Mathematics - 2014-02-09 (page 4 of 5)

Ted Shifrin

22:00

Yeah. I have to teach/learn probability next fall for the first (and last) time ever. I expect you guys will help me out when I get stuck :P

Mike

@TedShifrin Lots of important people found it interesting. I respect their work. I personally find the subject incredibly dull.

Ted Shifrin

Actually, @Kevin, combinatorics will have more stuff with generating functions and Stirling numbers of different sorts.

Kevin Driscoll

@Ted Ah okay! A friend of mine got a question of that nature during a phone interview for a consulting job

Mike

@TedShifrin Depends on the course. Mine only did the more interesting stuff in the latter half.

(generating functions, Polya counting)

Kevin Driscoll

Given a set of dice with some numbers on them, give another set whose distribution has the same average

something like that...... generating functions were required

Pedro Tamaroff

22:02

@TedShifrin Well, I am taking Advanced Calculus and Algebra II next semester.

Ted Shifrin

One of my former students (who's working for McKenzie now) was asked in an interview a bunch of questions. This is the one he couldn't get, shockingly. Suppose Kevin bicycles ten miles in exactly an hour. Is there a one-half hour interval in which he went exactly five miles?

Mike

First we spent a lot of time with n black balls, m white balls, and an urn.

Ted Shifrin

I have to do binomial coeffs and that sort of stuff at the beginning of the probability course, too, @Mike.

Pedro Tamaroff

@TedShifrin I do know most of the Advanced Calculus course, while I know say less than half of the Algebra course.

Mike

@PedroTamaroff Don't take Advanced Calc. Come on, ask them to let you into a real analysis class.

Ted Shifrin

22:03

So, take an exam to exempt the Adv. Calc. class, @Pedro, and move on.

Mike

Real meaning 'actual' here.

Pedro Tamaroff

@TedShifrin Dunno if I have the balls to do that. =)

Exemption exams are not forgiveful.

Ted Shifrin

You don't need to take the exam if an adviser gives you my advice. I thought it would make you feel legitimate to do so.

Pedro Tamaroff

Come again?

Mike

@PedroTamaroff Talk to your advisor, tell him you know literally all of that stuff.

You do.

Kevin Driscoll

22:05

@Pedro Ted means you oculd just sign up for the advanced course if an advisor tells you to, no exam required

Ted Shifrin

I'm sure that a faculty adviser can clear you to take appropriate stuff without your having to exempt every course you already "know."

Kevin Driscoll

But if you don't feel OK doing htat then maybe take hte exam anyway

Mike

Get your faculty advisor to devise an appropriate plan of study for you that doesn't involve retaking things you know.

Ted Shifrin

Sadly, if advisers in BA are like advisers in this country, most of them are incompetent.

Kevin Driscoll

Ya, for people in their 1st or 2nd year they often have a general advisor (outside their intended major) who doesnt really know what they should or shouldnt be taking

when it comes ot advanced studies

user4140

22:06

@TedShifrin that's pretty mean.

Pedro Tamaroff

@Mike I see. Well, I am taking a pretty basic course now.

Ted Shifrin

Even my colleagues who advise math majors their 3rd and 4th years are woefully skilled at it, @Kevin.

It's not an accident I have 70-80 advisees @user4140.

Pedro Tamaroff

Some classes ago we proved that $x_0=0,x_{n+1}=\dfrac{x_n^2+1}2$ converges. =/

user4140

what does that mean?

Pedro Tamaroff

What does what mean?

Kevin Driscoll

22:08

@Ted Yes. I was poorly advised. For some reason Duke physics basically assigns all the phys majors to 1 advisor who is also the director for undergraduate studies in the department

Ted Shifrin

He's asking me, @Pedro. It means that students want me to advise them because I do a good job of it.

Kevin Driscoll

He never had the time or inclination to give me useful, specific advice

Ted Shifrin

However, when I retire in a year, they're all going to have to manage somehow. I worry about some of our Honors students, actually, but ... oh well. My ego notwithstanding, they will survive.

