7:00 PM
Hello everybody. I'm trying to find an unbiased estimator for a sample where variables have the following pmf: 0.2 if x = a, 0.3 if x = 6a, 0.5 if x = 10a, but i dont know where to start
i thought of maximum likelihood
(a is the parameter)

Uh. Final.
That's a bizarre autocorrect.

LOL. I'm done. The grad class doesn't have a final. There will be a takehome from the kid doing Spivak as a 1-person class.
@Huy: I finally thought about your question. The answer is no. The matrix $$\begin{bmatrix} 1&0&1\\0&1&1\\1&1&1\end{bmatrix}$$ is indefinite.

Oh! Vacation time then.

Not really, @Mike. Also have to start thinking about an MAA lecture I'm giving in March.

Where and on what topic?

7:09 PM
at a regional meeting of the SE MAA ... I'm probably going to do three approaches to one of my favorite problems: the electric company problem (you know that?).

@TedShifrin: What about if we add a condition that it has to be transitive? I.e. if (1,3) = 1 and (2,3) = 1, then (1,2) = 1?

@TedShifrin Stack Exchange meeting?

Can you phrase that purely in terms of the linear algebra?

I don't, but I'd love to hear about it!

LOL, @leo, sorry, no. Southeast :P
Where do you locate a point so as to minimize the sum of its distances to the vertices of a triangle?

7:12 PM
The fermat point?

@TedShifrin yes I was surprised. It would be nice if something like that happens. With the people around here in math.se there will be good talks. But it is as with the community blog I guess. That's all. Would be nice.

SSShhhh @ Sanchez :P
I know (at least) three ways of proving/deriving/constructing it. So I want to do this, since college math majors don't learn geometry of any sort anymore :(

Well, I have 37 students signed up for my diff geo class this spring. Yikes. :)

I seriously have to find out if they offer any geometry course in my uni.

7:16 PM
Oops, my bad - thought that was the baby case for electric company problem, which you were introducing @TedShifrin

No, you're right, @Sanchez. I was just hushing you up :)

Oh, you were asking me! I thought it was to someone else's question, sorry.

I get tired of relentlessly pinging people I'm talking to, @Mike :P

At this point of the conversation, I think I'm going to hve to say it's at the Fernat point. :p

Stop cheating, @Mike.

7:20 PM
@tedshifrin do you think geometry should be taught before or after trigonometry?

A naive answer would be the center of mass of the triangle, then.

We're talking different sorts of geometry here, @badass. But before, of course, for high school.

(I know it's unlikely to be true but I also think it's a good first guess!)

Yeah, or the circumcenter or the incenter ...

No idea what those are, honestly. I'd guess the latter is the intersection of the bisectors?

7:25 PM
Yup. For fun with vectors, you should do the exercise of proving that the medians are all concurrent, the perp bisectors are all concurrent, and the angle bisectors are all concurrent. The three points you get are collinear and there's a 1:2 ratio in lengths :P

@tedshifrin normally it is algebra and trigonometry then geometry, why?

It sure didn't used to be, @badass, but in the US high school math education has gone to the dogs completely. I don't know what it is where you are. Geometry (with proofs) is more sophisticated, but I don't see the point of doing trig before you've thought about basic geometry.

@badass My experience was geometry before algebra. It was a miserable class for me taught by a teacher who didn't want to be there.

@Mike: Only fair, since the students didn't want to be, either :P

I was the only student, and I absolutely did!

7:27 PM
I've had plenty of students who didn't respond positively to my positive energy and enthusiasm ...
Um, you were the only student? Home schooled?

No. Just a bizarre situation.

I'll say.
In general, teaching small classes is enervating and frustrating. I prefer at least 10 in a class to get some energy and critical mass.

I'd taken algebra at my previous school, and the next one had no high school to stick other students in. They weren't allowed (or something) to just have me not take a math class or just learn it myself, so they had the teacher assign me some problems from a book every class and work while he taught algebra.

OH, that's too bad for you. Well, now you can read Pedoe's book (Dover) and love geometry.

You dont like one on one?

7:30 PM
Gads, I answer several questions today and half the votes come from a very lhf. It figures.

