Mathematics

12:00 AM

My teacher forgot to upload my grades and now I'm going to have a week full of bureacracy and paper work to fix the f***ing mistake.

Clarinetist

@DonLarynx - Yeah, that's what I'm doing... I'm trying data science, but it is going to require quite a bit of work. Hopefully it'll all work out at the end.

Don Larynx

@ModdedBear: Looks like it should be easy for you, as that requires no strength :)

Modded Bear

mabye, but paperwork is like kryptonite.

Daniel Fischer

@evinda A red-black tree? Also not something I know the rules of, I'm afraid.

Don Larynx

@Clarinetist that's good! But also engage in one more area, preferably outside mathematics in general. Otherwise, you'll be worried about spending your life dealing with numbers.

Modded Bear

12:03 AM

For example calisthenics

sports is the best hobby imho

@DonLarynx yeah, cardio is for girls

although I do sneak into the pilates classes once in a while.

Clarinetist

@DonLarynx - True, true indeed. It's just hard to do *anything* really, when you work full-time and are expected to progress through exams. If I could do anything with my life, it would be some combination of the following:

1) Piano lessons and/or composing
2) Teach math/statistics/actuarial science at a university
3) Publish an actuarial textbook or study manual

Don Larynx

@ModdedBear or should I say Dr. Fernandez, for the week being, you will be okay. Send me some extra kryptonite in case you are winning in our next challenge.

Alex Wertheim

@Clarinetist: you are a pianist, then?

Clarinetist

@AlexWertheim - Yes, and clarinetist. Clarinet for about 11 years now (been on a hiatus since I graduated last May) and Piano for about 5 years, but off and on. I'd like to improve my piano skills.

Modded Bear

@DonLarynx you better not slow down in PE. Because when I decide to punch, I will punch hard.

Alex Wertheim

12:07 AM

@Clarinetist: neat. Working on any piece in particular at the moment?

Don Larynx

If you ever decide to. Ha

Clarinetist

@AlexWertheim - Just trying to get back to composing at the moment. It's just hard to be inspired when I live in a city where everything seems to be business and insurance.

Don Larynx

What city is that?

Clarinetist

Des Moines, IA.

evinda

@DanielFischer A ok...

Alex Wertheim

12:09 AM

I could see how that might be difficult. Doesn't seem like there's much soul or romance in business/insurance. :)

Clarinetist

@AlexWertheim - Nah, not really. :P Especially when you're an actuary out here. Silence permeates the departments I've been in. You only talk to people when you have a question or if there's a department outing. And even those outings, dang, they're awkward as heck.

Alexander Gruber

Okay let me tell y'all a thing and get some reactions

Alex Wertheim

How comes your prep for the subject GRE?

Clarinetist

@AlexWertheim - Right now, I'm not really sure what to do with that exam. I'm definitely going to take the General GRE again. My Q score wasn't bad, but not the best either.

Alex Wertheim

@Alexander: is it a story all about how your life got turned upside down?

Clarinetist

12:14 AM

The only reason that I've been switching between YES, I'M GOING TO TAKE IT and I MIGHT NOT is because I don't know if I'm going to have the time right now, and I don't know if I necessarily need it for what I want.

Alexander Gruber

@AlexWertheim Now I'd like to take a minute just sit right there

I'll tell you how I'm going to calibrate some particle detectors using combinatorial optimization.

Alex Wertheim

:)

@Clarinetist: I see, makes sense. Well, whatever you decide, good luck!

Clarinetist

Thanks @AlexWertheim

Modded Bear

@AlexanderGruber that's awesome

Alexander Gruber

So, suppose we've got a machine with a bunch of keys, say 100 of them, call them $\text{k}_i$. Whenever a key is touched, it sends a signal to the machine, saying $\text{k}_i$ was touched at time $t_i$.

We can't personally go in and press any of the keys, but every once in a while, some person will come in and randomly press a bunch of keys and leave. Then we get that data

Modded Bear

12:18 AM

so a person goes in at time $t$ and presses a subset of the keys simultaneously?

or at different times?

Alexander Gruber

@ModdedBear We'll say that every time a person comes in and presses a bunch of keys, that constitutes an "event", and events restart the clock.