Kevin Driscoll

I didnt really prepare myself for grad school until my senior year whne my independent study advisor was like "You nee dot do X, Y, Z or you won't get accepted"

Ted Shifrin

Right, @Kevin. Being director of undergrad studies doesn't necessarily make one talented and or interested in advising. Someone has to do it.

Mike

22:09

@PedroTamaroff You're wasting your time, man. I wasted too much of my time doing stuff like that and I sincerely regret it. Don't be like me, take all the high-level stuff you can, don't waste time with the stuff you know.

Complex analysis

@TedShifrin your students must have been very lucky to have you as an advisor .

Mike

@TedShifrin I'll advise your students for you.

What could possibly go wrong?

Ted Shifrin

LOL, sure, @Mike. I've been doing Physics majors for a few years, too :P

Pedro Tamaroff

@TedShifrin You know Mariano has a slightly different point of view. He tells me to take the courses, and study by my self the other stuff.

Ted Shifrin

Until they get to junior status. (Honors students, that is.)

@Pedro. That's really interesting. Why does he say that?

Pedro Tamaroff

22:11

He doesn't have a "rush it" philosophy. When I suggested the idea of skipping courses, he said: "What would happen if you graduated tomorrow?"

Ted Shifrin

I have placed several of our super-strong undergrads in graduate real analysis the fall of their junior year -- fabulous teacher, and they're ready for it, and they want it. They know enough to be successful and have a gung-ho attitude. Why make them wait until graduate school to progress?

Mike

@TedShifrin Does your partner know?

user4140

But what you said was still pretty mean.

Ted Shifrin

Fine, @user4140. I am opinionated. You do not need to like what I say ... or listen to it.

What are you talking about, @Mike?

user4140

you can be opinionated without being mean

Ted Shifrin

22:13

@Pedro, it might be Mariano is picking up on your reluctance to take risk. But I disagree with him.

Mike

@TedShifrin That you've been doing physics students for the last couple years... :P

Ted Shifrin

@user4140: It was not an ad hominem attack on any particular person. Therefore, it was not mean. It was the truth.

Mike

@Pedro There's a difference between rushing and not wasting your time. A huge one.

Pedro Tamaroff

@TedShifrin What happened?

Ted Shifrin

LOL ... oh @Mike. Would that there were the partner to which you refer :D

user4140

22:14

first you say you are opinionated and then you say you only say the truth?

Ted Shifrin

@user4140 ... I am not going to respond to you any further. If you do not like me, ignore me.

Pedro Tamaroff

@Mike Well, maybe I can talk with someone about it, see what they think. It is a bit bothersome to be taking a class where I am learning about $\limsup$s and $\liminf$s.

Mike

@Pedro Good :)

user4140

It's not that I don't like you, I was just pretty surprised by your response, I feel like you anger easily.

usukidoll

oooo a bunny

user4140

22:17

where?

Pedro Tamaroff

@user4140 What is the problem?

usukidoll

@user4140 Grumpy Ted is always like that ;)

Mike

(Reminder to all that there's an ignore feature in chat, which I have found exceptionally helpful)

usukidoll

@user4140 there's the bunny playbites on @PedroTamaroff 's ear then lets go

user4140

I don't think there is one.

oh, Pedro is the bunny.

usukidoll

22:18

pets bunny

yeah the bugs bunny pic

Ted Shifrin

LOL @usukidoll

usukidoll

I wonder if @TedShifrin is related to the movie Ted.. hmmmmmmmmm...

Ted Shifrin

What movie Ted?

