Mathematics - 2018-05-25 (page 3 of 3)

Daminark

10:00 PM

That'd make my day, whenever day I read it

Of all the possible typos, holy crap

Balarka Sen

lmao

MatheinBoulomenos

@Symposium are you learning a programming language?

Symposium

@MatheinBoulomenos No, why?

MatheinBoulomenos

just a joke

because you usually start with a program that outputs "Hello world!"

Alessandro Codenotti

@Daminark that'd be futurist math I suppose

MatheinBoulomenos

10:07 PM

In a colloquium talk, a number theorist refered to some result as a "short exercise". The grad student next to me told me that it takes a whole book to prove that "short exercise"

Symposium

@MatheinBoulomenos Oh lol. Yeah, true. I thought it had something to do with the name Symposium. I'm very slow on this Friday night!

Lozansky

Ugh I despise questions that presumes knowledge of the number of days in a given month

Balarka Sen

@AlessandroCodenotti pikapakpakpakpak UUUU ZANG TUMB TUMB

i remember reading the first chapter of that book

its pretty darn great

Symposium

For years I thought February always ended with 28 days O_o

MatheinBoulomenos

quote from a French mathetician who gave a colloquium talk "So far, we did topology and thus we drew pictures. Now we're going to move to algebraic geometry, where we draw categories and functors instead of pictures"

Balarka Sen

10:10 PM

"No we're going to"... so you aren't going to move to algebraic geometry?

Daminark

@Alessandro good lord

Balarka Sen

That's great!

MatheinBoulomenos

typo

Balarka Sen

naw u the truth just slipped up

admit it

Lozansky

They should cyclically permute leap days, just to be fair to the other months

Daminark

10:13 PM

They should use a random number generator to decide when the leap day is

MatheinBoulomenos

they should split the leap days evenly among the days a in year, so every day has a few more seconds

Balarka Sen

the whole year should be a single day

takes the trophy and leaves

Lozansky

Carpe annos

Anonymous

I'm a bit confused about whether $(P(G),\subseteq)$ would be lattice and whether $(\text{sub}(G),\subseteq)$ would be a sublattice of it

Anonymous

I know that $(\text{sub}(G),\subseteq)$ is a lattice

Anonymous

10:23 PM

@MatheinBoulomenos Around for a bit?

MatheinBoulomenos

yeah I'm here

Anonymous

Halp plz :P

MatheinBoulomenos

Can you explain the notation?

Anonymous

@MatheinBoulomenos P(G) probably refers to the power set

Balarka Sen

Bryan Mills jumps a fence

►

Anonymous

10:24 PM

of a group $G$

Balarka Sen

This might be the greatest stunt scene ever

MatheinBoulomenos

So $\operatorname{sub}(G)$ are the subgroups of $G$?

Anonymous

@MatheinBoulomenos Yes

MatheinBoulomenos

that's not a sublattice

the joins are different

Anonymous

@MatheinBoulomenos Could you elaborate? I'm pretty confused at this point

Anonymous

10:26 PM

First of all. Is $P(G)$ a lattice?

Anonymous

I guess so

MatheinBoulomenos

the least upper bound of two subgroups (so the smallest subgroup containing those two subgroups) is generally not the same as the smallest subset containing those subgroups

yeah

Anonymous

@MatheinBoulomenos I see. What would be the least upper bound for P(G)'s subsets?

MatheinBoulomenos

you take the union

Anonymous

Find the groups containing them and take union?

Anonymous

10:28 PM

*union

MatheinBoulomenos

are talking about least upper bounds in $P(G)$ or in $\operatorname{sub}(G)$?

the greatest lower bounds both in $P(G)$ and $\operatorname{sub}(G)$ are both intersections

the least upper bounds in $P(G)$ are given by unions

the least upper boudns in $\operatorname{sub}(G)$ of $H$ and $K$ is given by the subgroup generated by $H \cup K$, one way to describe it is to take the intersection of all subgroups that contain both $H$ and $K$

Anonymous

@MatheinBoulomenos Yep, I got that one

Anonymous

What about $P(G)$?