Modded Bear

ok, so then the buttons get pressed at different times by the person right?

Alexander Gruber

So if they only pressed one key during an event, it would always register as time $0$

right

Modded Bear

ok

Alexander Gruber

We'll assume that the events are far enough apart that they're distinguishable.

Modded Bear

12:20 AM

k

Alexander Gruber

So, the problem is this, we think that each individual key may have a different activation time. In other words, if somebody came in and all the keys were pressed at once, the times the machine recorded for each key would be their "true zero," $\text{z}_i$. These are assumed to be consistent

But, we don't know what they are

Modded Bear

when you say all the keys where pressed at once you mean by the same person right? not at the same time.

Alexander Gruber

I mean, at the same time.

Modded Bear

oh ok

then the machine would tell you all the keys got pressed at the same time. Or not?

Alexander Gruber

So, I'm saying, if we had an experiment where someone pressed $k_1$ and $k_2$, the $t_1$ and $t_2$ couldn't be trusted, because $z_1$ and $z_2$ may be different. Does that make sense?

@ModdedBear Yeah. It'd record times for all of them.

Modded Bear

12:24 AM

ok

I didn't get that "true zero" part

Samuel Yusim

what happens to t_i if key i gets pressed more than once

not that I have any idea what you guys are talking about

Alexander Gruber

Basically the event timer may start recording times differently for different keys. If $k_1$ and $k_2$ were pressed both at once, maybe we would see $t_1=1$ and $t_2=2$, which is non-desirable.

@SamuelYusim All but the first one would be dropped. Good question (Meaning, only the time of the first press of each key is recorded)

Modded Bear

ok, I think I'm getting it

so if you press six keys at once you'll get times $1,2,3,4,5,6$?

Alexander Gruber

@ModdedBear we'll get $1,2,1+(z_3-z_1),1+(z_4-z_1),1+(z_5-z_1),1+(z_6-z_1)$

whatever those may be

Modded Bear

oh, I got it

each key takes up a certain ammount of time to activate?

So some are slower than others?

Alexander Gruber

12:30 AM

Exactly

And we don't know what the activation times are

All we have is the actual data the machine gives us, and we can't measure the "true" times the keys are hit

So one would think this would be a hopeless problem. We are blind because we can't trust our own eyes

my idea is this

Modded Bear

wait

Alexander Gruber

ok

Modded Bear

ok, sorry

I'm ready

Alexander Gruber

So if we kept looking for events with $k_1$ and $k_2$ in it and we always found data like [event 1: $t_1=2$ , $t_2=3$], [event 2: $t_1=12$ , $t_2=13$], [event 3: $t_1=8$ , $t_2=9$] etc

it'd be pretty obvious that $k_1$ was $1$ second ahead of $k_2$

Modded Bear

wouldn't one event be enough?

Alexander Gruber

12:36 AM

It would if we were 100% sure that they were pressed at the same time.

Modded Bear

oh right

ok

I got it

Alexander Gruber

My idea is this... within a single event, it isn't possible to tell how accurate the timing delay we get is. But, timing delays should be transitive.

$k_1$ should always be $z_2-z_1$ ahead of $k_2$, $k_3$ should always be $z_3-z_2$ ahead of $k_2$, then $k_3$ should always be $z_3-z_1$ ahead of $k_1$. Within a single event, we would measure $t_2-t_1$ and $t_3-t_2$ and $t_3-t_1$ for these values

Don Larynx

How does $(n+1)(n)(n+2)(3n+5) = (n)(n+1)(n-1)(3n+2) + 12n(n+1)^2$ I just don't see it.

Alexander Gruber

But over multiple events, we can measure those values and compare $t_2-t_1+t_3-t_2$ from one event to $t_3-t_1$ in another event.

Modded Bear

makes sense

Alexander Gruber

12:43 AM

the closer those two values are, the more likely it is that it's the real $z_3-z_1$

so i'm trying to figure out if that's really a good way of looking for those $z_j-z_i$'s or not

finding the most consistent set of measurements would amount to finding a minimal spanning tree on a graph with vertex set $\{k_i\}$, with edges weighted by $t_i-t_j$ over all events

@DonLarynx how bout by interpolation?

in $\mathbb{Z}[n]$?

