There's a certain rule for a sum of sign-alternating decreasing finite series, correct?

Like, (n-1)-(n-2)+(n-3)...-(n-(n-1))

@Studentmath What do you mean by "rule"?

A result

Known result

1/4(something)

I just don't recall it precisely

sure, sum over the even terms and odd terms separately via knowing that $1+2+\dots + n = \frac{n(n-1)}{2}$

Thanks @mike !

@Studentmath For (n-1)-(n-2)+(n-3)...-(n-(n-1)), of course.

@Mike Why did you inserted your last name?

There's a second Mike now.

Hey Prof. @Ted

Hello, Professor @TedShifrin

Howdy @Mike @DanielF @Studentmath @Balarka @jack ... Whew, we just did our departmental graduation thingy ... Time for a martini!

It's always a time for a martini for you, isn't it?

Yes :)

You worried I'm an alcoholic?

Departmental xyz, @Ted? A stiff one is due.

@TedShifrin I forgot you to ask, isn't R. B. King in UGA too?

Yup, got my pic taken with lots of graduates ... Even a few I never taught.

I have no idea @Balarka ... Who is that?

@TedShifrin Well, he is a chemist, actually. But wrote a book explaining the Kiepert-Perron algorithm on solving quintics.

One of my favorite profs in college — French lit— from whom I took 6 or 7 classes was a serious alcoholic, but still a fab teacher.

ohhh, yes, I know him well. From duplicate bridge. Totally strange man.@BalarkaSen

@TedShifrin Ah? That's interesting.

But I enjoyed reading his book. That's what got me interested in theory of equations, really.

I've never looked at his writing.

@TedShifrin Well, it might interest you.

Quintics have clever geometric/algebro-geometric interpretations.

Yes, I have a poster on that put out by Wolfram 20 years ago :)

@TedShifrin Poster?

Uh huh ... Large colored piece of paper that hangs on the wall.

Alcoholism can't be that bad, Churchill was one after all.

@TedShifrin What's the content?

Well, @Studentmath, don't worry; I'm not :)

Using analysis to solve the quintic, @Balarka. I'll have to look at it more closely if you are curious. It's in my office at school.

OK, do tell me if you have the chance to look at it.

I am kind of obsessed with quintics =)

You obsess a lot for a kid your age, @Balarka!

This is a really nice one I am working on right now, I love his ideas: Given the complete graph $K_n$, let the vertices be marked {$v_1,v_2,...v_n$}. For every j>i, if |i-j| is odd the edge $v_i v_j$ is from $v_i$ to $v_j$, and the opposite if even. We set c($v_i v_j$)=|i-j|, and $v_1$ is the source, $v_n$ the sink. I need to find max flow and min cut in the net.

@TedShifrin Do you prefer to write new words (e.g., being defined) in italics or bold or not at all?

@MikeMiller It would be a little inconvenient to not write them at all when they're being defined.

@Mike: Depends on context. Sometimes I write DEFINITION first.

LOL@Daniel

In this section there's a series of like ten definitions.

I'd rather just emphasize each new word somehow.

What are you eriting?

I'm TeXing up a book... :P

Don't you have more important things to do? Whose book?

Gunning's, and yes. But I figure if I spend half an hour a day on it instead of otherwise wasting my time, I can finish it before I leave.

I told you you could have mine :)

Hi @Ted

Salut @Gabriel :)

Italics is OK, @Mike.

Thanks.

I am getting really odd result here, think I will just ask over the forums.

I wish I could just give up and write an answer :(

Huh? @Daniel

I'm trying to have somebody figure out his homework, @Ted.

@DanielFischer I did that the other day, in person

Good job, @Mike.

I mean the giving up and writing an answer. :(

I didn't want to help someone in calculus struggling with combining $\frac 1{x+h} - \frac 1x$ into a single fraction... especially after I saw $\frac 1{x+h} = \frac 1x + \frac 1h$.

Aaaw.

@MikeMiller Yay you got a full username.

I applaud you, @Damiel. We pedagogues have to stick together on this site.

Hi @Pedro.