MatheinBoulomenos

both $P(G)$ and $\operatorname{sub}(G)$ are lattices, but $\operatorname{sub}(G)$ is not a sublattice, since the least upper bounds are different

in $P(G)$, the least upper bound of $X$ and $Y$ is just $X \cup Y$

Anonymous

Makes some sense

Anonymous

10:33 PM

I was getting confused because of the fact that union of subgroups is normally not a subgroup. But here we are rather taking union of sets

MatheinBoulomenos

right

Anonymous

Gotcha! Thanks a ton :D

MatheinBoulomenos

np

Annabelle

Hi! Um simple question but: I have this sentence.

`Test, at the 1% level of significance, whether the average amount someone travels for work is more than 15km.`

How would I get started on this?

GFauxPas

are you given the distribution?

Annabelle

10:43 PM

Normally distributed is what it says

Ted Shifrin

With what mean?

And what standard deviation?

GFauxPas

Khan Academy has excellent videos on these types of problems by the way, highly recommend

hi Ted

Ted Shifrin

hi @GFauxPas

Annabelle

Mean is 14.75, Students are 80.

I watched some videos, but I honestly get confused every time they bring up Z values, and other sorts of stuff.

Ted Shifrin

$\sigma$?

Annabelle

10:45 PM

22 is what I got for standard deviation.

For example, 1% level of significance, that is p = 0.01?

Ted Shifrin

That seems remarkably huge.

Annabelle

Eh it's just a random dataset teacher gave

So I'm not surprised

Ted Shifrin

There are numbers going out to 37 and 59?

With a normal distribution, you'd need a much larger mean.

Annabelle

Highest is 36

Ted Shifrin

Yeah, so you need to be surprised if you're getting $\sigma = 22$. Is that maybe $\sigma^2$?

Annabelle

10:48 PM

Isn't $σ$ standard deviation?

Ted Shifrin

Think about what you know about normal distributions and what percentage lie within $2\sigma$ of the mean.

Yes, it cannot be 22.

Annabelle

That's what excel seems to be saying when I put in the data

Ted Shifrin

Hmm, well, I give up.

Annabelle

Oh

I see

Nevermind I typed it wrong

It's uh

7.9

Ted Shifrin

OK, that's still larger than I would have expected for a normal distribution with mean 14.75.

But at least plausible.

Annabelle

10:51 PM

So how do I test something at a certain percentage of significance?

Ted Shifrin

That's more statistics than I know.

RIP Okay

Hi chat :D'

Hi!

:D

10:52 PM

But you need to know how many standard deviations above the mean 15 is ... and then the normal distribution will tell you the probability that you're past that. It's quite large.

MatheinBoulomenos

Hi @KasmirKhaan

Ted Shifrin

hi Kasmir.

Kasmir Khaan

@TedShifrin do you know how to do net adjustment ?

Ted Shifrin

I have no idea what it means.

Kasmir Khaan

@MatheinBoulomenos My hero ! :D

haha okay

it is someting that engeneers use i think

my friend asked me about it , i too had no idea ><

GFauxPas

10:53 PM

I never grokked probability, I'm gonna try again this summer now that I have some measure theory under my belt, hopefully that will give me a fresh perspective that might be more natural for me

Ted Shifrin

Today is my stooopidity day.

Anonymous

@MatheinBoulomenos Any idea of what an example of an infinite complemented lattice would be?

Ted Shifrin

I've taught probability but I don't know statistics language.

Kasmir Khaan

I think engneer ppl think alot of math haha

i have no idea if it is in statistics

Anonymous

And an infinite distributive lattice

Ted Shifrin

10:54 PM

No, @GFauxPas, it'll just be abstract measure theory, with no reference to concrete questions.

GFauxPas

oh :(

Kasmir Khaan

that was a wierd "haha"

Ted Shifrin

No, the statistics was with reference to Annabelle's question.

GFauxPas

bummer

MatheinBoulomenos

I have no idea about probablity or statistics

Kasmir Khaan

10:55 PM

aha okay ! :D

GFauxPas

but at least I have a new way of thinking about events/random variables

Ted Shifrin

They're just measurable functions on a measure space (with total measure $1$).

