Mathematics - 2012-06-29 (page 1 of 3)

@BenjaLim Oh, that book does the classification of surfaces which is a good thing. That is not found in Hatcher. But only Lee's Topological Manifolds treats that and the case for curves as well.

BenjaLim

not so wordy perhaps @DylanMoreland

really chapter 0 is so wordy!

user19161

12:31 AM

@DylanMoreland Though that book does not deal with the higher homotopy groups.

BenjaLim

and he talks about "gluing" this side to that

Dylan Moreland

Well, that's important stuff.

BenjaLim

perhaps a lot of readers are not familiar with quotiening out by an equivalence

that's what's meant

Dylan Moreland

Well, you should know about the quotient topology before starting algebraic topology.

BenjaLim

however I feel uncomfortable when I'm not told specifically what the equivalence is

Dylan Moreland

12:32 AM

Munkres certainly talks about this early on in his Topology.

BenjaLim

@DylanMoreland I do.

I just finished that bit at the end of chapter 2 yesterday

Dylan Moreland

There was some question about this on the main site.

Like, how rigorous to be with identifications and homotopies.

BenjaLim

yeah

I feel like people should state specifically what the equivalence is

Dylan Moreland

I don't know if any good conclusion was reached, in the end.

user19161

@ben Another book I like is Bredon's Topology and Geometry. It has point-set, differential and algebraic topology all in one.

BenjaLim

12:33 AM

Like when you say "you glue the boundary of a circle together"

you are actually saying let $X$ be the unit circle

Dylan Moreland

No, that's perfectly rigorous.

BenjaLim

and the gluing is $X/ \sim$

Dylan Moreland

If you wrote that out every time it would be a horrible read.

Peter Tamaroff

@robjohn What you prove is termwise convergence, right?

BenjaLim

where $(x,y ) \sim (v,w) \iff ( x^2 + y^2 = 1 \iff v^2 + w^2 = 1)$ @DylanMoreland

Dylan Moreland

12:34 AM

You have to make some allowances for human behavior.

robjohn

@PeterTamaroff Nope. I show that the sum of the absolute difference of the terms can be made as small as you like by choosing a big enough $n$.

BenjaLim

@DylanMoreland Maybe i'm just not pro but n00b and that's why I feel uncomfortable with the "handwaving" ?

user19161

There is a difference between using shorthand for well-defined operations and handwaving thus omitting a proof.

Dylan Moreland

For stuff like that I think you can write (and you have written) down the formal definition.

Have you gotten to the "house with two rooms" in Hatcher yet? That's more what I'm talking about.

BenjaLim

quotiening out by an equivalence :D :D

robjohn

12:35 AM

@JasperLoy forget handwaving... Proof by Intimidation!

BenjaLim

yeah

user19161

@BenjaLim That's typical of a pro by the way, to feel uncomfortable.

BenjaLim

I saw that

Dylan Moreland

Or, for example, showing that a hollow 3-D box and the 2-sphere are homotopy equivalent.

No one wants to write that down.

user19161

Noobies won't even feel uncomfortable vos they don't even know the proof is a little incomplete.

BenjaLim

12:36 AM

@DylanMoreland but for beginners

Dylan Moreland

Or that the $2$-disk with the boundary collapsed is the $2$-sphere.

BenjaLim

It's like to a pro asking to prove that $\Bbb{R}[x]$ is a ring, no one wants to write out the proof

but for a n00b it's good to see all the details

that's why I like KCd's notes

Dylan Moreland

I think the signal to beginners is, "you'd better get used to this", for better or worse.

robjohn

@BenjaLim All mathematicians are the same. There is one mathematician. I've gotten a Fields Medal by modding out by an equivalence!

BenjaLim

he writes out every single detail

Dylan Moreland

12:37 AM

Yes, he spells things out. Not for algebraic topology, though.

BenjaLim

@robjohn vaughan jones?

Dylan Moreland

KCd is a treasure.