Oh, is there a @Pedro?

@DanielFischer Hello!

@TedShifrin

@Pedro: One more check-up with the cancer doctor down! :)

@TedShifrin You got that! =)

I will see my endocrinologist in five days.

Checkin' my thyroid and stuff.

Ah ... I didn't know you had issues. Thinking good thoughts ...

@Ted Pedro has a lot of issues. ;)

@Mike: How did you find out our favorite person had been suspended?

@TedShifrin Nah, I don't. But there is a family history of some sorts.

@TedShifrin There was a meta thread complaining about it.

Just feeding my hypochondria.

=O

Ah ... He has an adoring fan base?

I guess so.

@MikeMiller Finally someone took action.

I guess I'll go look.

It's not visible unless you look for it

@PedroTamaroff Let's get ironic.

@MikeMiller Aight. Long time no irony.

Anyone here with some knowledge in graph-theory?

@PedroTamaroff Link me.

On FB.

@Studentmath Hey, I told you I took a course. Now that you've reduced it to "some knowledge" it might be within my level.

@Studentmath For unusual definitions of "some".

You recall max flow-min cut theorem?

Network flows

NOPE

darn..

What's your question @Studentmath?

I think I am a bit lost with it/don't understand it right. The way I get it, if I find a flow with value same as the capacity of a source-sink cut, I can say the source-sink cut is of minimum value and the flow is of maximum value immediately. Correct?

Hmmm does somebody happen to know some hypothesis on $f$ such that $||f^{(n+1)}||_\infty=o(\frac{1}{2^n n!})$ ?

@GabrielR. Context?

hmph

someone wanna help me figure out what a certain font is?

@Studentmath Yes, that is correct.

@MikeM I can try

@Pedro @Mike Watch me get banned now :)

@TedShifrin Oh? No! Wait.

What did you do?

Teeeeeeeeeeeeeeeeeeeeeeeeed.

@Studentmath: I taught that once 20+ years ago.

I replied to Oliver on there, @Pedro. He apparently idolizes all us professors.

@PedroTamaroff It's related to Lagrange interpolation at Chebyshev nodes (a bound on the remainder to get uniform convergence)

In order: O U T R

Or he's Mhenni with a new identity :)

Alright. I have this question: Given the complete graph $K_n$, let the vertices be marked {$v_1,v_2,...v_n$}. For every j>i, if |i-j| is odd the edge $v_i v_j$ is from $v_i$ to $v_j$, and the opposite if even. We set c($v_i v_j$)=|i-j|, and $v_1$ is the source, $v_n$ the sink. I need to find max flow and min cut in the net.

@MikeM that's a font..? Let me try.

That's not mathcal or mathscr or mathfrak.

The U will be the most identifiable one... if that U matches up we've probably found the right font

@Mike: in those ancient days Gunning wrote those in by hand. Use frak or script.

@TedShifrin I'm aware; none of the U's match that. They look like actual U's. I think all future readers should be as confused by what the hell that letter is as I was.

MS paint

@MikeM

Yes... I painted it, @Studentmath

it's me drawing what the symbols look like

I tried to pull a slight joke there, failed it seems

I type such things, @Mike; I would use a script U for an open cover. See Griffiths Harris, etc.

@TedShifrin But $\mathcal U$ looks like a U.

It's so unrealistic.

No, script, not cal.

$\mathscr U$

@GabrielR. I have no idea... hehe.

I also use Lucida script sometimes ...

See, they both look like real letters.

Hmm...

So, \mathcal for sheaves, \mathscr for covers?

@Pedro: Will you come find me when I'm banned? :D

@TedShifrin But I don't think your comment is ban worthy!

What am I missing?

I'll have a good chuckle if you get banned, @TedShifrin

Good enough for round 1, Mike. If you define macros, you can change the defn later.

I have no idea what is ban-worthy, @Pedro.