That's why we shouldn't be answering LHF, @robjohn.

@TedShifrin Because they get voted on a lot?

@TedShifrin I'll do thT when I get the chance. I never really got to appreciate (classical) geometry.
LHF...?

No, because we should leave them to less qualified answerers ... we don't need the votes and they need the experience of answering.

Low hanging

7:31 PM
low-hanging fruit ... I didn't know that until recently, either, @Mike.

I find the mass of those questions rather annoying.

Yeah, even in the 9 months I've been here, it's gotten totally ridiculous. I ignore most of the questions totally now.

I like to answer questions where the OP has made some clear nontrivial effort, but even then they probably should have searched.

I try to ask questions and make the OP do some work, and then some asshole has to come in and show off how smart he is and give the solution. So I'm pretty much quitting.

If we don't learn how the easy stuff is done right how do we learn how to do the hard stuff?

7:36 PM
There are books full of solutions and proofs and examples. Show me what you have tried and where you get stuck, and then I'll help you learn. You don't need more stuff to copy/memorize.

I have always felt that exercises are key in learning math, and if you spoil that method, you'll learn nearly nothing.

Of course, @Mike. And it's the exercises in my 4 books I'm proudest of.

Teachers constantly complain about students not having strong enough back grounds

People always complain about the massive number of homework problems in SCU's first discrete math course, but without those I feel like nobody would make it through abstract.

Well, memorizing what someone else does for you is NOT the solution.
I was upset with my own students that when I gave them a linear algebra proof that was disguised from the ones I'd shown them how to do they were (except for the best students) at a loss to even start. I'm going to give them a talking-to about that when next semester starts. Studying does not mean memorizing past problems.

7:42 PM
At some point you do need to memorize

It's become clearer as I've taken more classes that, fundamentally, you should be studying the proof methods far more than the theorems. Because once you know the ideas, re-deriving the theorems (or doing similar exercises) is not very hard.

definitions, yes.
I did tell my class that the proof of the Maximum Value Theorem (on a compact set) would be on the final, and most of them memorized the proof. So be it.

There are implicit caveats up there, of course

8:00 PM
hey can any topology guru help me review my solutions. here ( dl.dropboxusercontent.com/u/40998563/Page1%20%281%29.pdf ) Its just general topology stuff. I need to present this in front of the class for few bonus points.

Wow that is a lot of work for a few bonus points

yes it is but I really need the bonus points. The problems that I am not sure I have done correct are question 2 and 4.

nice argument for 5!
it's cleaner than what I suggested yesterday

@FernandoMartin I am glad you say that. But I cannot Take credit for that. Somebody taught me that yesterday.
@FernandoMartin did you check my solutions for number 2 and 4?

8:15 PM
yep, they look alright to me
I'd write a bit more about why that open cover has no finite subcover though

Like?

Like saying exactly why it has no finite subcover

Can I say the cover covers all of R which expands to infinity? Is that good enough?

that's hand wavy

huh? u taking about my writing?

8:20 PM
no, hand wavy means easy on details
Suppose I have a finite dimensional vector space $V$ equipped with a bilinear form $B$. Is there a standard bilinear form for $V^*$?

Oh sorry, English is not my first language. anyways I will think of way to make it better

8:33 PM

LOL

@leo hahaha

8:45 PM
Greetings!

@Chris'ssis great chrissy!

@Charlie howdy! :D How are you doing?

@Chris'ssis I'm fine, abd you? :)

I admire a nice question. :-)

@Chris'ssis you always do :)

8:50 PM
If $x,y,z \in (0,\infty)$, $x+y+z \ge 3$, then prove that
$$x^n+y^n+z^n\ge3, \forall n\in \mathbb{N}$$
@Charlie This is the question I admire. It was given on a middle school contest.
@Charlie I simply love it! It's too nice to be real!

What do they already know to solve the problem?

haha, geo sum formula
no, that doesn't work

power mean/jensen/am-gm is the usual way

@Chris'ssis :)

@Charlie I hope you love it too! :D

8:55 PM
@Sanchez what are you referring to by Jensen's?

The inequality Chris's sis posted.