Peter Tamaroff

@robjohn Ok, what is the important difference between that and this:

$$\left| {\frac{z}{{{2^n}}}\left( {\cot \frac{{z + k\pi }}{{{2^n}}} + \cot \frac{{z - k\pi }}{{{2^n}}}} \right) - \frac{{2{z^2}}}{{{z^2} - {k^2}{\pi ^2}}}} \right| < \frac{{\left| z \right|}}{{{2^{n - 1}}}} < \epsilon $$

BenjaLim

@DylanMoreland Yeah when I meet him I wanna give him a big hug kiss and thank you

Peter Tamaroff

???

user19161

12:38 AM

@BenjaLim KCd? Is his identity a secret?

robjohn

@DylanMoreland dunno him

BenjaLim

@JasperLoy EVERYBODY knows him as KCd

user19161

@BenjaLim Where is he?

Dylan Moreland

@BenjaLim Well, that's an example, I guess.

robjohn

@PeterTamaroff between that and what?

BenjaLim

12:38 AM

@JasperLoy math.uconn.edu/~kconrad

user19161

@BenjaLim Ah I see.

BenjaLim

@DylanMoreland Good that at least I know the formal meaning of gluing the boundary of the unit disk

Dylan Moreland

@BenjaLim I'm a little confused by your notation up there. Are you gluing two $2$-disks or balls or whatever?

Peter Tamaroff

@robjohn Oh, wait right.

BenjaLim

I'm gluing the boundary of the unit circle @DylanMoreland

robjohn

12:41 AM

@BenjaLim epoxy or wilhold?

Peter Tamaroff

So I am missing an error term

Dylan Moreland

Ah. Then you have it right, I think.

BenjaLim

@robjohn You will love bunnings warehouse: bunnings.com.au

Dylan Moreland

I guess everything in the interior of the disk should be identified with itself, but again, no one writes this down.

BenjaLim

@DylanMoreland Well in the quotient space, every point in the interior is in an equivalence class of itself

Dylan Moreland

12:42 AM

Yep :) I'm just saying that if we're going to be all about rigor then an equivalence relation on $D$ had better contain $((x, y), (x, y))$ for each $(x, y) \in D$.

BenjaLim

meaning to say...?

user19161

@ben You were asking about how to visualise the quotient topology that day? Well, just think of everything in the divisor as one point, that's it.

robjohn

@PeterTamaroff I find an $m$ so that the terms past that contribute very little to either sum

Dylan Moreland

@BenjaLim Ah, nevermind. Not worth worrying about. I think you know what you're doing.

BenjaLim

:D

Peter Tamaroff

12:44 AM

@robjohn Right. Well, I guess my answer is flawed then. I should delete that, I guess.

user19161

@PeterTamaroff You sound very professional now.

robjohn

$\displaystyle\sum_{k>m}|a_k-b_k|\le\sum_{k>m}|a_k|+\sum_{k>m}|b_k|$

BenjaLim

@DylanMoreland When I make a figure using playdough I'm trying to turn the unit disk into the 2-sphere.....

but can't visualise it

ahhh the spatial side of my brain is retarded

robjohn

@PeterTamaroff If you control the tails, your middle part should work

Peter Tamaroff

@robjohn Tell me, how can I control the tails?

user19161

12:46 AM

@robjohn Yeah in sequences only the end matters. Perhaps the same may be said of a man's life.

robjohn

@PeterTamaroff You see my $m$ is computed first to control the tails of each sum, the small $k$ terms, of which there are a finite number can be controlled in a normal way.

Peter Tamaroff

@JasperLoy "Flawed" doesn't sound as bad as "wrong".

Hhehee

robjohn

I think your estimate for $\left|\frac1x-\cot(x)\right|$ with the $1$ will work just as well as mine with the $|z|$

@JasperLoy Controlling the tail is everything in sequences and red light districts.

user19161

@robjohn LOL.

user19161

Some of the jokes are so deep I wonder who will understand.

