Mathematics - 2014-02-08 (page 1 of 4)

skullpatrol

00:00

@balarka welcome to the real world

robjohn

@BalarkaSen: are you letting Ted get to you? Don't let people get in the way of math.

@JasperLoy Indeed

@JasperLoy and I missed the whole thing.

Jasper Loy

Well, I don't know the exact context, but never mind, it's over and it's a small thing.

skullpatrol

Not to me :(

robjohn

@BalarkaSen concentrate on the friendly people.

Balarka Sen

Not to me either :(

skullpatrol

00:02

I tried to stop it. But was too late

Balarka Sen

@robjohn I don't see whom are and whom are not. Nevermind, I need to get some sleep now.

Jasper Loy

Anyway @skull I was quite upset when you said "maybe you don't want it to happen", but never mind.

robjohn

@BalarkaSen sleep well and wake happier.

Balarka Sen

Sure. But I'll stay in the forums from now on.

skullpatrol

@jasper I'm sorry.

Jasper Loy

00:04

@robjohn I spent a ton of money on hardback versions of my nine holy books, but I am happy that I got them.

robjohn

@BalarkaSen do what you feel you have to.

Balarka Sen

At least they are all friendly

robjohn

@JasperLoy cool

Jasper Loy

@skullpatrol It's alright now, pal.

Balarka Sen

and stay in math

robjohn

00:04

@BalarkaSen as long as you think so.

Jasper Loy

@robjohn Do you know what happens if the amazon delivery guy comes to my home and nobody is in?

robjohn

@BalarkaSen I would not let one bad day affect me so much, but that is me.

skullpatrol

@balarka I am going to join you in staying away

robjohn

@JasperLoy It depends on the situation. If you can tell them not to require a signature and your front door looks secure, they should leave it.

Jasper Loy

@robjohn Well, what if I don't tell them anything? I hope they don't put the precious books outside, because someone is gonna take them away!

robjohn

00:09

@JasperLoy Ah, if where they would leave them does not look secure, they may hold them. It depends on who actually delivers them (FedEx, DHL, UPS, etc)

Jasper Loy

@robjohn My friend told me that they would leave it at a post office and drop a note for me to collect it, but I don't trust this friend's words usually.

skullpatrol

I'm sorry @jasper for saying such a mean thing pal.

Jasper Loy

@skullpatrol It's OK. =)

skullpatrol

It's not OK

robjohn

@JasperLoy I have no idea what your postal service is like

Jasper Loy

00:13

@robjohn OK, I guess I will try to be around that day and I will ask the man what he would do if there was nobody.

robjohn

@JasperLoy sounds like a good plan

@JasperLoy Did they give you a tracking number?

Jasper Loy

@robjohn Well, there is an order number, and there is a place I can click which says "track packages".

robjohn

@JasperLoy that will probably send you to the carrier's website and enter the tracking number

Ethan

@robjohn did you get a B.S. in Mathematics from ucla?

Jasper Loy

@robjohn OK, this is the first time I ever ordered anything online, using my mum's credit card since I don't have one.

robjohn

00:17

@Ethan yes

Ethan

it says under major CAS for me at ucla

oh

Jasper Loy

@Ethan If I were you living near UCLA I would definitely go there for both undergrad and grad, it's a great choice.

robjohn

@Ethan is that for math, or something else?

Ethan

math

user4140

loool you can get banned for saying strong words
?

Jasper Loy

00:18

@user4140 It has always been the case.

user4140

Guess I'm lucky I'm a gentleman

Jasper Loy

But if I say fuck me, probably nobody would flag it.

robjohn

@Ethan It could be for the school: "Communication Arts and Sciences"

Ethan

gota finish that

user4140

mabye somebody will flag you.

robjohn

00:19

@user4140 if enough people flag you. So it depends on who listening in the room

Ethan

I didn't even finish their testing by the required deadline, so I'm still sort of confused

user4140

I would have like to go to UCLA, unfortunately I'm too ugly to go there.

Jasper Loy

@user4140 What has it got to do with looks?

user4140

They have a strict policy.

no people below 8.5 iin the hotness scale.

