Mathematics - 2012-07-03 (page 2 of 6)

Peter Tamaroff

03:00

@BenjaLim Sup, playa?

BenjaLim

@PeterTamaroff How come you asked about comm. algebra?

@AlexBecker Hey :D

I'm starting to miss commutative algebra

I think if I have the time

I will look at primary decomposition and dimension theory

Alex Becker

@BenjaLim Hey Ben :D

BenjaLim

@AlexBecker You're younger than me no?

Peter Tamaroff

@BenjaLim Dunno, I was curious.

BenjaLim

@PeterTamaroff I suggest if you want to venture to commutative algebra

it will be at least another 6 months ~ 1 year before you can do it

because

Alex Becker

03:01

@PeterTamaroff The formatting looks kind of off to me. How did you format it?

@BenjaLim Probably. I'm 18, and you just finished your second year, right?

Peter Tamaroff

@AlexBecker I just read a TeX 101, so don't expect much.

BenjaLim

@AlexBecker You're a year younger than I am

Peter Tamaroff

@AlexBecker I turn 19 on Saturday!

@BenjaLim You already finished second year?

BenjaLim

@PeterTamaroff No going to second semester

@AlexBecker What do you think of Matsumura's two books?

@AlexBecker I am doing algebraic topology next semester

Peter Tamaroff

@BenjaLim Oh, OK. As I told you I have put together the proof of the logarithm

BenjaLim

03:03

My copy of Hatcher arrived yesterdayand it looks really dense

Alex Becker

@BenjaLim Is your school year inverted from ours?

BenjaLim

@AlexBecker Kinda northern and southern hemispheres are the other way round

We are winter now and it's freezing

user19161

@peter I sent you an email.

BenjaLim

@PeterTamaroff In your paper you have taken $\log x = \int_1^x \frac{1}{t} dt $ yes?

Alex Becker

@BenjaLim Haven't read them. Only Alg. Top. book I've read was "Topology" by Hocking and Young, which was dense but worthwhile. I have a friend working through Hatcher ATM, he also says it is quite dense.

BenjaLim

03:04

@AlexBecker Bloody dense man

Peter Tamaroff

@BenjaLim I did.

BenjaLim

I mean he does a calculation of $\pi_1(S^1) \cong \Bbb{Z}$

and he has some group homomorphism

he handwaves a bit in checking it's a group homomorphism

have to write out all the details

user19161

@AlexBecker Hocking and Young is a classic but usually people use other books these days.

Peter Tamaroff

@BenjaLim Why do you ask?

BenjaLim

@AlexBecker Do you recommend doing chap 8 of Munkres and then going on to his elements of algebraic topology?

@PeterTamaroff I needed to know what the definition of log was that you were taking

Peter Tamaroff

03:06

@BenjaLim Oh, well, I can also take $\log x = \lim\limits_{k \to 0} \dfrac{x^{k}-1}{k}$

BenjaLim

@AlexBecker Our lecturer for algebraic topology did his phd at U Chicago: maths.anu.edu.au/~angeltveit

oh no

Peter Tamaroff

@BenjaLim I would call it a paper, also. =)

BenjaLim

he did his phd at MIT

Alex Becker

@BenjaLim Like I said, I haven't read any other books on algebraic topology. The only two top books I've read are "Topology" by H&Y and "Introduction to Topology" by Mendelson, and only the first dealt with Alg. Geo.

BenjaLim

I'm mistaken

I'm looking at that book now

user19161

03:08

Bredon's Topology and Geometry cover point set, differential and algebraic topology. It is very dense.

BenjaLim

@AlexBecker The only reason I bought Hatcher was that that was the course text

user19161

@BenjaLim Also available online for free.

BenjaLim

@JasperLoy I knew that like a year ago

I only bought it because my eyes are going

Peter Tamaroff

@AlexBecker At what age did you start undergrad studies?

Alex Becker

@PeterTamaroff Depends on what you mean. I started taking Calc at university at 15, took lin alg, vect calc and comm alg at 16, real analysis and computability theory at 17, just turned 18.

BenjaLim

03:10

@AlexBecker We have jarod alper, scott morrison and david smyth coming next year

well jarod alper is already here

Alex Becker

@BenjaLim Are they Uchicago grads?

