10:02 PM

Teaching has also gotten more fun now that my classes are willing to ask questions... this week I've been able to use the first half or so of discussion for answering questions

ugh @user939259

I set a=-995003, b=-1, c=13233077

It takes a knack to encourage student comfort and interaction, but once you learn to do it, you'll enjoy teaching way more than the average bear, @Mike. Of course, most mathematicians don't give a s***.

the point is x=3, y=2442556

10:04 PM
Whoa, @user939259. What are we doing?

@TedShifrin Trying to calculate the distance from that point to the line

Oh, distance from a point to a line.

those are some big points

What crazy numbers. Who in the world writes such things?

@MikeMiller Big is the only way I do things ;-)

10:04 PM
So you're going to tell me you have a stupid formula you're plugging into?

@Ted user939259 does.

no, his teacher (or computer program) did

Well, I hope it's a smart formula. It's just |ax + by + c|/sqrt(a^2 + b^2)
I took that directly from wikipedia and verified it at a couple other sties
*sites

I care more about your understanding that formula than getting a calculator to do the stupid numbers.
But what's the problem?

The problem is that the formula gives me a distance of around 7, which doesn't make sense at all
By just inspecting the graph, I expect something around 100,000 or so

10:06 PM
It's far from clear that it doesn't make sense. That's a crazy line, to go with the crazy point.
Why do you expect something so huge?

Here's the graph: imgur.com/BnSGnaP

@user939259 Roughly $7$ looks reasonable. Look at the $y$ for $x = 10$.

Note that the y axis is on a scale of *10^7

But what is the blue in your picture, @user939259?

@DanielFischer I agree if x=10 is the closest point, but by inspection of that graph it looks like it should be around x=8

10:08 PM
You pass $y=2442556$ somewhere between $x = 9$ and $x = 11$.

@TedShifrin For line bundles we have an inverse line bundle, i.e., another for which $E \otimes E^* = \varepsilon$, where $\varepsilon$ is the trivial line bundle. This is essentially because 1-matrices commute, so we can just define $g^\ast_{\alpha \beta} = g^{-1}_{\alpha \beta}$, and this new set of things still verify the cocyle condition. For a general vector bundle $E$, is there a "stable inverse" - another vector bundle $E^*$ (I'd like of the same rank)
such that $E \otimes E^\ast = \varepsilon^n$ for some $n$?

I'm seriously not going to plug numbers into your formula on my calculator. But the formula is correct.

I mean, yeah, I figured wikipedia and 3 other websites weren't wrong...I know the formula is correct

That's a good question to which I should instantly know the answer, @Mike, but I don't. I suspect NO.

I assume I'm misinterpreting / misusing it somehow

10:11 PM
What would Chern class formulas tell you, @Mike? I suspect it's wrong. Sadly, one of our grad students stole my Hirzebruch (forever) ... but even though I know how to do this, I don't want to sit down and write it out.

yikes! I can't say anything about the chern class yet.

You need to use multiplicative property of Chern character to do this.

Another thing I'll jot down to look at later.

My vector bundles are real, @Ted.

10:12 PM
No big difference (except for torsion issues). Might as well think about it in the complex case.

OK.
Well, if I do pontryagin classes, I guess there aren't torsion issues. But I only know one type of class right now. ;)

Stable questions are about direct sums ... typically.
Sadly, I don't know how to get around the formality of some of this stuff, even though I always try to make it all geometric.

Luckily, I like some of the formality

Luckily, I'm retiring and get to be stupid :P

I'm also looking at some stuff Hatcher wrote about vector bundles and characteristic classes... I might be one of two people who isn't that fond of Milnor's style

10:14 PM

I hate Milnor's book on Characteristic Classes. Hate.

lol, it's what I was reading.

But his books on diff top and h-cobordism and Morse theory are wonderful.

@user939259 You have $y = 2442556$ for $x = 10.844712025993891$, so the distance cannot be more than $7.8447...$. Moving $x$ a little towards $3$ will decrease the distance a bit, but very soon will increase it again, so the distance will be close to that.

@TedShifrin Are you going to move away from the south when you retire?