I'm 8.4

remember to add a photograph looking sharp

robjohn

@user4140 I can tell you for sure that that is not the case.

Ethan

00:22

thats exactly what my picture is right now

haha

user4140

seriously?

Ethan

lol no they pool together all the pretty looking applicants and deny everyone else

user4140

tell me one single person below 8.5 that got in.

hotness can come from the voice too.

Jasper Loy

@user4140 Don't confuse @Ethan lol.

robjohn

@user4140 so you're saying they graduate supermodels and phonesex operators?

Ethan

00:24

lol

Jasper Loy

@ethan Too many removeds.

user4140

no, they already are that when they go in.

Theta30

@robjohn he is saying they graduate hot and smart students

Jasper Loy

@ethan I think UCLA will be one of my choices if I apply.

Theta30

@JasperLoy great

user4140

00:25

sure, just make sure you get a nice haircut before the application.

Ethan

@JasperLoy good lol if i end up going there, also did UChicago and some other LAS's

user4140

and practice that deep voice.

It needs to come from the lower abdominal wall.

Jasper Loy

My voice is very deep.

I like singing Italian opera.

user4140

just make sure you don't do soprano stuff

Ethan

@JasperLoy

got like 7 hours'

user4140

00:27

They usually go for the tenor, for their male grad students

Jasper Loy

@Ethan OK, go for it.

user4140

but cases of baritones and countertenors have been recorded

Jasper Loy

@user4140 Are you on drugs, lol.

Pedro Tamaroff

Hello?

Ethan

@JasperLoy I have to list adults who I look up to or who can speak on my behalf

4 of em*

user4140

00:29

For example Terence Tao came in with a voice barely lower than jazz. But they attribute this to his sharp looks.

Alizter

@PedroTamaroff Hi

user4140

Just make sure if they speak on your behalf they speek using a low, confident voice

Jasper Loy

@Ethan You may start with your family members and your teachers.

user4140

who is duke?

Ethan

@JasperLoy can't do family members already did the 1 teacher who knows me, and I did dan brum and eric naslund

user4140

00:30

en.wikipedia.org/wiki/Bill_Duke?

Jasper Loy

@Ethan Geezis, Dan and Eric? You should use people you know in real life.

user4140

this guy?

Ethan

@JasperLoy I have had google+ hangouts with em if that counts

user4140

nvm.math.ucla.edu/~wdduke

Ethan

@user4140 bam there u go

Jasper Loy

00:31

@Ethan OK, so 1 more person to go, lol.

user4140

you know barry white?

nvm he's dead

Ethan

because they listed 7

user4140

uhm bb king will do

Jasper Loy

math.stackexchange.com/users/122283/sanath-devalapurkar Geezis, this guy is only 13.

Ethan

@user4140 lol a recuriter at my school handed out a pamflift there was a picture of him writing some crap about seive theory on a whiteboard on it

Pedro Tamaroff

00:34

@JasperLoy He knows nothing about math, though. =P

Jasper Loy

@PedroTamaroff I wonder why he calls himself a theoretical physicist. Has he got a PhD?

Pedro Tamaroff

@skullpatrol

@JasperLoy Hardly believable.

Jasper Loy

@ethan You only have a few hours left, hurry!!!

Pedro Tamaroff

@JasperLoy Look at this awful answer.

STAHP ETHAN.

Ethan

@JasperLoy alright wait can I list you?

user4140

00:36

I used to think I was too old for mat, but really who cares it's a marathon not a short race, the way I see it if you live a healthy life you might even have more years to do math.

Pedro Tamaroff

@user4140 ;)

Ethan

@user4140 lol don't think like that

user4140

why not

?

Ethan

because it really doesn't mean anything

Jasper Loy

@PedroTamaroff Looks awful.

user4140

00:37

what doesn't?

Jasper Loy

@Ethan Well, you may, but I am only a banana.

Ethan

well I mean you can't really compare yourself to others

user4140

what do you mean?

Ethan

nvm

i don't know anything

user4140

well sure, every person is unique and whatnot, but you should still agree that Terrence Tao is better and math than you, atleast today.

what do you think about this assertion?

