Mathematics - 2012-03-15 (page 1 of 4)

Skullpatrol

00:00

I can't seem to stop watching his "Brief History of Time" over and over again.

Paul Slevin

ive not actually seen it or read it. I should

Skullpatrol

You will be amazed.

N3buchadnezzar

I found the series "Great minds, Great Theorems" really good

I would not mind it being more mathematical intense, and a tad more rigourous. But for a layman documentary it is quite impressive.

Skullpatrol

@N3buchadnezzar What did you think of A Brief History of Time?

N3buchadnezzar

@Skullpatrol Mind boogling

Skullpatrol

00:05

Indeed!

@PaulSlevin You must watch "A Brief History of Time" when you get a chance.

N3buchadnezzar

I was able to get some work on my integration document, and be able to dance with some girls. I would say this has been a succsessfull day.

Paul Slevin

i will in the summer holidays

when i finally am one with work haha

John Smith

hello

N3buchadnezzar

Kannappan Sampath

Nice. ^

John Smith

00:15

what are those problems?

N3buchadnezzar

@JohnSmith Intermediate

Kannappan Sampath

@N3buchadnezzar Some of them are a little hard if not for the trick! =)

N3buchadnezzar

@KannappanSampath Nah, these are the easy intermediate problems. Tougher problems will follow =p

John Smith

Anyone here know about additive partitions of integers?

Kannappan Sampath

@N3buchadnezzar But do you agree with my belief?

N3buchadnezzar

00:21

I really love that
$$ \int \tan x \tan 2x \tan 3x \mathrm{d}x = \int \tan 3x - \tan 2x - \tan x \, \mathrm{d}x $$

@KannappanSampath Belief ? Eh, tricks are not really tricks after having seen them enough times. If I have a short introduction, explaining different methods. Like symmetry and f(x)=f(a-x) and so on, these problems should be solvable.

It is not like these problems are solved by introducing a new variable, then differenting twice, to obtain the answer either :p

Kannappan Sampath

Oh well let's not argue!

N3buchadnezzar

@KannappanSampath I think we agree though!

Paul Slevin

What is the etiquette for asking questions on the main site?

i feel like im asking one every day

is that too much

N3buchadnezzar

@PaulSlevin No more than 40 a month, other than that it is fine. If you put some effort into your questions.

Skullpatrol

"An idea which can be used only once is a trick. If one can use it more than once it becomes a method."

Paul Slevin

00:25

OK, I do usually put effort in

but sometimes I just get so stuck and I can't progress

N3buchadnezzar

@PaulSlevin that is when you start asking =)

@Skullpatrol When I first saw how to integrate $(x^2+1)/(x^4+1)$ I was a little depressed. They divided top and bottom by x^2 and factored the denominator into $(x+1/x)^2+2$ or something.

I felt that this was taken out of thin air, and way to specialized to be useful for anything else.

Later I found atleast 4/5 other integrals that could be solved by applying the same method ;)

Like $1/(x^4+1)$ and $\sqrt{\tan x}$

Asaf Karagila

Screw this. I am going to sleep.

N3buchadnezzar

@AsafKaragila starts screwing like a maniac

Skullpatrol

@N3buchadnezzar I agree that the birth of the recognition of a method can cause some depression ...

N3buchadnezzar

And now we just introduce the variable $\zeta$

If we look at this completely unreleated integral, differentiate twice we obtain our integral!

Hence solved.

Skullpatrol

00:35

;-)

Kannappan Sampath

@Asaf In your example don't you mean that there must be infinitely many distinct terms in the subsequence all increasing?

Paul Slevin

night guys

Kannappan Sampath

Night @Paul

Skullpatrol

Later @PaulSlevin

@N3buchadnezzar mathoverflow.net/questions/48248/what-do-named-tricks-share

N3buchadnezzar

=)

Skullpatrol

00:51

unanticipatability is the essence of trickhood

t.b.

02:52

oh, boy...