10:15 PM
That's the plan, @Alizter.
I'm going to move within hours of @Mike to torture him.

I need to learn some characteristic classes and Morse theory, @Ted, so I checked out those two books. I have only looked at characteristic classes so far and I really dislike it. Do you have a nicer source?

@TedShifrin What like make him give up his seat on the bus?

@Alizter If he thinks I'll give him my seat on the bus he's got another thing coming.

I don't know Hatcher's stuff on that, @Mike. I learned most of it (and have taught it) from the diff geo/curvature perspective. Even though it's formal, I like Hirzebruch's classic.

A difficult question?

10:16 PM
Shouldn't that be "another think"?

@TedShifrin Google says you're right... this is the first time I've ever seen it spelled that way. It makes more sense though, and is funnier.

LOL

Borel-Hirzebruch, CC of Homog Spaces?

Topological Methods in Algebraic Geometry, I think, @Mike. If you want my copy, you need to steal it from one of our grad students.

10:19 PM
Is it ok to edit and extend an OP such that the question becomes more general , when a bounty has already been placed and that answer has already been given ?

That's too complicated for me, @mick. I quit.

I just imagined @Mike punching a graduate student.
sits down with popcorn

It would make an interesting battle, @Alizter.

yes.

@Alizter im not a graduate student ... its not about me i guess.
@TedShifrin lol quit with what ?

10:20 PM

@mick: everything.

@TedShifrin This is all differentiable, despite the title? At least at present, I'm looking for the algebraic topological/differential geometrical POV... if there's an algebraic geometrical one, it'll have to come later :)

@TedShifrin suicide ? :)

Yes, @Mike, you're safe to look. It's very much couched in terms of generating functions for various characteristic classes.

@Alizter which question ? on main ?

10:21 PM
@mick Grow up.

@Alizter im just checking if you meant something on chat or the question i placed a bounty on ...

@TedShifrin the library won't let me make any more purchase requests. :P

@MikeMiller How fast do you read?
Or is this the fire wood?

Surely UCLA has that book. It's a classic.

@Alizter oh , yeah well thats the only way to quit with everything :p

10:23 PM
@Chris'ssis I just took a shower; one of the wonders for mathematical thought. I can show that that sum is less than $\frac{17}{18}\log(2)$, I believe

@TedShifrin I tried to request a recent book a friend recommended me on Morse theory.

Heya @robjohn.
Well, @Mike, in that case, maybe you need to come export half my library.

That reminds me. I should probably move from my place. It's been 5 hours.

@TedShifrin Hey, Ted!

They do indeed have Hirzebruch's

10:24 PM
@robjohn really? How? :-)

oh ... stop being an alarmist, @Mike.

@Mike @Ted!

Hi @BalarkaSen Bye @BalarkaSen

@TedShifrin I just can't believe they won't let me burn money at will!

@Balarka: It's my dinner-time.
Well, @Mike, CA's budget is in baddddd shape. Recondite math books don't rate.
UCLA doesn't have Harvard or Chicago's budget.

10:25 PM
@TedShifrin Oh noes.

@TedShifrin IIRC, between 10 and 20% of UCLA's budget is from the state.

Endowment is crucial for lots of things. Typically, public universities don't fare so well.

You might be surprised at how extensive the math stacks are... no Harvard, but we do get an entire floor of the stacks in the engineering library.

Yeah, the UGA math library is quite good ... with lots of old MAA stuff, too.

10:27 PM
I am trying to prove that convex sets in R^n can be separated by open balls, R^n being equipped with the usual topology. Should I think algebraically or geometrically?

@BalarkaSen Disjoint compact convex sets?

It is true for any two disjoint closed subsets, @Balarka.

Closed.

Oh, balls.

Disjoint.

10:28 PM
Yeah, yeah, I'm slow.

And yes @TedShifrin, open balls.

I would think geometrically. but I would also question what the difference is. :)

LOL ... I would put a balloon around one of the sets.

@MikeMiller Like invoking the algebraic formulation of convexity and do stuff with teh Euclidean metric...

@BalarkaSen Not sufficient. Let one of them be a line, or hyperplane.