Ethan

00:39

there really is so much stuff out there

Jasper Loy

Who cares about Terry Tao? Care about yourself first!

user4140

yes, of course I agree looking at things like that is wrong.

Ethan

besides there are plenty of burn outs

user4140

But there is still a part of me I cannot shut down that desires skill.

Ethan

nvm dnt listen to me i dnt know anything

user4140

00:41

I know I should look at it like, I'm doing math, this is fun, I don't care if I'm learning to add.

Ethan

@JasperLoy can I talk with you in a seperate chat

Jasper Loy

@Ethan I suggest we use email...

user4140

anyways, can someone help me with a problem I have?

let G be an abelian group of order n with k|n. Prove G has a subgroup of order k using complete induction...

I don't know fundamental theorem of finitely generated abelian groups.

Ethan

@JasperLoy emailed u

user4140

any help?

Pedro Tamaroff

00:45

@user4140 You need Cauchy's theorem, that's all.

The result is trivial for G=1 or G of prime order, so you may assume G is (nontrivial) of composite order.

user4140

ok

hmmmm

Pedro Tamaroff

And assume the result true for every group of order less than G.

Now, pick a prime factor of G and obtain a nontrivial element of order p.

user4140

sure

Jasper Loy

@Ethan OK, I replied, we'll continue talking there for a while.

Pedro Tamaroff

Say this element is x, then take the quotient by <x>.

You get an abelian group of order less than G, strictly.

Should I say more?

user4140

00:48

no, thanks

did you read dummit and foote?

Pedro Tamaroff

Yeah, I am reading that book and Hungerford.

Reading Hungerford right now.

user4140

makes sense

Pedro Tamaroff

What does?

user4140

that problem, you answered it like he proves cauchy for abelina groups

Pedro Tamaroff

Oh, well you can extend Cauchy for any group using the class equation.

user4140

00:52

yes

but that's how he does it for abelian

he proves both

Pedro Tamaroff

In fact you can prove Sylow's first theorem in in full using the class equation.

Which is the generalization of Cauchy's theorem.

And the proof is exactly the same.

@user4140 Here.

user4140

That is really sweet.

Pedro Tamaroff

Yeah, I agree.

user4140

Cya guys, gotta work out, does triceps need hardening.

Pedro Tamaroff

those?

"does" sounds for like "das"; i.e. the German "das Auto"; say.

@anon

@Alizter Hello.

Ethan

01:03

@PedroTamaroff

you there?

Pedro Tamaroff

Yes.

This is dog.

If you think I've taught you things, and if it involves nothing that binds me legally to another thing, go ahead.

Ethan

no nothing like that

Pedro Tamaroff

Just don't put this chat as a reference! =)

Ethan

no reference all gone haha

which uni do you go to?

I already did jasper, naslund and brum

i trust you guys more then any of my math teachers lol tho i already used them

Pedro Tamaroff

I attend the University of Buenos Aires.

(UBA)

Ethan

01:09

was it hard to go there? it says "It is currently the best ranked Argentine university in college and university rankings" on wikipedia

don't students over there do like some huge test

to decide which uni's they go to

Pedro Tamaroff

Well, not a test, but you need to pass the CBC, which is kind of a filter.

Anyone can attend, foreigners included. But you need to work, surely.

Ethan

holy crap 300,000 undergrads

what do you graduate with like a bachelors degree?

Pedro Tamaroff

No, the careers lasts 6 years, so a bit more than that.

Ethan

oh wow

how long have you been there?

Pedro Tamaroff

You can start a PhD after you finish.

No MSc needed.

Ethan

01:14

but the PhD would have to be there?

Pedro Tamaroff

Nope.

(I don't think so, at least.)

Ethan

whats it called?

Pedro Tamaroff

Maybe you can ask Mariano when he comes by.

@Ethan What is what called?

Ethan

the degree you earn for 6 years

Pedro Tamaroff

I'd say it's equivalent to a Bachelor's + Masters, maybe?

Ethan

01:16

youve been there for more then 4 years?

Pedro Tamaroff

Licentiate

@Ethan Two years.