Dylan Moreland

12:51 AM

Killing it with the jokes today.

Peter Tamaroff

Do any of you know a place I can translate some greek writing?

robjohn

@PeterTamaroff modern or classical?

user19161

@robjohn Wow, you seem to know a bit or two about Greek!

user19161

There are people who study Latin in the ELU room.

robjohn

@JasperLoy I studied Latin and know there is a difference between modern and classical Greek

user19161

12:57 AM

@robjohn Why did you study Latin btw?

robjohn

@JasperLoy Why not? It was a geeky thing to do in high school :-)

user19161

@robjohn Hmm. Was it a school subject?

robjohn

@JasperLoy yes. I took one year in junior high and four years in high school.

@JasperLoy I even took a class in college, but that was just a reading class.

user19161

@robjohn Wow. Well I guess not many countries offer Latin as a subject in school these days.

robjohn

@JasperLoy I really have no idea about that. There is a League of high schools (both state and national) that have conventions (or did when I was in high school)

NJCL - Natioinal Junior Classical League

BenjaLim

1:18 AM

@robjohn I'm stuck here....math.stackexchange.com/questions/164418/uniform-convergence/…

Dylan Moreland

1:40 AM

@BenjaLim Don't you hate it when people don't say what they've done?

3

Mark Dominus

@peter In the past I have found it is easy to find some graduate student who is happy to get paid to translate things. You call up the nearby department of whatever and ask the department secretary to put you in touch with someone.

BenjaLim

@DylanMoreland Exactly.

Mark Dominus

math.stackexchange.com/questions/164410/… is a really carefully-explained and well-posed question. I don't know why it doesn't have more upvotes.

BenjaLim

Hmmm I'm not sure about the step where I say that $|f(x_{i-1}) - f(x_{j-1})| < \epsilon$

namely because I don't know if $|x_{i-1} - x_{j-1}| < \delta$

Peter Tamaroff

@MarkDominus It is just a short phrase.

@robjohn Probably calssical. It has some accents which I can't even write here

$${\text{'A}}\varepsilon \iota {\text{ }}o{\text{ }}\alpha \nu \theta \rho \omega \pi o\varsigma {\text{ }}\alpha \rho \iota \theta \mu \eta \tau \iota \zeta \varepsilon \iota $$

The middle word is "Anthropos"

Mark Dominus

2:01 AM

aei o anthropos arithmetizei

Peter Tamaroff

THe last seems to be "Arithmetizei"?

@MarkDominus But what does it mean?

Mark Dominus

man is always counting

Peter Tamaroff

@MarkDominus You know greek?

Mark Dominus

mathforum.org/kb/…

A little, but Google knows more. :)

I have also seen that translated as "Man ever arithmetizes."

Peter Tamaroff

@MarkDominus Oh. It is in this book I bought "God created the integers"

Seems Dedeking said it.

Mark Dominus

2:03 AM

books.google.com/…

Yes. I have seen it before, but not in Greek.

Peter Tamaroff

@MarkDominus Yeah, this book has a part of ¿What are numbers and what are they for? (Or whatever it is called in english, I see it is in German there). It is really interesting.

Mark Dominus

I bet it is.

Dylan Moreland

Makoto sure does like to edit.

Eugene

@DylanMoreland yes. 21 revisions to prove a question he himself asked...

Mark Dominus

Some writers are born tinkerers.

Frank Science

2:15 AM

I've received an e-mail.

Peter Tamaroff

@FrankScience ???

Frank Science

PLEASE SEND YOUR POSTAL MAILING ADDRESS SO THAT I CAN SEND A REPLY TO YOUR EMAIL FROM PROF. DONALD KNUTH.

Peter Tamaroff

@FrankScience Doesn't seem legit.

Frank Science

What?

Peter Tamaroff

@FrankScience If it was written in CAPS LOCK like that, I'm doubting it is serious.

Frank Science

2:17 AM

@PeterTamaroff Yes, but there's no downcase over his e-mail.