GFauxPas

right but $\mu(\{t: X(t) > 0.5\})$ seems more concrete that $\operatorname{Pr}(X > 0.5)$ in some sense. Maybe

Kasmir Khaan

Ted if i want to learn about least square adjustment

what book / lectures / course i should take?

GFauxPas

I dunno, the point is I'll look at it again and see if its easier for me this time, I havent tried in a while

Ted Shifrin

10:57 PM

You're lying to yourself, @GFauxPas.

GFauxPas

yeah probably

Ted Shifrin

What do you mean adjustment, @Kasmir?

GFauxPas

don't we all though

Ted Shifrin

You mean least squares fit to data?

Um, no, @GFauxPas.

Kasmir Khaan

Yes i think that what they mean ><

GFauxPas

10:57 PM

:(

Kasmir Khaan

its engi lango am sorry =p

GFauxPas

unrelated note, I'm excited about this proofwiki.org/wiki/User:GFauxPas/Sandbox

Ted Shifrin

It's a standard application of projection in linear algebra, @Kasmir. You can find it in one of my lectures. Or you can look at any number of books or Wikipedia.

You can find it even in calculus books, as a basic max/min problem in two variables.

GFauxPas

look how pretty my graph is

Kasmir Khaan

I rather take it on your book :D

Mancala

10:58 PM

Could anyone help me understand what geodetic plans mean in the context of hyperbolic surfaces?

Kasmir Khaan

what is the name of your book ? :D

Ted Shifrin

But what's going on is projection. You want to solve $Ax=b$ but $b$ is not in the image of $A$. So you project $b$ onto the image and solve that. Setting up linear equations fits that model.

Kasmir Khaan

if we have more than a linear model

Ted Shifrin

It's actually in one of the 3500 lectures, Kasmir. It should be labeled. Near the end.

Kasmir Khaan

okay ! i shall take a look now :D

i wish under summer i follow that serie from strat to end

MatheinBoulomenos

11:00 PM

a weird thing happened in the number theory course I TA

Mancala

Kasmir Khaan

most of what i needed was there :D

Ted Shifrin

The students passed, @Mathein?

loch

I think it's nice that you have a precise way of saying what probability is (i.e. with measure theory) - whereas my memory is that before that i guess it's kind of muddly esp. when you're talking about continuous random variables and beyond (it's ok when things are finite because there your measure is just the obvious one ) - but actually i don't really rmb what happened when i first learnt prob/stat anyway

but im no probabilist (or analyst) so idk

MatheinBoulomenos

that'd be pretty unusual, yeah

Daminark

11:00 PM

Just do what combo does and stick to finite probability spaces :P

Ted Shifrin

That can be confusing, too, Demonark.

MatheinBoulomenos

there was one exercise which no student solved, then on the next exercise sheet, there was an exercise that said "use the result from the previous exercise (that nobody solved)" without stating the result (and they had to turn that in before I showed them the solution)

Ted Shifrin

So they didn't know which previous exercise, @Mathein? I'm not quite following.

MatheinBoulomenos

No, they know which exercise

Ted Shifrin

So you can use a result without knowing the proof?

MatheinBoulomenos

11:02 PM

but the exercise was "determine the image of this map" and they don't know what the image is

Ted Shifrin

Oh, so, yeah, that's a crummy exercise.

MatheinBoulomenos

you can't use a result without knowing the result, that's the problem here

loch

rip

Ted Shifrin

The new problem should have said: You should have found that the answer to #3b was ...

MatheinBoulomenos

yeah

I should probably give feedback to the guy who makes the exercises

Daminark

11:05 PM

Do you say it that way because this person is different from the professor?

MatheinBoulomenos

yeah

it's the assistant of the professor (though the professor could still make some exercises, of course)

Ted Shifrin

It's always good when the person writing the homeworks has no idea what the course is covering, too. :P

Daminark

Wait so the prof has an assistant and a TA?

MatheinBoulomenos

yeah

Ted Shifrin

Professors in Europe have essentially 0 contact with students, Demonark.