Kannappan Sampath

@leo I am sorry I have to ask you this: We are planning to discuss topology with ample help from resident topologists here. So, would you be doing topology with us/ helping me do it?

leo

hi @tb. I can not reply you in the other room

t.b.

@KannappanSampath Kannappan, can you grant leo access/write rights to "Got Loopy", please?

Kannappan Sampath

@tb Sure yes why not!

leo

just some questions, few minutes

t.b.

02:56

And why not leave it open to everybody for the moment. As long as nobody starts cluttering up the chat, I see no problem.

@leo shoot!

Kannappan Sampath

@tb Yes, done. I am afraid cluttering would happen though.

t.b.

@KannappanSampath okay, I don't know. I didn't have this impression in the other (open) rooms. It's your room after all.

Kannappan Sampath

@tb Well, I agree with you here. :-)

t.b.

@leo didn't you have a question?

I think this is a duplicate

leo

I don't know what room use for it.

wait a second

t.b.

03:10

@leo well, if it is a topology question ask in the other room, else ask here.

leo

ok

Is the Exercise 24, page 43 of Stein Shakarchi

I'll type in a second

Kannappan Sampath

I think it's time for breakfast and some probability lectures. Bye @tb. Thanks for that topology help. :-)

t.b.

@KannappanSampath have a good day!

@leo I don't have the book, I'm afraid.

(by the way there are many Stein-Shakarchi books :))

leo

@KannappanSampath Have good day!

Mr_CryptoPrime

Hi, all. I was wondering if someone could help me how to understand how to convert pi (or any irrational number) from the numerical base-10 to the alphabetical base-26? (like here: cadaeic.net/picode.htm)

leo

03:14

@tb Oh yes. Is the Measure theory related

Does there exist an enumeration of the rationals $\{r_n\}_{n=1}^\infty$, such that the complement of $$\bigcup_{n=1}^\infty\left( r_n-\frac{1}{n},r_n+\frac{1}{n} \right)$$ in $\mathbb{R}$ is non-empty?

t.b.

@leo yes

@leo I like Robert Israel's deleted solution best:

> Let $\alpha$ be some irrational number that you want to be in that complement. For each positive integer $n$, consider the rational numbers $p/q$ (in lowest terms) with $|p/q - \alpha| > 1/n$, and choose one with $|p|+|q|$ smallest that has not already been chosen as $r_j$ for $j < n$.

> Somewhat more generally, you can get that complement to contain any set of irrationals with no rational accumulation point.

Kannappan Sampath

03:45

Well I thought I should post this link:

sbseminar.wordpress.com/2012/03/13/…

leo

@KannappanSampath Indeed

t.b.

03:59

@KannappanSampath déjà vu

Benjamin Lim

@tb Got an assignment back today

t.b.

What assignment?

Benjamin Lim

Field theory

Tutor was being ridiculously harsh so I went to talk to the lecturer

he said he would talk to the tutor

t.b.

what does ridiculously harsh mean?

Benjamin Lim

Like say 8 marks taken off for basically a few typos here and there, using mathematica to crunch algebra

I don't really care what marks I get but it is very frustrating

Indeed my lecturer agreed that everything was right except for a few nitpicks here and there

t.b.

04:03

What does 8 marks mean? (I don't know the grading system you have)

Benjamin Lim

the whole question was worth 20

It was basically calculating the power sums $p_1$, $p_2$, $p_3$ and $p_4$

Sometimes it's hard dealing with things like that, especially when the degree you're enrolled in says you have to maintain an 80% average every semester

t.b.

Hm. It is very hard for me to say anything sensible (I only know part of your side of the story)... But given that the lecturer will talk to the tutor, I wouldn't get too worked up about this right now.

Benjamin Lim

yeah thanks :D

I don't know if as an undergrad you had to deal with things like that

t.b.

@leo got it?

Benjamin Lim

i should go to bed now

really tired

t.b.