Peter Tamaroff

@FrankScience Hm. Who sent it?

Frank Science

@PeterTamaroff Arden King

Peter Tamaroff

@FrankScience And did you contact them before?

Frank Science

@PeterTamaroff Might be the one here

@PeterTamaroff I've reported a bug for Concrete Mathematics to knuth-bug, but eventually I found that I'm wrong.

Peter Tamaroff

Stare at the pic for more than 10 seconds and win the ultimate prize

@FrankScience Oh, then go for it.

Mark Dominus

2:21 AM

HELLO AND GOD BLESS. I AM DR DONALD KNUTH, PROFESSOR EMERITUS OF STANDFORD UNIVERSITY. I SEEK YOUR ASSISTANCE IN TRANSFERING US$14000000 MILLION US DOLLARS FORMERLY HELD BY JEFFREY D. ULLAMAN.

10

Peter Tamaroff

@MarkDominus Hhahaahhahaa

Frank Science

@PeterTamaroff It seems that it's a mail that Knuth explains why I'm wrong.

Mark Dominus

I reported an error in Concrete Mathematics once. Graham wrote back to tell me he disagreed, but I think he was mistaken.

Peter Tamaroff

@FrankScience I suppose.

Mark Dominus

@peter Today I got email with this very strange From header:

From: "MR. BEN BERNANKE" <africanbungo@aol.com>

Frank Science

2:23 AM

@MarkDominus Which one?

Peter Tamaroff

@MarkDominus LOL

Frank Science

@MarkDominus I've read CMath once.

Mark Dominus

@FrankScience They used the wrong kind of quotation marks. I forget where it was.

Frank Science

@MarkDominus Not mathematical error?

Mark Dominus

@PeterTamaroff Bernanke is the head of the Federal Reserve, which is like the U.S. central bank.

@FrankScience No, typographic.

Frank Science

2:25 AM

@MarkDominus Oh, I get it.

@MarkDominus I was too self-confident that I made sure that the proof on CMath is wrong, so I reported bug, but eventually, I found that I was wrong.

@PeterTamaroff I don't know how to write the postal address because I'm not in English-speaking-country.

Peter Tamaroff

@FrankScience Where are you?

Frank Science

@PeterTamaroff In China

Mark Dominus

You don't know how to write where you are in English?

Can't you go to the article about your town on Chinese Wikipedia and then click the cross-link to the English Wikipedia article about the same place?

Or you have them write the whole address in Chinese, and then put "PEOPLE'S REPUBLIC OF CHINA" on the bottom.

Frank Science

@MarkDominus Thanks. I'll got to the post office and ask about the oversea mail.

@MarkDominus By the way, have you paid money for the mail

Mark Dominus

2:40 AM

Have I paid money for what mail?

Frank Science

@MarkDominus KNUTH'S REPLY

Mark Dominus

Sorry, I don't understand.

Frank Science

IS IT NECESSARY TO PAY MONEY TO RECEIVE AN INTERNATIONAL MAIL?

Mark Dominus

Not in this country. I don't know what the rules are in China.

Usually, the sender pays the postage.

Frank Science

@MarkDominus What about the mail you've received? Knuth wrote and somebody else sent?

Mark Dominus

2:47 AM

I have never received mail from Knuth. I have received mail from Ron Graham, but he sent it himself. I have corresponded with Saul Kripke, who has someone else, I think a graduate student, send and receive all his email for him.

Hmm, maybe I did once write to Knuth. It would have been a long time ago. I don't remember.

Frank Science

Ron Graham? The official site means that we need to send to knuth-bug@... to report the bugs in CMath.

Mark Dominus

Maybe it was Knuth I wrote to about Concrete Mathematics.

I forget.

It would have been around 1996, so it's hard to remember the details.

Frank Science

3:07 AM

@MarkDominus Well, typo.

Peter Tamaroff

Any of you is good at physics?

leo

@PeterTamaroff What kind of?