MatheinBoulomenos

11:06 PM

that's not true

the prof which is now my advisor greeted in my first semester when he saw me somewhere randomly and I was one student of 600 in the course

Ted Shifrin

Well, you're far from the typical math student at your uni.

philmcole

Please give feedback. Nothing is worse than having excercises which you can't possibly solve. In my first year we had a physics/programming class in which an excercise requested the derivation of the hamiltonian operators where we didn't even have them introduced yet in the main physics course. @MatheinBoulomenos

Ted Shifrin

@philmcole: I had lots of office hours and they were quite well-attended because I wrote challenging homeworks (usually).

But that sounds like lack of coordination ...

MatheinBoulomenos

the assistant is making the exercises and if the prof is sick or at a conference etc. he's giving the lecture. He also does all the formal stuff so the prof basically only has to give the lectures

I do the grading and I present solutions to the exercises

the assistant is a post doc

philmcole

Or like the first excercise (like 10 days into the first semester) in the physics course was to use the taylor approximation of sine which most of us hadn't heard about yet

MatheinBoulomenos

11:09 PM

@philmcole yeah, I'll do that

Sir Cumference

Howdy

Symposium

I absolutely love any class that that has optional and marked starred questions.

Ted Shifrin

I always had challenge problems (which relatively few students even attempted) ... or graduate problems for split undergraduate/graduate courses, and grad students and undergrads taking the grad course for Honors credit had to do several of those a week.

MatheinBoulomenos

I could only solve one exercise in my ANT course by introducing two completely new concepts and proving a lot of lemmas about them, so I ended up with over 10 pages of lemmas on decomposition groups and double cosets (both hadn't been introduced in the lecture)

philmcole

Yeah lack of coordination and also disconnected excercise writers which don't know the level of the students at all, probably haven't even seen them... @Ted

Ted Shifrin

11:11 PM

I had a handful of students each year who would work on challenge problems regularly.

MatheinBoulomenos

the TA didn't have a shorter solution for that ...

Ted Shifrin

@philmcole: Most courses I'm aware of, the professor writes the homeworks (which at least means choosing exercises from the text) based on what he plans to cover.

That seems ridiculous, @Mathein, but excellent for you.

MatheinBoulomenos

yeah I learned a lot

tbf, I knew the concepts because I saw them in some other contexts

Ted Shifrin

As I said, you're far from a typical math student, even by European standards.

I would have gone to the prof to ask for how he expected it to be done.

philmcole

@TedShifrin At my university mostly profs don't bother with excercises which is bad IMO. Everything is done by assistants which often don't care and know much about the students.

Daminark

11:14 PM

Most of my professors just have homework problems, occasionally some would give an extra credit problem or two (never more than, say, 1-2/quarter)

Ted Shifrin

Where are you a student, @philmcole?

GFauxPas

oh Ted I think I got an answer to the exercise you gave me

$\dfrac {\ln t}{\ln t}$ at $0$

Ted Shifrin

Oh, I had some every week, Demonark. I think that's better.

philmcole

@TedShifrin Zurich, Switzerland

Daminark

I know one professor regularly gives supplementary problems and recommends you do them if you were to, say, ask him for a rec

GFauxPas

11:14 PM

is that cheating

MatheinBoulomenos

well, the exercises by that prof were really long anyway. We ended up with over 20 pages of solutions regularly. One time our solutions were too much for our stapler to handle

Daminark

Then there's combo, which has an interesting problem structure

MatheinBoulomenos

There was one exercise which had 12 different parts in which we basically proved all results from a whole chapter in a book on number theory

loch

That's some hardcore stuff

Daminark

The professor lectures and the problems are assigned as he lectures. He has many types of problems

Ted Shifrin

11:16 PM

@GFauxPas, that is not what I had in mind. But I don't see how it answers the question, anyhow. I wanted $\lim f(x)/g(x)$ to exist ("0/0") and asked whether $\lim f'(x)/g'(x)$ had to exist.

Daminark

DO exercises are the most common, which are ones you should do but not hand in

HW problems are graded

Ted Shifrin

Ah, @philmcole. The European system is not very student-oriented.