04:09

@BenjaminLim Not really, no. There was one course where I wasn't interested enough to do the boring homework, so I didn't quite fulfill the requirements. So in order to be admitted to the exam, the prof wanted me to pass an extra exam. I told him that this was too stupid and chose another course.

@BenjaminLim good night, then

leo

@tb I see simpler the Brian's answer

I mean, I see more simple the Brian's answer

hhh

How can one deduce the error formula for measuring something like density with partial derivatives?

Is the err just the sum: f_{x} \Delta x + f_{y} \Delta y + ...?

leo

that's my broken english

hhh

Suppose $T=-\tan(\beta)\left(\tan(\alpha)-\tan(\beta)\right)^{-1}$ where each $\beta$, $\alpha$ and $d$ have some error in measurement, what is the err in T?

t.b.

@leo I would say: I think Brian's answer is simpler.

leo

04:19

@hhh I remember something like that, but I'm not sure

@hhh the Larson & Hostetler book of Calculus have something related

hhh

...well, I asked a q:

http://math.stackexchange.com/questions/120370/deduce-the-measurement-error-with-partial-derivatives

to work with the issue...

but I will try to google the book...

@leo is that book in Internet?

leo

good night all!

t.b.

good night, leo

hhh

Night!

leo

and thanks @tb

Matt N.

06:57

Morning.

t.b.

Hi, Matt!

Matt N.

Wrong question, huh.

t.b.

Fine :)

I was so annoyed yesterday by some electrician guy who messed up my bathroom but then I slept early and now the grumpiness seems to be gone.

Now I'm waiting for him to come again and clean the mess up...

Matt N.

I assumed it must've been something more serious than that seeing as it lasted for more than a day.

I'd clean it up myself. I'd never trust a random guy/girl to be clean enough.

: )

Skullpatrol

Hi all.

Matt N.

07:04

Hi.

t.b.

Well, the actual cleaning will be my job, of course, but he has to fix the things he destroyed... This is so silly. They had to deactivate a power plug because it was too close to the shower (there apparently is a law saying that it may not be closer than 90 cm, they measured and it was 85...). I told him that he could as well leave it because I'm going to re-install it as soon as he's gone. He didn't listen :/

Matt N.

Interesting. Is this law new? Sounds like we're turing into an English speaking country. There they assume people are too dim to handle dangerous things with care and sockets are banned from bathrooms completely.

Going to make some coffee.

t.b.

I have no idea. It apparently was okay when they checked it last time... Probably I should just have turned the shower head in the other direction.

Skullpatrol

Hi @JonasTeuwen @KannappanSampath Welcome.

Jonas Teuwen

Hi.

t.b.

07:10

Hi

Kannappan Sampath

Hi all of you!

Matt N.

@tb : D This all happened because you splashed water into the socket?

Hi Jonas, Hi Kannappan!

Jonas Teuwen

Hi.

t.b.

@MattN No, they had an official check of all electrical installations and I don't know what else in the entire neighborhood. The socket is in a mirror cabinet, and it worked just fine for 20 years, but when he measured the distance, he measured the distance to the shower head...

Matt N.

That's idiotic.

Skullpatrol

07:16

So why not just disconnect the socket and leave it at that?

t.b.

That's what I'm saying. Anyway, he took the opportunity to smash up the lamp shades and one mirror of the cabinet, so he's got to come today and fix that...

@Skullpatrol Because I actually want to use it.

And I see no reason why I shouldn't except for this silly law that doesn't make any sense.

Skullpatrol

Well, you could have tried to appeal the law.

Matt N.

Yes. I'll sign it. : )

While you're at it you can also do one to ban church bells...

Skullpatrol

@tb 5cm is a small enough difference that your appeal would be considered reasonable.

t.b.

@Skullpatrol yeah, right. I want to use it now and it takes me 5 minutes to re-connect the thing, so I won't waste 5 weeks of my life for fighting against the windmills of the local administration.

@MattN maybe we should file a petition that as soon as there are people living closer than 50 meters to a church, the bells must be turned off. It's too dangerous to let all those people go crazy. We need to protect them...