@Chris'ssis it's cute, and relatively simple :) I.like

@Charlie Indeed, it's elementary.

Well, it seems silly that they'd be allowed to prove Jensen's inequality by quoting Jensen's inequality...

Ah
I mean $f(x_1) + ... + f(x_n) \ge n f((x_1+ ... + x_n)/n)$ for convex function $f$

8:58 PM
@Mike Low Hanging Fruit

@Chris'ssis :)

@robjohn Most of my rep yesterday came from the easiest question I answered all day - same old story :)

Ah... another downvote for what I think is a good answer.

@robjohn where?

@robjohn were you downvoted?

9:02 PM
@OldJohn That is usually the case. The hard questions just don't get the traffic

@robjohn very true

@robjohn just found it :)

@OldJohn Ah :-)

@robjohn I think things are better now ;)

9:04 PM
guys, what is considered "a graduate student" ?

@Chris'ssis I think I know who downvoted, but I won't ever know for sure, unless they comment.

@robjohn is it a known user with a good reputation?

a student that has a BSc ? or master degree? or both

Someone who's been accepted to a graduate program? Unless you're asking a more philosophical question.

9:05 PM
no pratical question

@Chris'ssis known? I don't think we have any unknown users...

but what is a graduate program

@Danny A graduate student is someone who is in school studying to obtain a master's degree or a Ph.D.

i dont really get this
@anorton oh

@robjohn what does it mean?

9:06 PM
@Danny I think more than a BSc, they would need to have taken a course in grad school after to be considered a grad student

@robjohn I suspect I know who my downvoter is too - my response is to answer more questions to compensate :)

@OldJohn Yep... I just get used to what my rep is mod 5 and now it has changed :-)

@robjohn we could all downvote you until it matches what it was before. :P

@Sanchez Ah, gotcha. The only Jensen's I knew was the formula which didn't seem very helpful... or available to middle schoolers :p

@OldJohn Since I comment and try to help people improve answers, I don't downvote
@anorton Thanks for the offer :-p

9:08 PM
@robjohn Yes! If anything, that is the most annoying part

@Mike, the measure theory one? or integral version?

@robjohn Never, but never all people will appreciate you. There are always exceptions.

@robjohn ok thx

@Chris'ssis Hey, if it's really bad, I can vote to close or delete :-)

I'm rather getting used to being disliked :)

9:09 PM
oh ted

@TedShifrin why are you disliked?

:)

@TedShifrin I don't dislike you ...
... well, not that much!

@TedShifrin nor do I

:)

9:11 PM
Brian Scott left in a huff the other day because I criticized his behavior, and a guy cursed me for rudeness because I lost patience with someone asking a homotopy question who needed multiple coaxings.
I didn't say it was universal. I'll work on it :)

@Sanchez the complex analysis one relating the integral of $\text{log}^+(f)$ to $f$'s zeroes and poles.

@OldJohn You know what? I just realized that when you cap, your rep mod 5 doesn't suffer from the downvotes :-)

@Mike, ah I see.

I think I've only capped once.

@robjohn I thought about that the other day - so long as you cap in the same 24 hours as the downvote :)

9:12 PM
I don't think the guy cursed you, but I also strongly disagree that you were being impatient with him.

@OldJohn yes.

You were being very patient and never once were rude - even when frustrated you were cajoling.

@TedShifrin Was that the one where you were discussing a line joining points on a sphere?

He thanked me for helping and told me he didn't appreciate my being rude (his word).

@Sanchez are they secretly the same thing, or just two different results of Jensen?

9:13 PM
Yes, @OldJohn (Al)

@TedShifrin I was impressed with your patience on that one!

Me too, especially after grading finals all day.
If he'd been my student, I would have ignored him after 3 tries until he figured it out.

@Mike, they are different.

Was he trying to prove $S^n$ is simply connected by doing a linear homotopy?

@Mike, en.wikipedia.org/wiki/Jensen's_inequality The most famous version of it is probably the one in probabilty theory, although what I quoted was merely the case when the measure space is finite with counting measure.

9:16 PM
No, homotopy between two maps that are never antipodal.

@Sanchez That's what I thought - I was hoping otherwise because those results being connected would be really cool :)
@TedShifrin And he was trying to pass from one to the other... linearly?