Daminark

Bonus problems are HW for grad students, extra credit for undergrads

Semiclassical

hi chat

Balarka Sen

Is every $n$-connected CW complex homotopy equivalent to a CW complex with $n$-skeleton consisting of a $0$-cell? I think so.

MatheinBoulomenos

11:16 PM

I had some really good assistants here

Daminark

(This is only in combo, which is cross-listed as undergrad and grad)

Ted Shifrin

Demonark, I did separate grad problems, too, for split courses. But what about first- and second-year courses?

philmcole

@TedShifrin Sadly, no. :(

Daminark

He doesn't teach many of those

Symposium

@MatheinBoulomenos Are you from Germany?

Ted Shifrin

11:17 PM

It's good to remind students that they should make an effort to get to know the professor and do some work to impress him/her if they want letters of rec.

MatheinBoulomenos

@BalarkaSen doesn't this follow from Postnikov towers?

@Symposium yeah

Daminark

But yeah he has Challenge Problems, which are hard, no credit, but the solution is a reward in itself and also if you wanna ask him for a rec, you should do some. They have no expiration date, even beyond the end of the class

Balarka Sen

@MatheinBoulomenos I don't know Postnikov towers, but I think I have an obstruction theory proof.

MatheinBoulomenos

Postnikov towers are basically obstruction theory

Ted Shifrin

I did that, too, in my multivariable course, Demonark. They had until the final exam to turn in challenge problems. (In the advanced courses, things were due each week.)

philmcole

11:19 PM

@TedShifrin But I hope I can go abroad for one semester. I want to go to the US, Canada or maybe Australia.

Daminark

I remember when he first assigned a challenge problem he was like yeah, let me know if you work on them so I don't talk about them in class (which is when they expire). If I never talk about the problem you can let me know in 5 years if you get it

philmcole

would be nice to see if the teaching is different

Ted Shifrin

The US isn't a fun place these days for foreign students. Applications have dropped way off. I wonder why.

Symposium

It's a mystery!

Ted Shifrin

Demonark: I've had a few questions that students have solved 5 years later and emailed me. Hysterical.

philmcole

11:20 PM

There are some programs with partner universities. I guess that's where I would go...

Ted Shifrin

@Symposium: Yes, he is.

Daminark

That's nice

Ted Shifrin

Well, @philmcole, I'll let you know if I know anything about them (in terms of math).

philmcole

Do you know about Purdue?

Ted Shifrin

I don't think I know anyone there any more.

I'd have to double-check.

philmcole

11:21 PM

Also I'm doing physics but I guess there are some math classes too which I'll need to take

Balarka Sen

Say $X$ was the $n$-connected CW-complex. $f : X^{(n)} \to e^0$ be the homotopy equivalence with a point. For every $(n+1)$-cell in $X$, attach an $(n+1)$-cell to $e^0$ and call the new space $Y_1$. Let $f : X^{(n)} \to Y_1$ be $f$ composed with inclusion. Obstruction to lifting $f$ to $X^{(n+1)}$ lies in $H_{n+1}(X^{(n+1)}, X^{(n)}, \pi_n Y_1)$.

That's zero.

Ted Shifrin

Oh, I know nothing about physics at most places.

Balarka Sen

Rinse lather repeat

Ted Shifrin

At UGA there are two awesome physics profs and the rest are OK to mediocre.

philmcole

I heard good things about UGA!

But I don't think they are partnering with my university :(

Ted Shifrin

11:24 PM

Purdue has a huge math department. I know about 5 of the older faculty. I don't know if they're still teaching; they're listed and it doesn't say retired.

Balarka Sen

Meh, you don't need this. Let $g : X^{(n+1)} \to Y_1$ be simply defined by $f$ on the $n$-skeleton, and sending the $n+1$ cells to the $n+1$ cells. This is just the map $X^{n+1} \to X^{n+1}/X^n$, which is a homotopy equivalence.

Daminark

Oh speaking of UGA, do you think that'd be a place worth looking at for grad school? Like, do they have a decent variety of fields represented (in particular, folk in algebra/NT/topology?)