Ethan

oh

Pedro Tamaroff

"In Argentina, the Licentiate degree (Spanish: Licenciatura), by which one becomes a licenciada (female) or a licenciado (male), is a four- to six-year degree.[4] This may become six years in some cases, under the accomplishment of the "licentia doctorandi" thesis dissertation, generally equivalent to an M.Sc. or M.A. in North American universities, or Master in any country of Europe given by the Bologna Process.

I have a dissertation, hence 6 years.

So there you go.

Jasper Loy

02:08

topuniversities.com/university-rankings/…

I still can't believe that where I studied is ranked 9 in the world for math last year. ^

Pedro Tamaroff

@JasperLoy Well, kudos for that man.

Jasper Loy

@PedroTamaroff I now prefer hardbacks to softbacks like you, though they are very expensive.

Ram

Hi All, how to prove that torsion sub group of H_{n-1}(X) is cyclic of order 2, where X is n dimensional pseudomanifold? Massey leaves it to the reader, but I couldn't

Pedro Tamaroff

@JasperLoy I sometimes buy softbacks, and if I like the book, make it hardback =)

@Ram No idea! =)

Jasper Loy

@PedroTamaroff How do you make it hardback?

agent154

02:16

What's up. Can somebody refresh my memory on the actual definition of the Euclidean Algorithm? That is, if $a>b$, $gcd(a,b)=gcd(b,?)$

what is the ? supposed to be?

Pedro Tamaroff

@JasperLoy There are people that do that.

Jasper Loy

@agent154 Do a google.

Ram

@PedroTamaroff, :(

Pedro Tamaroff

@agent154 $\gcd(a,b)=\gcd(a,b-ka)$ for any $k$.

agent154

@JasperLoy I tried and couldn't find what I was looking for

Pedro Tamaroff

02:17

Thus, $\gcd(a,b)=\gcd(a,b\mod a)$.

Jasper Loy

Euclidean algorithm

. EXAMPLES CAN BE FOUND BELOW, E.G., IN THE "Matrix method" SECTION. --> In mathematics, the Euclidean algorithm, or Euclid's algorithm, is a method for computing the greatest common divisor (GCD) of two (usually positive) integers, also known as the greatest common factor (GCF) or highest common factor (HCF). It is named after the Greek mathematician Euclid, who described it in Books VII and X of his Elements. The GCD of two positive integers is the largest integer that divides both of them without leaving a remainder (the GCD of two integers in general is defined in a more subtle...

agent154

@JasperLoy I did see that, but I wasn't in the mood to read that wall of text to find what pedro told me. I know how to apply the algorithm on paper, but I am trying to code it into c# for a Project Euler question and didn't know what to put. But thanks anyhow

Pedro Tamaroff

02:37

@robjohn

robjohn

@PedroTamaroff yes?

Pedro Tamaroff

I have a cool problem to solve.

And maybe you can help.

robjohn

@PedroTamaroff okay

Pedro Tamaroff

Consider $[-n,n]^3$.

I want to count lattice points $(x,y,z)$ such that $|x+y+z|\leqslant s$, where $s$ is another positive integer.

Well, not count.

robjohn

@PedroTamaroff you mean $x,y,z\in\mathbb{Z}$?

Pedro Tamaroff

02:40

Rather prove there are $$\frac{1}{2\pi}\int_{-\pi}^\pi D_n(t)^3D_s(t)dt$$ points where $D_k$ is the Dirichlet kernel $$\sum_{|j|\leqslant k}e^{ikt}$$

@robjohn Aha.

robjohn

Okay. I would consider looking at the Fourier Transform the integral

Pedro Tamaroff

What is the other "side"?

agent154

What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

Is this asking for the least common multiple? Just want to make sure I understand the question.

Pedro Tamaroff

You want a number such that $1,2,\ldots,20$ divide it, or additionally that the quotient is even?

agent154

It just must divide without remainder

Pedro Tamaroff

02:47

Ah, then (of course) you're looking at the LCM.

=)

agent154

I thought that $\frac{1\cdot 2\cdot 3\cdots 20}{gcd(1,2,3,\dots,20)}$ would be what I'm looking for, but that doesn't seem to work as $gcd(1,2,3,\dots,20)=1$

I suppose if I remove the primes from consideration in the GCD function, that would work

Mike

hello folks

robjohn

@PedroTamaroff I have to go get dinner for people. I will have more time for this later. You know that the Fourier Transform of the Dirichlet Kernel is points on a line, right?