Yes, @Mike. It's the right approach, once you do what's 1000% standard and project back :)

I feel sorry for the poster of this. He is clearly finding some problems, but almost nobody seems to be interested. I guess it is not a popular topic :(

It is a lot to read. I expect a professional number theorist could answer in a moment.

@TedShifrin I suspect that Schnirelmann density is a bit of a backwater, even for number theorists
everyone seems to be interested in algebraic number theory these days - maybe a consequence of the solution of FLT and other things

9:26 PM
Well, I've been where people like Pomerance, Granville, and their students have been, along with combinatorial types of analysts (Magyar, Lyall), so they all know it. I've now read the question. I'm expecting $n_r$ can't be arbitrary.

@TedShifrin I actually have a book on that stuff somewhere, but never got around to reading more than the first 4-5 pages. One day I might get back to finish it ... maybe.

Heya @WillJagy :)

I dunno, statistical number theory seems surprisingly common.

It's become pretty popular, yes.

@TedShifrin, did we overlap in graduate school? Schnirelmann density is easy to work with but heavily dependent on the first few values. natural and Dirichlet densities are more work but are what one really wants.

9:35 PM
@WillJagy Hi there young fella

I dunno whether you'd put Bhargava's or Poonen's recent work in that category, but it's pretty interesting! (density of hyper geometric curves with one rational point; average size of p-Selmer groups)

Will, no, I don't think so. We've crossed paths on SE several times. Is Pete still avoiding you? :)

@OldJohn, been busy, two or three days to produce ths anser, still not what was requested: mathoverflow.net/questions/150673/…

@Will: I was at Berkeley 74-79. Will most likely back visiting friends this summer.

@WillJagy Looks like a question just up your street!

9:39 PM
@TedShifrin, bit surprising that Pete got back to me, maybe September, I worked out a lot of minor questions, and he submitted the manuscript on Nov. 29, to Acta Arithmetica....Maybe I know your name as a recent (at the time, 1980) advisee of someone there.
That's it, Chern, 1979. I got there in 1980.

I was a student of Chern's and had lots of friends still there into the early 80s (particularly geometry, alg geo, and Kirby students).

@OldJohn, yes. There is a fellow named John Voight, now at Dartmouth, who lives for this stuff, helped with the Pete article. He says he is busy for a few weeks. Anyway, it is clear that lots of Hilbert quaternions are not the sum of two squares, 2-adic stuff. Much harder is to show that, allowing multiplication of such sums by a unit on the left, we recover all of them. Voight knows enough to do the hard part, I really do not. Oh, it turns out the actor's first name is Jon, no letter 'h'
@TedShifrin, saw Kirby on Friday but did not speak with him. Was hoping to run into Voight, on sabbatical here until March

Rob was actually in Athens recently, but I was tied up and didn't see him this time.

Hey can someone please review this question again, now that i expanded it? math.stackexchange.com/questions/597960/elgamal-like-encryption

Indubitably Voight is at Dartmouth to work with Pomerance?

9:49 PM
When you say tied up, are you referring to whips and a dominatrix? Voight, yes, although he has lots of activity with some pre/postdocs of Gabriele Nebe at Aachen in Germany.

Well, I think I'd be on the other side of that tying, then, @Will :) @OldJohn, I think I answered that guy's question — rather, got him to give enough definitions that he answered it :)

Never expected to see BDSM on MSE!

@TedShifrin Nice work!

Well, @Mike, this wasn't entirely my fault :)

Hey, I don't like to assign blame.

9:56 PM
I love to assign blame. One of my favorite things.

I'm trying to figure out where I've seen Professor Voight's name before...

I know you're young and impressionable, so I'll keep quiet :D

By association is my best guess, I think.
Oh, oops, I think I managed to confuse him with Paul Voutier. Embarassing.

@Ted is this the question under discussion? math.stackexchange.com/questions/598706/…

Yes, @Will. @OldJohn posted about it here.

10:16 PM
@WillJagy hi

hello

@WillJagy long time I haven't seen you around! :-) How are you doing?

alright. I answer on MSE Main.

Good!