Don Larynx

interpolation? How do I do that? In $\Bbb{Z}[n]$

Alexander Gruber

@DonLarynx both sides are $4^\text{th}$ degree polynomials. If they agree at 5 points, they are the same.

Pedro Tamaroff

@AlexanderGruber Hehe, $\Bbb Z[n]$ looks so weird.

Alexander Gruber

they're both the same at $0$ and $-1$, that's obv

Don Larynx

But if they agree at only 5 points, they don't necessarily agree for six. Wouldn't this make them not the same?

Modded Bear

12:52 AM

@DonLarynx if two polynomials $P$ and $Q$ of degree $n$ agree in $n+1$ points they are the same

becuase the polynomial $P-Q$ of degree $n$ or less would have $n+1$ roots. Thus $P-Q$ is the zero polynomial.

Don Larynx

Wow @Modded I learned that last semester. WTH?

Alexander Gruber

plugging in $n=1$ gives $48=48$, check

then $-2$ gives $0=-2\times -1 \times -3 \times -4 + 12\times -2 \times 4 = 0$

then pick your favorite number for your 5th and you'll be doin good

@Alex!

@TedShifrin Hola

Back still better?

12:58 AM

Yeah! Biked to the gulf this week.

Ted Shifrin

Oh, I'm so glad for you.

Alexander Gruber

@TedShifrin So I just gave in and ordered a dip pen

Ted Shifrin

LOL, I still use my Parker 51 that's 50+ years old. @Pedro and several of my students are fountain pen devotees.

Alexander Gruber

@TedShifrin Yeah, I am too.

Ted Shifrin

Nerds unite :)

Alexander Gruber

1:09 AM

@TedShifrin if you ever get to Cincinnati you should check out Appointments.

Ted Shifrin

OK

r9m

1:54 AM

@Chris'ssis ?? -_-'' wha was dat?=P

Kevin Driscoll

My lab mate uses a fountain pen

I use an electronic pen and a writing tablet. Paper is soooooo 2000 and LATE

Modded Bear

electronic pen and tablet is for noobs lol

r9m

@KevinDriscoll what kind of lab is it ?

Kevin Driscoll

@r9m My lab?

r9m

@KevinDriscoll yes

Kevin Driscoll

2:07 AM

Technically, its in our minds. We're theorists.

So by lab mate I really mean we're in the same group and share an office

r9m

@KevinDriscoll what kind ? :)

Kevin Driscoll

@r9m We do Cold Atom Theory

r9m

@KevinDriscoll that sounds totally cool, although I have no idea what a cold atom is (pardon my ignorance)

Kevin Driscoll

@r9m Usually we consider alkali metal atoms, although with our particular research it doesn't really matter. By cold we mean they are in the micro to nano-kelvin scale

Which means they could be a billion times colder than outer space

r9m

@KevinDriscoll wow!! cool !!!

Julian Rachman

2:17 AM

Hey. I have always had this speculation: when is a mathematician considered a mathematician amongst the mathematics community?

Kevin Driscoll

They're cooled so much because at the scale almost all classical motion is suppressed. The atoms act essentially as ideal quantum mechanical objects

r9m

@KevinDriscoll I see ! I just started reading the wiki page :)

Julian Rachman

Hey. I have always had this speculation: when is a mathematician considered a mathematician amongst the mathematics community? I.e., They can create a website and such.

Don Larynx

That's called a web designer @Julian

Julian Rachman

No. Like can create a website for their work. Like I consider myself an amature and that I cant create a website because it will make me look stupid

Don Larynx

2:24 AM

Make you look stupid amongst whom, @Julian?

Julian Rachman

And I asked another question too: when is a mathematician considered a mathematician amongst the mathematics community?

Don Larynx

When they produce a work, @Julian.

Julian Rachman

Idk. It is just that like the website will look stupid if you dont have any work. but i have written notes and have one expository. but that is it.

i have a blog now, but I have been looking at personal webpages and they are better than a blog to me. But I have only seem ones for people that have published a paper. and that makes me wonder...