There's Bob and Carol and Ted and Alice ... back from the 70s or some long time ago.

user4140

The one about a bear?

usukidoll

Ted (film)

Ted (stylized as ted) is a 2012 American comedy film directed, co-produced, and co-written by Seth MacFarlane, with MacFarlane, Mark Wahlberg and Mila Kunis in leading roles. The supporting cast includes Joel McHale and Giovanni Ribisi. The film is MacFarlane's feature-length directorial debut, produced by Media Rights Capital and distributed by Universal Pictures. It was released on June 29, 2012, to critical and commercial success, becoming the 12th highest-grossing film of 2012, the highest-grossing R-rated film of the year, and the highest-grossing original R-rated comedy of all time....

user4140

22:19

lol yeh, that one

usukidoll

@user4140 yeah the one about the bear

Mike

Movie sucked.

user4140

That one sucks

usukidoll

has anyone looked up Sochi Problems XD

anon

comedy movies are almost always forgettable

user4140

22:20

yes, my dad watches fox news

so I know everything about sochi problems unfortunately

Mike

oh boy let's not go into that one

user4140

into which one?

usukidoll

about sochi problems

user4140

oh.

usukidoll

besides the bad translations and falling doorknobs in hotels

Ted Shifrin

22:21

Fox News is probably in favor of gay-bashing, anyhow. [OK, that is stated to be argumentative.]

user4140

Oh, I only knew about the bad Hotel conditions

usukidoll

one image made me go O_o do not flush toilet paper in toilet...put it in the bin.. UM WHATTTTTTTTTTTT! So unhygenic

user4140

guess I don't know it all

@usukidoll lol, doesn't sound so terrible

Mike

The problems there are sadder than funny, I think, because they're representative of the way the people might live

usukidoll

-.- not unless everyone does #2

Pedro Tamaroff

22:23

@TedShifrin So, to be honest, I have no study plan whatsoever.

Mike

@Pedro Make one!

user4140

could someone explain why cooked quinoa has less protein than raw quinoa according to the FDA?

Makes no sense to me.

Ted Shifrin

I'm sorry, @Pedro. You should find some faculty member who actually knows what you can do who'll give good advice. I would have guessed Mariano would be a good choice, but perhaps not, unless you make it clear to him you are unhappy with the status quo.

user4140

and the difference in protein is quite substancial

Pedro Tamaroff

@TedShifrin I haven't spoken with him seriously, really.

user4140

22:24

I thought it was pretty hard to denaturalize protein.

Pedro Tamaroff

@user4140 Ask a biologist, man.

@user4140 No, it is pretty easy.

Mike

There's a key difference between rushing through the courses you need to take and graduating tomorrow - and taking courses more suited to you.

Pedro Tamaroff

When you cook egg, you denaturalize.

Mike

Is Mariano a prof at BA?

Pedro Tamaroff

When you cook meat, you denaturalize.

@Mike UBA? Yes, he recently got a position.

user4140

22:25

But it's still protein right?

Pedro Tamaroff

@user4140 Well, it changes.

Loses properties.

Alizter

@user4140 It unravels from it's special coil

user4140

how could you explaint this difference?

Pedro Tamaroff

That's why it is called "denaturalization".

Mike

@Pedro Ah, gotcha.

user4140

22:26

ndb.nal.usda.gov/ndb/foods/show/…

The difference is huge

Mike

who care

Alizter

s

usukidoll

D:

user4140

who are you talking to?

Anyone have a reasonable explanation?

Pedro Tamaroff

Heat changes stuff!

Science!

usukidoll

22:28

blah I have to finish the latex......in x amount of minutes. I'm just chillin :P

Alizter

Mike

@alizter if one tilt does not care, it is not worth the effort to add the 's'

Alizter

Go ask there

Pedro Tamaroff

@TedShifrin You there?

Ted Shifrin

Yup, @Pedro.

Pedro Tamaroff

22:30

Well, I just don't want you to judge Mariano before knowing him. =) He really motivated me to study and get to know what I know now.

usukidoll

I ate Mariano he was delicious .. I added some Cajun spices

Kevin Driscoll

unions of open sets must be open, but unions of closed set could be open or closed, right?