If I'm the judge, jury, and executioner, anything is ban-worthy.,

@PedroTamaroff I'd say that for normal($C^\infty$ works here, ) functions it's pretty difficult to outrun something as fast as $\frac{1}{2^n n!}$ but it needs work

Hey anyone interested in K-theory and fancy a chat? I have something I want to straighten out

You just don't want to pay off on the dinner, @Mike.

the operator theory flavour....

@Karl in the case of my question, wouldn't the capacity of cutting the sink t will always be the same as the net flow?

Ah, new Mike has an F now.

@MikeF I actually spent a little time on that recently, though both me and the professor I was studying it with got sick of it.

So I can authoritatively talk about... the definition.

@Studentmath Seems necessary, doesn't it, since the underlying graph is complete.

No, smooth is no problem, @Studentmath, although I don't know your question. Whitney proved cool theorems. Only with analytic is there an issue.

OK, i'm outta here for now ...

@MikeMiller

The thing is working kinda awfully for me.

Try hitting it.

well the problem I'm thinking about isn't too far from the definition

I'm trying to write down a precise condition on a *-algebra such that it is not necessary to pass to matrices before defining the K-groups

roughly speaking....

Sound up your alley?

I'm not sure such a definition is possible. Even for AF-algebras you need to define them in terms of matrices so that addition is defined correctly, and $K_0^+$ is generated by projections, but doesn't only consist of projections.

So at best you'd have to work with finite-dimensional *-algebras, I think.

right I understand it's not always possible

I don't know that it's ever possible, though... is it?

how would you define addition (other than "a projection stably equivalent to $P \oplus Q$"?)

So would the net flow/capacity of c always be max/min for every n?

well given a *-algebra A, it's certainly possible to talk about the set of murray von neumann equivalence classes in A

denote that by, say, V(A)

right

does one really recover $K_0^+$ this way?

now, addition of murray von neumann equivalence classes is well-defined, provided you can find orthogonal representatives.

sure

Nah, it isn't right. Since not all the edges are directed at the sink t, some are at the opposite direction, so it's impossible for it to be so.

you're already at the limit of my knowledge, I think, @MikeF

this would probably be a good MO question...

OK well thanks anyway

Sorry :(

@Mike Miller: so what sorts of things are you interested in?

More geometry than analysis. I was just taking a C*-algebras course this quarter with a professor who does research in operator algebras for funsies. He doesn't work with the algebraic perspective much, though, so he wasn't so into K-theory.

@Karl Nah, that would be wrong for sure. The net flow is everything that comes into the sink minus everything that gets out of the sink. The capacity is only what comes out of it, so it won't be equal as the minus here always has a value. Also deleting all the vertices will have larger capacity than the net flow.

Can't think of a certain cut having the same value and the net flow value..

Though I think I have an idea..

Is it possible for val(f) to be negetive?

@Jas ಥ_ಥ

@ಠ_ಠ What's wrong, is Conway giving the class a hard time?

Yes

And all my other classes too

Is it too late to drop any of them?

@ಠ_ಠ You'd be better off if you didn't waste time whining here and worked. =D

whining is good

@ಠ_ಠ What gives?

@Pedro Studying

@ಠ_ಠ You can still drop the worst one, right?

@skull No the drop date was last month

@skull I have finals next week

Just a suggestion for damage control...

...think about your GPA

@ಠ_ಠ Ask for an exception.

Go to the prof of the worst coarse.

I hope it's not Conway :(

There are no exceptions, @skull. What universe do you go to college in?

sigh

@TedShifrin grown, yes Professor.

I think I need to redefine my theorem/lemma/etc environments to support referring back to them

@Mike, seriously, dude, this is a long job. In LaTeX that is automatic pretty much.

I'm quite bad at LaTeX.

I found a set of theorem environments that don't support jack, which I have been using for like a year. :D Now to stop using them.

Then punt this. You have way too much to do. Someone else may have done it. Email Gunning (is he still alive?)

Have you met Conway @TedShifrin?

@TedShifrin I got it to work.

You use \label and \ref @Mike.

Yep, I got it.

Silly me.

But you'll get stuck on lots more. I know. I've done four books.

@skull I don't think professors in our system have any power over who is enrolled/dropped from their courses