@Don

Don Larynx

2:42 AM

You have nothing to prove to anyone but yourself @JulianRachman. Some notes and an expository is better than nothing.

Julian Rachman

That is true. But then I want to display it so should I use a webpage? Or should i wait till i have more or a publication? Because i was told like dont get it unless you have published something

@Don

Don Larynx

Remember owning a website costs money, it's basically e-land. Land costs money. Ask yourself if it will be worth it.

Julian Rachman

I found one that is free and can be programmed from scratch using HTML.

I can send you the link if you would like

But I think I will stick with my blog for now. It was just a hunch.

:)

@Don

Samuel Yusim

3:08 AM

the universal property of tensor products is weird and while kind of cool I can't say I like it yet

whenever I use it I get a bad feeling for some reason

user105491

3:34 AM

@Samuel It becomes more natural once you think of it in terms of category theory

r9m

I am grieved to declare that yesterday I broke the 344 consecutive days visits to M.Se ! :(((((( disaster !!

user105491

basically it then becomes the existence of a map that leads to the commutativity of a triangle

user105491

See en.wikipedia.org/wiki/Universal_property#Formal_definition for example

user105491

@r9m That is a lot more than my personal high!

user105491

:-)

r9m

3:37 AM

@SanathDevalapurkar I wanted to reach 365 somehow ! I couldn't login yesterday :( da** our servers :((

user105491

i feel for you

user105491

are you at a university?

r9m

ya ... the uni with possibly the worst internet service in India :(

user105491

ah, you're in india?

user105491

i used to study there

user105491

3:39 AM

until i moved to the us with my parents

r9m

I see :) ..

@user153330 I hope there was no actual mating involved ! =P rofl

Kevin Driscoll

3:57 AM

I dont know what I would do if our internet went down

Id be very much beside myself

sometimes we have a minor outage in the middle of then night

even after midnight, they already have people working on it

walkar

I know that feeling. When a page takes more than a couple of seconds to load I get a bit nervous. In some places, we've definitely been spoiled by consistent and speedy access to the world at large.

Don Larynx

The probability that you get a particular number on one roll is 1/6 . Roll it 6 times to get a probability of 1.

True or false?

r9m

When I go back home from the uni in the summer/winter vacations .. it's a 28 hr journey by train .. no internet :P most of the time I stare out of the window but after sunset I simply stare at my co-passengers until they freak out! :P

walkar

@DonLarynx False.

r9m

@DanielFischer are the mod duties are affecting the tropical rainforest ?!! :O

nywy .. Time to watch 'we'll never have paris' .. :D bbl

Don Larynx

4:15 AM

@walkar false. How come?

r9m

@robjohn many thanks for the answer at the integral ineq problem :-)

Julian Rachman

Hello!

walkar

4:34 AM

@DonLarynx Presuming each roll is independent, the probability that the number will not be rolled is 5/6, each roll has independent probability so to find the probability of the number not occurring after repeated rolls we multiply the chances together. (5/6)(5/6)...(5/6) six times gives us 15625/46656 chance of not rolling it after six tries. The probability we will see it at least once in six rolls is then 1-15625/46656 = 31031/46656.

@DonLarynx That, of course, assumes the dice is fair.

Don Larynx

5:20 AM

Thanks @walkar

mathguy

5:43 AM

Could someone recommend a book to practice probabilities based interview questions? It doesn't necessarily have to be geared toward interview questions, but I want to know about how to calculate things like expected values and related topics (I don't honestly know what related topics there are in probability). I have a basic knowledge but would like to become comfortable with the topic.

walkar

@DonLarynx No problem! Next time ask it as a question instead of on chat so I can get some rep from it, eh? Hahaha!

mathguy

To clarify on my original post, when I say 'practice probabilities based...' I meant to say 'learn probabilties based...'

Kevin Driscoll

5:58 AM

@mathguy Im not sure anyone here would know. Those kind of questions usually get asked in wallst or consulting type job interviews.

mathguy

@KevinDriscoll Well it was worth a try =/....but yea that is what i was going for

Kevin Driscoll

@mathguy Ya sorry. Most of the people who hang out in chat are academics. I dont know everyones background though so there may be someone.

Transcript for

$Mathematics$ Mathematics