Peter Tamaroff

3:23 AM

@leo Basic hydrostatics

BenjaLim

OMG THE BASS IS SUPER ****** HEAVY

Peter Tamaroff

Principle of Archimedes, plus some Netwonian basic mechanics.

Eugene

@PeterTamaroff yes i am phenomenal at it

BenjaLim

@Eugene Hey

People have told me

read chapter 8 of munkres

then go to his elements of algebraic topology

@Eugene Or:

Can I just use Hatcher from chapter 1?

Eugene

@BenjaLim what's wrong with rotman?

Peter Tamaroff

3:24 AM

@Eugene Ok. Give me a hand here

BenjaLim

@Eugene I get a headache when I see functors

Peter Tamaroff

@BenjaLim Basses tend to be heavy!

Eugene

@PeterTamaroff yes the answer is 6

BenjaLim

@PeterTamaroff OMG it is so heavy

Eugene

@BenjaLim didn't you say you like commutative algebra?

Peter Tamaroff

3:25 AM

@Eugene F**l of Euge!

@BenjaLim Are you talking about an actual bass, or music?

BenjaLim

@Eugene well yes I do. That's why I would rather deal with exact sequences than all the pictures

@PeterTamaroff Not a bass guitar. That's heavy, but I'm talkin bout'

Eugene

@BenjaLim but commutative algebra is eventually a bunch of functors

BenjaLim

THOSE PHAT BEATS THAT ARE PUMPIN OUT OF THE SPEAKERS

@Eugene Yeah like "localisation is an exact functor" ...

Peter Tamaroff

@BenjaLim Listen to the WHO!

@BenjaLim And solve this while you're at it.

BenjaLim

@PeterTamaroff youtube.com/watch?v=Ylw3BEdSldA

@PeterTamaroff My physics is useless

I quit physics after first semester physics

Eugene

3:27 AM

@BenjaLim if you don't like functors you should be in analysis..

BenjaLim

@Eugene IS THAT AN INSULT???????????????????????????????????

Peter Tamaroff

@BenjaLim At least the picture is good.

BenjaLim

@PeterTamaroff you straight as an arrow?

Eugene

@BenjaLim no it's just the inevitability of categories in algebra/geometry.

BenjaLim

@Eugene Can I just deal with the AT without having to worry about natural transformations and yoneda lemma?

Eugene

3:29 AM

@BenjaLim i'm not sure since i don't do much AT. but if you want to do geometry you'll need the homological algebra

BenjaLim

@Eugene but surely you have done a course on it?

Eugene

@BenjaLim on AT? why would i?

BenjaLim

seriously wtf?

Are you not a grad student?

Eugene

yes so?

BenjaLim

@Eugene How do you deal with sheaf cohomology, singular homology, étale cohomology, etc?????????????????????????????

Correct me if i'm wrong but you plan to do arithmetic geometry?

Eugene

3:31 AM

@BenjaLim read?

BenjaLim

Those concepts are central to it no??

@Eugene huh?

Eugene

@BenjaLim there are whole books on these topics you know...

BenjaLim

@Eugene you at least need to know them for arithmetic geometry no?

Eugene

yes. that's why you READ books

BenjaLim

I swear to god my algebra lecturer jim borger who is a number theorist has taken a course in algebraic topology

@Eugene I meant to say AT was the foundation for all of those

Eugene

3:32 AM

@BenjaLim you needn't know homotopy for geometry

and these concepts can be found in geometry books

BenjaLim

@Eugene Well I think you should do a course in AT

Eugene

@BenjaLim not all that interested

BenjaLim

@Eugene I plan to do algebra but even I will take Analysis III: studyat.anu.edu.au/courses/MATH3325;details.html

Peter Tamaroff

This is a cool recreative puzzle

BenjaLim

@Eugene see what I mean

Peter Tamaroff

3:33 AM

@BenjaLim Are you taking Anal I now?

Or II?