BenjaLim

@PeterTamaroff My lecturer Jim Borger said to me: It's not a race, by the time you're in your early twenties you will know all these topics

@AlexBecker Jarod alper and david smyth are algebraic geometers, alper supervised by ravi vakil

scott morrison is a moderator on MO

@AlexBecker I think vigleik was a U Chicago undergrad

@PeterTamaroff In the words of Jim Borger: "No rush to learn étale cohomology"

user19161

@BenjaLim Yeah, many mathematicians are very productive when young and decline as they age. Exceptions are Erdos.

Peter Tamaroff

@AlexBecker Wow, that's cool. In here I finished High School at 18, which is the usual time span. I started my pre-univ courses this year which are (basic) Calc and Linear algebra, and mandatory Physics and Chemistry courses and hope to start my first year of studies next year.

BenjaLim

@JasperLoy You forgot Euler

@PeterTamaroff Seriously there is no rush.

This is not a race to see who can talk about moduli spaces and natural transformations first.

Alex Becker

03:13

@JasperLoy There are plenty of examples. Hilbert, Nuemann, Noether, etc.

user19161

So @peter you got my email?

Alex Becker

Hell, don't forget Wiles.

BenjaLim

@AlexBecker I am starting to miss commutative algebra

Abstract as hell

Peter Tamaroff

@JasperLoy Yeah. I hope the best for you. =)

BenjaLim

but was bloody deep

Peter Tamaroff

03:14

@BenjaLim I know! But I crave knowledge.

BenjaLim

@PeterTamaroff The time will come when you can take a flat resolution.

Peter Tamaroff

@BenjaLim What do you mean? Flat resolution?

BenjaLim

planetmath.org/FlatResolution.html

user19161

@BenjaLim I have taken a flat ... pancake.

Peter Tamaroff

I have a problem here.

BenjaLim

03:16

@AlexBecker Hmm if hatcher is the course text

Should I learn from it now or use some other text?

user19161

@BenjaLim It's best not to see it as a race. Sometimes we get so caught up in races we forget the joy of doing mathematics.

BenjaLim

He emphasises a lot on CW complexes from the beginning

@JasperLoy That is exactly what I said. It is not a race to see who can calculate $\pi_1(S^1)$ first.

user19161

@BenjaLim If it is the course text I suggest you use it since it is the standard these days.

BenjaLim

I am finding it denser than AM

Peter Tamaroff

When we say "Arrange each $E_{\alpha}$, with $\alpha \in A$ in a sequence..." ($E_{i}$ is an indexed familiy of subsets of a set $S$) we're implicitly assuming $\{ E_n \}$ is countable, right?

BenjaLim

03:19

Where did you read this?

Peter Tamaroff

@BenjaLim Rudin.

Precisely, 2.12

BenjaLim

crap I don't have my copy now

state the theorem

it's the chapter on topology

user19161

@PeterTamaroff Let me see.

Alex Becker

@PeterTamaroff Probably, seeing as it's in Rudin.

BenjaLim

what is it again

Peter Tamaroff

03:20

Let $\{E_a \}$ be an indexed familiy of subsets of a set $S$. If each $E$ is countable, their union is.

BenjaLim

Rudin's definition of countable is retarded

By countable he means denumerable

Peter Tamaroff

@BenjaLim What is yours?

BenjaLim

which is not the usual definition of countable that people take

user19161

@PeterTamaroff page?

Peter Tamaroff

29

@BenjaLim What is yours?

BenjaLim

03:21

@PeterTamaroff We say that a set $S$ is countable

if there exists an injective function $f : S \rightarrow \Bbb{Z}$

In this definition

finite sets are countable

whereas in Rudin he calls these things "at most countable"

user19161

@peter He is taking a countable union of countable sets there.

Peter Tamaroff

@BenjaLim I think it is irrelevant to consider a finiet set to be countable or at most countable.

BenjaLim

@PeterTamaroff For set theory

Peter Tamaroff

@JasperLoy Yes, I know.

BenjaLim

I suggest you look at Munkres chapter 1

Peter Tamaroff

03:23

My main concern is

BenjaLim

I learned set theory from there

very very good

user19161

@BenjaLim Munkres is for topology, Rudin is for analysis and neither is for set theory. QED.

BenjaLim

@JasperLoy Ask asaf about rudin's definition of countable

Peter Tamaroff

he says "let every set $E_n$ be arranged in a sequence"

BenjaLim

@PeterTamaroff yes

Peter Tamaroff

03:24

By that he's assuming implicitly that $\{E_n\}$ is bijectable with $\Bbb N$

Thus countable.