Pedro Tamaroff

@KevinDriscoll Yes.

Counterexample?

user4140

is this topology?

Mike

yes

Pedro Tamaroff

22:34

@user4140 No, this is dog.

user4140

you mean the union of two closed sets?

Kevin Driscoll

@Pedro Let X = {1,2} with the trivial topology. {1} and {2} are closed, but {1,2} equals X and therefore must be open

Pedro Tamaroff

@KevinDriscoll X is also closed.

user4140

or any family of sets?

Pedro Tamaroff

Remember "not closed $\neq$ open."

Ted Shifrin

22:34

I have tons of respect for Mariano, @Pedro. And you are a very determined mathematician. I just hate to see you suffer through courses intended for students well below your knowledge level. I have plenty of advisees for whom our undergrad real analysis is too challenging and others for whom it's appropriate (based on their coursework, self-studying, and knowledge level) to skip it and move on.

Pedro Tamaroff

Rather, $A$ is closed if what is not $A$ is open.

user4140

►

2

Kevin Driscoll

@pedro Ah yes, it is both here

Ted Shifrin

@Kevin: Any finite union of closed is closed. Only infinite unions can mess up.

Pedro Tamaroff

@KevinDriscoll As Ted says: finite intersections of open sets are open.

user4140

22:35

I find that video really funny

Ted Shifrin

I remind my students that sets aren't like doors. Not open ≠ closed :P

Mike

Do you talk about ajar sets?

Just to confuse them.

Ted Shifrin

From time to time, yes :P

Some student in my multivariable math class suggested that a few years ago :P

Karl Kronenfeld

lol

Things like [0,1), right?

user4140

what are ajar sets?

Ted Shifrin

22:37

What about $\{1/n: n\in\Bbb N\}\subset\Bbb R$, @Karl? :D

Mike

any set that is neither open nor closed

Karl Kronenfeld

@TedShifrin Yeah, same concept. :P

user4140

why can't google point me to them?

Karl Kronenfeld

Because my paper isn't posted yet.

Ted Shifrin

Damn, a failure in google ...

Mike

22:38

@Ted There's some trouble with that one, since $0 \in \mathbb N$ :D

user4140

Is it widely used notation?

Ted Shifrin

Not to me, @Mike ... as you well know.

Ram

Hi all, In projective space of dimension m + n + 1 choose two complementary linear subspaces of dimensions m > 0 and n > 0. How can I show that these two subspaces of dimensions m,n span projective space of m+n+1 (In other words, why sum of dim. of spaces of complementary linear subspaces is 1 less than the projective space)

Ted Shifrin

someone please tell @user4140 the truth.

Karl Kronenfeld

:)

user4140

22:39

@TedShifrin I volunteer you

Ted Shifrin

@Ram: Turn it into a question about linear subspaces in $m+n+2$ space.

Mike

@Ted Your example still works as long as we move to $\Bbb P^1(\Bbb R)$

Ted Shifrin

spanks @Mike hard

Mike

Ok, I'll do it.

user4140

so what is the truth?

Ted Shifrin

22:40

@user4140: You don't trust me, anyhow. They were being humorous ... a door that is neither open nor closed is ajar. And one of my students did volunteer that terminology, but it is not standard math terminology. However, clopen is :P

user4140

oh I see.

Ram

@TedShifrin, yes thanks :)

Alizter

Is there a name for a non-surjective and non-injective function?

user4140

useless crap?

Mike

@user4140 The concept of ajar set, due to Tamaroff, revolutionized modern mathematics. However, since it left no open problems, secret math cabals decide to hide it - less mathematicians be jobless!

Ted Shifrin

22:41

if you'd said or, @Alizter, we could have said non-bijective. But I don't know a word, no.

user4140

as opposed to usefull crap

lol

Alizter

@TedShifrin Yes, I have a little table with surjectivity and injectivity and I was wondering for the "useless" case

user4140

do they really have interesting properties

?