10:29 PM
Yeah, @Daniel, sure compactness.

@DanielFischer Oh, closed and bounded.

What's the 'geometric formulation' of convexity?
@BalarkaSen = compact, in $\Bbb R^n$

@BalarkaSen So compact.

I haven't studied compactness in general metric spaces, don't dogpile on me!

@Ted I'm going to go grab that book, then.

10:30 PM
@BalarkaSen Have you heard of separating hyperplanes?

We're not in a general metric space! We're in a very special one!

OK, forget it.

Vewwy special

Let me think about it myself.

I think I can get Balarka to solve most problems just by giving him a hard time and being completely unhelpful.

10:31 PM
@MikeMiller Give him a hard time about the Riemann hypothesis. I'd really like to see that proved.

@MikeMiller Yes, I feel awful when people solve my questions instead of just helping me with terminology and whatnots.

@Mike: That's because @Balarka really is a mathematician, despite his obnoxious young age :P
LOL @DanielF

@BalarkaSen The more you prattle on, the longer it takes for you to prove the Riemann hypothesis.

Dinnertime for me ... I leave you in pieces (there's a new phrase for you, @Balarka).

LOL @Ted
@Ted wait a sec!
Did you see the Hippa version of Ted?
Ted Shifrin, Athens, GA, USA
38 5

10:34 PM
Oh hell ... @Balarka

LOLOLOL

How can he reuse my actual name?
@Hippa: no longer speaking to you, for real

Even the website.

This is worse than all the wanton downvotes I'm getting.

I'd never do that.

10:35 PM
I might need to flag that.

@DanielFischer it is easy to show that $\frac{\log(n)}{n-1}$ is decreasing for $n\ge2$. Thus, $$\sum_{k=2}^\infty\frac{\log(n)}{n!}\le\log(2)\left(\frac1{2!}+\frac2{3!} +\frac{\log(4)}{3}\sum_{n=4}^\infty\frac{n-1}{n!}\right)$$

Seriously, @robjohn, how does the MSE network allow a reuse of a name?

There are tons of duplicate names. I don't know.

Sigh. Maybe I should just slink away into a corner and die ... :P
Oh, thanks for editing, @robjohn ... that made absolutely no sense to me.

Sigh.

10:38 PM
Yes, @Balarka, but that was a permutation of your name. Did @Hippa permute me?

That'd be Sawarnik.

someone should create chuck norris ... we already have Obama here :)

@Ted StackExchange encourages users to use their real names. As a result, usernames needn't be unique, since there's more than one Mike Miller.

Maybe I need to transmogrify to a fake.
I have trouble with all the Johns.
And I don't mean in a bordello.
I know one of them (we were grad students together), but there are multiple others.

goodnight all !

10:40 PM
Anyhow, I'm outta here.

You handle then quite well, @Ted?

Just a link to the fake account, you know.

11:00 PM
Well it was going to happen. I nicked myself and am probably gonna die from blood loss.

Hello @alizter, lol.

gurgles in blood
@JasperLoy Before I talk to you I should probably put some clothes on.

@Alizter It's OK. I am not going to look at you, lol. I wanted to say "I like to look at naked people" but I will probably be flagged, lol.

You just said it

Hi @Studentmath

11:06 PM
And yesterday Alizter said "butt naked", lol.
There is a variant of that, "buck naked".
I think they both mean completely naked.

@Alizter @Jasper \o
How are you today?

@studentmath I don't know what else to say, so I will say "Hi!"

and other stuff

@Alizter Pedro Nicolas Tamaroff?

@JasperLoy Prime Number Theorem. Much more interesting than Pedro's middle names.

11:09 PM
@Alizter Pedro might disagree
I'm very quickly sold out to anything that approaches a problem through probability

Anyway, I would like to say again that all of you should watch "If I Stay", very good movie, lol.

CareBare -> Weapon of Choice
@Studentmath Probabilistic number theory

@alizter Do you have a girlfriend?

@JasperLoy no
why?

Nothing, just being a busybody as usual, lol.

11:12 PM
@JasperLoy do you have a girlfriend then?