BenjaLim

you can think of "countable" as "can enumerate as a sequence indexed by $\Bbb{N}$

user19161

Rudin is not doing formal set theory there. To do that you have to do mathematical logic first.

BenjaLim

@PeterTamaroff Are you talking about each $E_n$ or the whole collection?

Peter Tamaroff

@BenjaLim That's what I'm saying.

user19161

So Rudin really is just doing some naive set theory.

Alex Becker

03:25

@PeterTamaroff Well he clearly means countable, because otherwise the theorem fails.

BenjaLim

@PeterTamaroff Check out Russell's paradox

that's cool

Peter Tamaroff

@AlexBecker Wait. No no.

Let me rephrase what he writes.

user19161

@ben You looked like someone I knew.

Peter Tamaroff

I think it is easy that way. Just left click and view it.

@BenjaLim I know that one!

BenjaLim

@PeterTamaroff What's wrong with the proof in rudin?

Peter Tamaroff

03:28

@BenjaLim I was misreading his construction, nmv!

BenjaLim

@PeterTamaroff The diagonal process is one super powerful thing to do in Maths, you even use it to prove Arzelà - Ascoli for $C[0,1]$!!!!

Peter Tamaroff

@BenjaLim I knooooooooooooooooooooooooow!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! (it is powerful, no Arzela Ascoli which I dunno what it is)

BenjaLim

that is powerful too

Eugene

@leo are you in fact messi?

Peter Tamaroff

@BenjaLim Though I'm interested in the fact important math results succumbs to a geometrical array of symbols. That is unsettling.

BenjaLim

03:30

no it is completely rigorous

the "diagonal process" is your injective function to $\Bbb{N}$

Peter Tamaroff

@BenjaLim "No, it is completely rigorous".

BenjaLim

?

Peter Tamaroff

Use commas, they can save your life.

user19161

@PeterTamaroff Haha.

BenjaLim

@PeterTamaroff In australia people are lazy when it comes to speech

Peter Tamaroff

03:31

@JasperLoy That's true.

BenjaLim

every thing is either left out or is shortened

leo

@Eugene indeed, right now I'm with 3 or 4 girls in mi presidential suite

user19161

@PeterTamaroff I know. Eats shoots and leaves.

Eugene

@leo that's ronaldo

leo

@Eugene no. Messi does :-) as well

user19161

03:32

@Eugene Hi Sir.

Eugene

@JasperLoy touches your feet

Peter Tamaroff

@JasperLoy HAHAHHAHAHAHAHA great panda story.

user19161

@PeterTamaroff The comma is very complicated. I actually dislike many of the comma answers on ELU.

Peter Tamaroff

@AlexBecker What is your critique on the formatting of the pdf? How can it be improved?

(I'd enjoy some feedback on the maths too =) )

user19161

@leo No wonder you cannot find the right epsilon and delta.

Alex Becker

03:34

@PeterTamaroff What program did you use to compose it? It doesn't look like TeX/LaTeX to me at all.

Fernando Martin

Hey guys, has any of you read Ferguson's book on Game Theory?

Peter Tamaroff

@AlexBecker I used TeXworks. Let me link you to a direct download. The online source is different.

user19161

Nope.

Fernando Martin

I'm stuck in a little theorem

user19161

@PeterTamaroff My favourite editor too!

Peter Tamaroff

03:36

@AlexBecker Isn't there a download link in the page I linked?

Alex Becker

@PeterTamaroff Yes there is. Ah that formats much better. Let me look over the math now :)

Peter Tamaroff

@AlexBecker =D

Mark Dominus

Bleh, I answered this thing about Farey sequences, and it turns out OP knows nothing at all about Farey sequences, and is asking me to prove every little thing about them from first principles, even stuff that is extremely simple, like $\frac ab < \frac{a+c}{b+d} < \frac cd$.

user19161

@MarkDominus Welcome to SE!

Alex Becker

@PeterTamaroff It looks good to me. A couple formatting things look weird, but no problems with the proof.

Peter Tamaroff

03:43

@AlexBecker Thanks. I have the original .tex. If you want you can improve the formatting. Since I know nothing about TeX I can't tell the difference now.

user19161

So @ben what do you think of my new avatar?

BenjaLim

I am not a fan of taylor lautner

user19161

@leo The standard for math.