Can you get interesting info from the ajar set of a topology?

Mike

ajar sets*

Karl Kronenfeld

@user4140 yeah, you can then classify all open/closed sets.

user4140

22:43

he ajar set is the set of ajar sets

Karl Kronenfeld

that's almost as good as telling me the topology!

Mike

remember, this is just the sets that are neither open nor have open complement. there are generally many of then

Ted Shifrin

Not clear @Karl

Karl Kronenfeld

which one?

Ted Shifrin

Yes.

Mike

22:44

He said almost as good @Ted

Ted Shifrin

You only have the topology with probability 50% :P

Oh wait, it's with probability 0.

user4140

lol

Ted Shifrin

Ergo, not useful.

Mike

Those are better odds than not having the ajar sets at all! Metaphorically.

user4140

but it might be of use

even if you can get the full topology

can't

Karl Kronenfeld

22:46

well, I was hoping that we could argue by contradiction involving infinite unions to rule out some classes of sets being open so they must be closed.

Ted Shifrin

I bet it's still probability 0, @Karl :P

Mike

@Karl I though that, but discrete topologies are problems

Ted Shifrin

Unless we have a finite set.

user4140

But it still isn't 100%

Karl Kronenfeld

@Mike hm, right I forgot that one kind of nontrivial topology where every set is either open or closed.

Ted Shifrin

22:47

Yup, discrete topology.

Karl Kronenfeld

nontrivial!

Ted Shifrin

Not exactly interesting, however. :P

Karl Kronenfeld

Oh, god.

I need to take a break or something.

Ted Shifrin

me too, @Karl.

user4140

complete and trivial look the same

Mike

22:48

@Karl Set your mind at ease from dumb math by looking at viXra

user4140

my protein question isn't getting attention

Karl Kronenfeld

@Mike lol ok

Ted Shifrin

Done grading @Mike?

Mike

@Ted About to start...

Karl Kronenfeld

@Mike "We generalize inversion mathematically" instead of, say, politically

Ted Shifrin

22:51

what is political inversion? I know one sociological use of the word.

Mike

@Karl What paper is that?

Ted Shifrin

do they mean inversion in spheres?

or inversion in algebra?

Karl Kronenfeld

vixra.org/abs/1402.0013

shit there are 8 parts

Ted Shifrin

ah, surely generalizing inversion in spheres

I'm not interested enough to look

Mike

@Ted They probably don't mean much of anything

Ted Shifrin

22:54

I don't know what vixra is ... is this the manufactured paper site?

Mike

No, it's arXiv for cranks.

Ted Shifrin

LOL ... does anyone vet it ?

Mike

No barrier to submission.

Ted Shifrin

ah ...

so I could enlarge my publication list grossly by publishing there :P

Mike

Funny stuff gets posted there sometimes.

Ted Shifrin

22:56

The question is: What percentage is humor and what percentage is people thinking they're doing serious mathematics?

Mike

@Ted Since you're about to retire, I don't think it could hurt :D

Oh, 99% is serious. But that doesn't stop it from being funny.

Ted Shifrin

Well, I'd have to take the time to produce the crap, @Mike. Sadly, I have a stack 1 foot high of folders of work that several of us did that we just gave up and never published.

Mike

If you just scanned it and uploaded it it would have more mathematical relevance than the bull on vixra. Probably be less funny though.

Karl Kronenfeld

@TedShifrin What's funny is they're called door spaces. :P

user4140

what is the difference from vixra and free to access math journals?

Mike

22:59

In this paper we introduce the concept of half-groups. This is a totally new concept and demands considerable attention.

Karl Kronenfeld

lol

Ted Shifrin

Not funny at all. It was singularity theory of theta divisors of genus-4 Abelian varieties. Generalizing stuff we did for genus 3. Literally folders and folders of work. But we ran out of energy/desire to write it up in acceptable fashion.

Really? @Karl

Transcript for

$Mathematics$ Mathematics