Also wrt whatever other considerations are relevant

GFauxPas

$\dfrac {(x \sin(1/x))}{|1 - x \cos x|}$?

Ted Shifrin

It's not upper echelon, Demonark, but there are excellent people and a number of grad students in those areas.

The grad atmosphere is more supportive at UGA than at other places I've been.

GFauxPas

Ted

Balarka Sen

11:27 PM

@MatheinBoulomenos Yeah dawg this is just super trivial. Let $X$ be the CW-complex, consider the map $X \to X/X^{(n)}$. This is a quotient map quotienting out a subspace which is homotopically trivial, so it's a homotopy equivalence.

Ted Shifrin

Huh? @GFauxPas

How does the first limit exist?

MatheinBoulomenos

@BalarkaSen true

Balarka Sen

$X/X^{(n)}$ is the new model for $X$ which has trivial $n$-skeleton.

GFauxPas

oh the limit exists but not as $0/0$

Ted Shifrin

So I'm stipulating that it's 0/0 so it makes sense to consider L'Hôpital.

GFauxPas

11:28 PM

right, well I have to go now but i'll think about it more :)

bye mathematician friends

Daminark

See you!

Balarka Sen

@MatheinBoulomenos Huh, I didn't know that.

MatheinBoulomenos

@BalarkaSen the idea of Postnikov towers is a bit like an analog of CW-complexes. When you decompose a space into a CW-complex, you build it from parts which are homologically simple to understand (but homotopically they might be complicated). So when you associate to a space it's Postnikov tower you build it from homotopically simple components, i.e. Eilenberg-Maclane spaces.
So if you have a space $X$, then you can find a tower of spaces $X_n \to \dots \to X_1 \to X_0$, such that all maps are fibrations and $\pi_k(X_n)=\pi_k(X)$ if $k\leq n$ and $0$ else. also there's a weak homotopy equi…

by the LES sequence of fibrations, the fibres in this sequence will be Eilenberg-Maclane spaces

Balarka Sen

Yeah I vaguely know that it's constructing $X$ as a twisted product of $K(\pi_n X, n)$'s.

Ah, so the point is maps $X \to K(\pi_n Y, n)$ are just upto homotopy in bijection with $H^n(X, \pi_n Y)$ perhaps.

Somehow that kicks in.

I had never thought of that

MatheinBoulomenos

yeah, that's how obstruction theory comes in

these Postnikov towers show that the weak homotopy type of a CW complex is determined by the homotopy groups and the obstruction classes

Jake S

11:39 PM

If I am calculating the sum of two subspaces in R3 and the sum of the cardinality of their basis is greater than 3, does this exclude the possibility of them being a direct sum?

Balarka Sen

Is there no fucking way to turn off windows update mechanism

That's literally the most cancerous thing I have ever encountered

It's impossible to stop it once it starts, and it starts without notification

Daminark

Delete Windows

MatheinBoulomenos

Linux master race

Balarka Sen

Can't delete windows when it's updating

Fuck this I'll just smash my laptop

I'll have the last laugh

Daminark

Lol I actually use Mac though before college I mostly used Windows

Symposium

11:47 PM

Get a window share program - I'll fix it for you.

Works better if you keep card details etc in your computer.

Daminark

There were three brands that I thought were somehow "endorsed" by the school first year (really it was just that they had more specialized tech support)

Balarka Sen

lmao

Daminark

Mac, Dell, and Lenovo

MatheinBoulomenos

be careful, Linux may cause you to drop out of college

Ubuntu Causes Girl To Drop Out of College

►

Daminark

I kinda wanted something that'd last and sorta didn't trust Dell too much for that reason, also couldn't really find a Lenovo computer at the time that wasn't either a massive brick, had crap battery life, or less power than I sorta wanted

Symposium

11:49 PM

Mac is expensive, but it doesn't have any of the ailments that windows does.

I got a cheap one in the block.

MatheinBoulomenos

Linux doesn't have internet, this video proves it

the internet CD doesn't work

Daminark

lamo

Symposium

Looool

Balarka Sen