Peter Tamaroff

@JasperLoy You should get Al Pacino in there, or Marlon Brando.

leo

chapter 9 is pretty useful

Peter Tamaroff

03:50

:5204086 That seems to be a quintessential TL;DR.

user19161

@leo useful

leo

@PeterTamaroff did you get it?

Peter Tamaroff

@leo Yes, thanks!

user19161

Hi @rob! You always look mean.

leo

@JasperLoy thanks!

user19161

03:50

@leo Also, get.

leo

@JasperLoy good

robjohn

@JasperLoy Who says I look mean? >8(

leo

what happen with the TeXrobjohn?

@MarkDominus Why not suggest some reference?

Eugene

how do new subjects in mathematics gain traction or get legitimized?

Mark Dominus

04:06

@leo Maybe I should have done that.

Peter Tamaroff

@Eugene If you're German, find a British guys that does it for you.

Mark Dominus

@Eugene One way is that someone solves some long-standing unsolved problem with the new tools.

Eugene

@PeterTamaroff that makes no sense

@MarkDominus yes but when does the line split between legitimate and crank math?

also tropical geometry came into being without all that

Mark Dominus

If a crank solves a long-standing unsolved problem, he is not a crank!

What is the difference between Grigori Perelman and a crank? Perelman's argument makes sense.

Eugene

@MarkDominus i guess the condition here is to the satisfaction of all mathematicians in the field

@MarkDominus yes but he didn't invent a new area of math like porton did.

Mark Dominus

04:08

Or at least there has to be a preponderance.

leo

@Eugene What is tropical geometry?

Peter Tamaroff

@Eugene Ask Einstein.

Eugene

@leo in a nutshell it's algebraic geometry reduced to convex polytopes.

Mark Dominus

I thought that Perelman invented a completely new technique.

Eugene

@PeterTamaroff i would but he's dead

@MarkDominus no. he used a method of hamilton's.

Mark Dominus

04:10

OK!

Then please substitute, say, Georg Cantor for Perelman.

Peter Tamaroff

@Eugene Really?

Eugene

@MarkDominus it was one of the reasons he gave when he snubbed the clay prize.

Peter Tamaroff

@MarkDominus =D

Eugene

@PeterTamaroff yes super dead.

Peter Tamaroff

@MarkDominus At least the mathematical community is not as vicious as it was in those days,

Poor ol' Cantor.

Eugene

04:11

@MarkDominus back then they weren't all that big on rigor though.

now people cry crank a lot faster

Mark Dominus

I think there's a big difference between an insufficiently rigorous argument and a crank argument.

Last year Ed Nelson claimed to have a proof that PA was inconsistent.

Alex Becker

@Eugene Not just mostly dead?

Eugene

@MarkDominus i agree. i just don't really know when that happens.

Mark Dominus

It was refuted, but it was clearly not a crank argument.

Eugene

@AlexBecker if only!

@MarkDominus i was thinking about curves over non-commutative rings.

Mark Dominus

04:13

Crank has a certain stink to it. Here is a nice example I ran into just today:

User talk:50.50.46.98

(talk) 09:59, 6 April 2012 (UTC)This is regarding the Wikipedia article on the Number 19. just recently a new textbook of non-linear mathematics has veen privately published with a Harvard Phd on its cover. It shows the prime role of 19 in mathematics, prime number and the Riemanns hypothesis. It is being currently reviewed Privately, but basically the following very basic mathematics, makes a mockery of your article on 19, besides the basic fact that 19 is the only number that makes this ligand equation with 360 ( 19-360/19=1/19). The book written by me and a partner is called "Torsade ...

Eugene

a lot of the theory hasn't been developed. so i was wondering what it would take for an accepted theory of curves over noncommutative rings to be developed.

Mark Dominus

Read the whole thing. It is very instructive.

There is a big difference between crank and merely wrong.

Eugene

@MarkDominus this reeks of crankery

i especially like the biblical quote in the MIDDLE of a "scholarly" article...

Mark Dominus

Yes, that is quite typical for crank articles.

Peter Tamaroff

@MarkDominus LOL, that can't be serious.

I'm turning 19 in three days, what will I do?

Mark Dominus

04:18

I think it is completely serious.

Peter Tamaroff

@MarkDominus I don't even know what point is trying to be made.

Eugene

@PeterTamaroff interesting observation here... when your first number in consideration ascends by two and the second descends by one, the sum increases by one. this is groundbreaking!!