BBL

Pedro Tamaroff

@Mike HAI

MAIK

@agent154 Nope.

Mike

I just took a nap but now I'm just as tired as when I started.

Pedro Tamaroff

02:59

@Mike Heh, that happens.

agent154

@PedroTamaroff what am I missing then?

I'd like to do this without resorting to doing prime factorization of the number

Mike

the power of love, no doubt

agent154

Unless my algorithm for the GCD is wrong, I seem to be getting 1 no matter what...

Mike

@agent154 $\text{lcm}(a,b) = \frac{ab}{\gcd (a,b)}$

but the issue is that this fails spectacularly if you try to generalize to more than two numbers.

Pedro Tamaroff

@agent154 $1\cdot 2\dot 3$, $4$ has already two but once, so $1\cdot 4\cdot 3$, six is already there so stop, $1\cdot 4\cdot 3\cdot 7$, eight has two but thrice, so $1\cdot 8\cdot 3\cdot 7$, &c.

agent154

03:02

But what about $lcm(a,b,c,...,n)$? Can that same formula be used? It's not working for me

Pedro Tamaroff

=D

Also, $\gcd(a,b,c)=\gcd(a,\gcd(b,c))$

@Mike Dude.

I like $\bf Cats$.

agent154

@PedroTamaroff Yeah, i've got the right GCD algorithm. I'm using a recursive algorithm to solve the GCD of 1 thru 20.

Mike

I like the animal, categories are pretty chill too.

agent154

but I suppose I didn't know that the LCM of more than 2 numbers can't be done this way

Pedro Tamaroff

@agent154 You want the LCM, not the GCD.

agent154

03:03

But I had assumed that I needed the GCD to get the LCM.

Pedro Tamaroff

@Mike I think I am getting the hang out of it.

I like using diagrams instead of words.

Mike

@Pedro Here's another reason Fld is terrible: there's no free elements.

Pedro Tamaroff

$\Bbb Q$ ain't free in $\bf Grp$.

Mike

Course not.

Pedro Tamaroff

${\rm hom}(\Bbb Q,S_3)=1$.

Mike

03:05

The free AbGrp objects are pretty easy to classify (especially if you have the structure theorem); the free Grp objects are easy to classify once you figure out what they are :p

agent154

@PedroTamaroff is $lcm(a,b,c)=lcm(a,lcm(b,c))$?

Pedro Tamaroff

@agent154 What do you think?

agent154

I'm tempted to say yes, since this applies to GCD as well, and GCD and LCM seem to be closely related. I don't know of a proof though

Pedro Tamaroff

@agent154 They are dual concepts, but be careful.

You either find a counterexample or prove it.

Pedro Tamaroff

03:21

@Mike

Mike

@Pedro

Pedro Tamaroff

Wait.

Mike

@Pedro Lord no, but I think you just realized that.

Pedro Tamaroff

What is a different way of saying there is one and only one morphism $I\to C$ with $I,C$ objects in a category, i.e. saying $I$ is initial?

A was looking for a statement in terms of ${\rm hom}(I,C)$.

Mike

@Pedro Is this for a specific problem? Or just an idea?

I would just say "I is initial".

Pedro Tamaroff

03:25

Well, I was thinking silly maybe, but say when $R,R'$ are rings, ${\rm hom}(R,R')$ is iso to stuff. =P

Mike

Well, we have a lot more structure in the category of rings than we do in an arbitrary category.

Pedro Tamaroff

OK.

Mike

In general, we can't do stuff like add morphisms. All we can do is compose them.

Pedro Tamaroff

Sure.

Mike

So $\hom(A,B)$ is usually just a set :P We get all our cool monoids when we talk $\hom(A,A)$.

Pedro Tamaroff

03:32

Yes, that I was sure.

=)

user4140

yeah those triceps

well now they aren't triceps

they are metal slabs

tungsten

in case you where wondering

user4140

03:53

google.com/…

Transcript for

$Mathematics$ Mathematics