BenjaLim

done it

Analysis II is next year first sem

Eugene

@BenjaLim i don't see your point. analysis is necessary since you have to take the quals. topology is not.

BenjaLim

My point is one should get a broad foundation in all these subjects

Peter Tamaroff

@BenjaLim Cool. I finished my epistemology course today. Got a 90% for an average (I had actually two 85%s in the mid terms, but it is regulation to crop it to the nearest tenth, so the joke's on them!)

@Eugene Topology is magic.

BenjaLim

@Eugene Don't look at me if 20 years down the road you want to be another john milnor :D

@PeterTamaroff you know your grade once you're finished???

Vamos!!

Peter Tamaroff

3:36 AM

@BenjaLim Didn't that guy found Knot theoy?

Eugene

@BenjaLim i think i'll be safe.

BenjaLim

not sure

Peter Tamaroff

@BenjaLim Well, actually we have two mid terms and a final, but if you have 70 avg between the two mid terms, you pass.

BenjaLim

but I know vaughan jones is very involved in it

Peter Tamaroff

So I'm done!

BenjaLim

3:36 AM

@PeterTamaroff you only need to pass the course

that is good

@PeterTamaroff In my degree we need to get 80% average in all science/maths courses

which I think is bullshit

because there is alot of scaling and fooling around happening

Peter Tamaroff

@BenjaLim Yikes. What do you mean?

BenjaLim

serious

and your marks get scaled up

people don't do well

Peter Tamaroff

@BenjaLim Scaled up?

BenjaLim

so the objective to get 80% average is basically trivial

well I mean the marks are trivial

By trivial here I mean "of no meaning/value" whatsoever

Peter Tamaroff

@BenjaLim What do you mean by scaling the marks?

BenjaLim

3:39 AM

@PeterTamaroff You get 80 -> pushed up to 90

Peter Tamaroff

@BenjaLim But then why are you complaining? I don't understand!

BenjaLim

I am complaining because then the requirement that we get 80% in all our courses is stupid

@PeterTamaroff Like for example

all of my mathematics courses the grades were all above 90%

last year

because of all the bullshit with scaling

but that is just trivial

@anon There is a flaw in the proof here: studyat.anu.edu.au/courses/MATH3325;details.html

sorry here: math.stackexchange.com/a/164424/5783

Peter Tamaroff

@BenjaLim So what is your grade then?

anon

I was gonna say, a flaw in a course description?

BenjaLim

I don't know that $|x_{i-1} - x_{j-1}| < \delta$

@PeterTamaroff My grade? I told you they were all 90 plus

on the transcript at leasst

Peter Tamaroff

3:43 AM

@BenjaLim But isn't scaling good then? What do you mean by scaling? Normalizing? A Gauss curve? Whaaaaaaaaaat!?!??!

BenjaLim

@PeterTamaroff I dunno

All I understand is - your marks get increased

Honestly

to make everything all LOOOOOOOK REEEEALLLLLLLY GOOOOD AND SHIIIINNNNNYYYYYYYYY @PeterTamaroff

anon

in hs my calc teacher would apply (x+100)/2 and then 100*(x/100)^0.4 to all grades

BenjaLim

So ThAT oN YoUR TrAN5RipT EvErYThinG lOoks nice

@anon the flaw

I can't fix it

anon

sigh

BenjaLim

@anon rep is 7070

what a number

Peter Tamaroff

3:49 AM

@BenjaLim LOL Strange.

BenjaLim

@PeterTamaroff For AFAIK my grades, just meaningless

I'd rather concentrate on the maths

Peter Tamaroff

@BenjaLim I lost the tail of my sequence. Now it is too late to fix it, too

BenjaLim

what sequence?

Peter Tamaroff

@BenjaLim Let me find it.

anon

would $|x_i-x_j|\le |i-j|\delta$ help? I really hate $\epsilon$-$\delta$ thinking.

14 trillion USD? What, Knuth has nation-state GDP-level wealth?

Transcript for

$Mathematics$ Mathematics