@Alizter No. I never had one, and may never have one, lol.

Sarah finally replied to my email. All she wrote was a .

@Alizter Really, a full stop?

@JasperLoy Yes.
I mean why not a comma?

@Alizter OK. I think she is a very busy person, lol. But I prefer to talk to her over email than chat. That way, we can share more secrets.

11:15 PM
What secrets?

I'm off, good night

bye @Studentmath

@Studentmath See you in your dreams!
@Alizter Well, secrets are secrets.

Hmm maybe I don't want to know

Don't forget me when you win the Fields medal, lol.

11:17 PM
@JasperLoy Why am I winning Fields?

@Alizter Well, there is a possibility, isn't there?

@JasperLoy Unless I reject it ;)

@Alizter Maybe I will tell you some of my secrets one day too.

@JasperLoy It's fine. I am not dying to know.

11:21 PM
@JasperLoy I think it was $\int( \log x^x )^n dx$ or something similar
I deleted my sent mails on wed

OK. $A$ and $B$ be compact convex sets in $\Bbb R^n$. $d(x, A)$ is a nonnegative real for any point $x \in A$ as $A$ is closed. Take the segment $\ell = \inf_{x \in B} d(x, A)$ and take the segment in $\ell$ of length $\ell/2 + \varepsilon$ with $0 < \varepsilon < \ell/2$.

She is really good at integration

The open sphere tangent to the line perpendicular to $\ell$ at $\ell/2 + \varepsilon$ (and tangent to that very point) of radius $r > \ell/2 + \varepsilon + d(A)$ contains $A$ entirely. Doing the same with $B$ gives an open sphere which contains $B$ entirely.
I can't figure out how convexity comes to play, though. Apparently it does.
@DanielFischer @Mike ^

@Alizter It's weird why so many girls on this site are good at integration: Sarah, Chris's Sis, Cleo and Anastasiya.

@JasperLoy I know...
@CareBear or @WeaponOfChoice?

11:23 PM
@WeaponofChoice Hello, our caring friend.

@Alizter I am very bad at integration, but I will be studying Calculus I soon, lol.

I see that Axiom of Choice meddled with the Weapon at last.

@JasperLoy I have my doubts on sarahs gender however i also care very little.

Integration doesn't really appeal to me though. Looks pretty... ad hoc.

@Alizter I have no doubt, unlike you.

11:24 PM
@robjohn Duplicate names are one thing. Using the name and website of another person means impersonating them. Violation of ToS 4(c):
> Under no circumstances will Subscriber use the Network or the Service to [...] (c) create a false identity or to impersonate another person,

@CareBear You are like a lawyer :P

@BalarkaSen If the sets aren't convex, the line perpendicular to $\ell$ can intersect one or both of the sets.

@JasperLoy Why is that. Or has this got something to do with secrets? Perhaps I should not ask.

@DanielFischer Ah, that must be it. So the BS stuff I wrote above is actually a proof O_o?

@TedShifrin You can flag any post of the user for mod attention, pointing out deliberate impersonation of you [violation of SE terms of service). I think they will rename.

11:26 PM
@Alizter Well, I trust her. =)

@WeaponofChoice Can't anything be done with this? I am actually offended...

@JasperLoy her email is a bit suspicious...

@Alizter Well, people have all kinds of weird email addresses.

There's less to go on there, since it's just a name, and a mangled one. It's not tied to a unique individual on the planet. @BalarkaSen

@BalarkaSen Ummm. If I understood it correctly, it contains the right idea and you can make a proof from it if you take the time to actually properly define everything and write down the details.

11:28 PM
Sigh.

Once skullpatrol also had an account with my name. He used my blue square as well.

@DanielFischer OK.

Well Im off
wayyy past my bed time
redbull is starting to wear off

@Alizter See you in your dreams!

@JasperLoy With my sleep clock I would be lucky to have dreams

11:56 PM
@MartinSleziak, the reason why I was asking was that I wanted to know whether you assign homework, and if so, how much time one would spend on it weekly and how much it would account for when calculating the final grade. Do you have any further input on that? I realize it differs from country to country, but how is it at your university?