Mark Dominus

I think the author is trying to claim that he has discovered a new and extremely important property of the number 19 previously unknown to mathematicians.

Peter Tamaroff

@MarkDominus That is sad.

Eugene

@PeterTamaroff you're just jealous you didn't think of it first!

@PeterTamaroff shame on you!!!

Peter Tamaroff

04:23

@Eugene hahaha =)

I'm happy with my infinite series proofs for the moment, which I came up with even before starting the uni

On december of last year, if I'm not wrong.

Yep, Dec 23.

BenjaLim

04:43

@PeterTamaroff

I encourage you to read this book:

amazon.com/The-Places-That-Scare-You/dp/1570624097

Peter Tamaroff

@BenjaLim I think personal realization is personal. (And I haven't finished any book I started reading - non-mathematical - in the last years).

BenjaLim

I just encouraged you to read this. I am not preaching the word of god or anything (I don't really believe in god anyway)

Peter Tamaroff

@BenjaLim Hey, I know. I just telling you my opinion on the matter.

BenjaLim

@PeterTamaroff What non- mathematical activities do you like to do?

I like camping a lot

Peter Tamaroff

@BenjaLim ...but in general I choose to ignore any preaching whatsoever =P

@BenjaLim I'm a tennis teacher =)

BenjaLim

04:48

@PeterTamaroff when people advise you on matters

is that preaching?

Many times people have said harsh words to me

my own supervisor, etc

@PeterTamaroff I hit my backhand with one hand

I think my forehand is retarded because the ball is always looping

the backhand has no such problem

Peter Tamaroff

@BenjaLim Not on day to day matters let's say, but on "spiritual" stuff.

BenjaLim

@PeterTamaroff A wise person listens with an open heart :D

Frank Science

@PeterTamaroff Now 2 a.m?

Peter Tamaroff

@BenjaLim Right on.

BenjaLim

@PeterTamaroff Some of the things that we discuss here can be classified as "spiritual"

Peter Tamaroff

04:49

@FrankScience 10 to 2 am

@BenjaLim Such as?

BenjaLim

advice about mathematical life

personal philosophies about maths,

Frank Science

@PeterTamaroff Well. It's not healthy to stay up.

BenjaLim

how to do maths, etc

Peter Tamaroff

@FrankScience It depends on how much you slept.

Doesn't it?

Frank Science

Not only.

I realized that you always stayed up.

Peter Tamaroff

04:52

@FrankScience "You always stay up".

@FrankScience Most of the times I do. That's because I'm on vacations.

And I'm studying. I need some extra time.

@BenjaLim Hm. Maybe.

But that doesn't affect how I interact with other people.

Frank Science

@PeterTamaroff How much do you sleep?

BenjaLim

@PeterTamaroff I never said it did :D

Peter Tamaroff

@FrankScience I slept roughly 6-7 hours from yesterday to today.

Frank Science

@PeterTamaroff So you can change to: 23:00~5:00

Peter Tamaroff

I went to bed at (past) 4 am and woke up at 10:30-11:00

Frank Science

04:54

That's only my suggestions.

Peter Tamaroff

@FrankScience And why is that better? The serenity of night is what I like.

BenjaLim

I was a big idiot before in this question :math.stackexchange.com/questions/164418/…

@PeterTamaroff I used to do that for 3 years

but in uni

in the day time I have to meet supervisors and stuff

can't afford to do that anymore

Frank Science

@PeterTamaroff I don't want to explain more, because of short of english.

Peter Tamaroff

@FrankScience Your english is OK. I understand you. What other language do you speak?

@BenjaLim What did you do?

BenjaLim

I tried to prove uniform equicontinuity

which did not address the problem

Peter Tamaroff

04:57

@BenjaLim LOL I have to get checked, I might have dislexia. I wrote "metirc" instead of "metric"

Frank Science

@PeterTamaroff Eh... I said what I can say, so something I was not able to say couldn't be displayed here.

BenjaLim

@PeterTamaroff Fyi it is dyslexia :D

@DylanMoreland I was a big idiot before, the uniform convergence is so easy: math.stackexchange.com/questions/164418/…

Peter Tamaroff

@BenjaLim It might also be that I was distracted by a book on spirituality =D

BenjaLim

which book?

Peter Tamaroff

@BenjaLim As Eugene says: "It's supposed to be facetious"

BenjaLim

04:59

what?

And how is it supposed to be facetious?

Transcript for

$Mathematics$ Mathematics