Asaf Karagila

07:22

Morning.

Skullpatrol

Hi @AsafKaragila

t.b.

Hi, Asaf. Lots of jury duty...

Matt N.

Morning Asaf.

Asaf Karagila

So I see.

t.b.

@JonasTeuwen why are you here so early?

You might like this one or that one by the way.

Skullpatrol

07:27

Well, I'm gonna go watch "A Brief History of Time" for the umpteenth time on youtube... anybody wanna join me?

Benjamin Lim

hey guys

@tb I saw your comment

Matt N.

Hi Benjamin.

Skullpatrol

Hi @BenjaminLim

t.b.

Hi Ben, which comment?

Benjamin Lim

about the course you took

I am feeling much better now.....somehow it's like here I can just talk about mathematics for the sake of it

t.b.

07:28

oh. Yeah, it was just numerical analysis of PDEs, so nothing I couldn't live without...

Benjamin Lim

Well this is fields and galois theory and if I want to do algebra that is critical

@tb How was time management like when you were an undergraduate?

Kannappan Sampath

Hi @Asaf

Hi @Ben

Benjamin Lim

hey

Skullpatrol

Hello @KannappanSampath Welcome.

Kannappan Sampath

Hello @Skullpatrol How do you do?

Skullpatrol

07:32

@KannappanSampath Fine thanks and you?

Matt N.

@tb Protect people, huh? I don't have a protector instinct.

Kannappan Sampath

I have screwed my exams very very badly! T_T

Asaf Karagila

Is it just because I didn't have any coffee yet?

Matt N.

@KannappanSampath I thought your exams were over? Did you have another one?

Benjamin Lim

@KannappanSampath What happened?

Kannappan Sampath

07:34

@MattN They were over and I happen to see my answer scripts!

Matt N.

@KannappanSampath Your grades, that is?

Which classes are we talking about?

Kannappan Sampath

@BenjaminLim I have integrated by parts wrongly! I had forgotten Zorn and all of that! : (

Matt N.

You had topology, probability and what else?

@AsafKaragila tl;dr

t.b.

@MattN I just thought it was in the same spirit as the socket law.

Skullpatrol

@MattN Have you seen "A Brief History of Time?"

Matt N.

07:46

@tb Now I see how you meant it. By the way: if the socket thing happened yesterday, what happened the day before?

@Skullpatrol No, but it's on my want to read list.

Skullpatrol

@MattN It's quicker to just watch it on youtube.

Matt N.

@Skullpatrol I think I'd much prefer the book.

Skullpatrol

@MattN I think there is a second book called "A Briefer History of Time." ;-)

Matt N.

Yes. I'm actually planning to read most of his books. : )

But first I'm going to read the Bourne trilogy which is sitting on my desk over there.

And Atiyah.

Skullpatrol

The Bourne Identity (novel)

The Bourne Identity is a 1980 spy fiction thriller novel by Robert Ludlum about a retrograde amnesiac who must discover who he is and why several groups, including an assassin and the CIA, are trying to kill him. It is the first of the original Bourne Trilogy by Ludlum, and in further posthumous novels by Eric Van Lustbader, featuring Jason Bourne. The Bourne Identity was named the second best spy novel of all-time, behind John le Carré's The Spy Who Came in from the Cold, by Peter Cannon in Publishers Weekly. The novel was adapted into a 1988 television movie starring Richard Chamber...

Matt N.

07:52

Yes, that's the book.

Kannappan Sampath

@MattN It was the probability. My Analysis course went well.

And, I screwed algebra up as well! : !

Matt N.

I see. Did you pass?

Kannappan Sampath

I did pass the course!

But, my grades are real low.

And, it was for very minor miscomputations. That's what pains.

Matt N.

Then that sucks.

Exams that depend on computing suck.

Just forget about it : )

Kannappan Sampath

I integrated by parts wrongly. It's not like I never knew that $\int e^{tx} \rm dx= \frac {e^{tx}} {t}$

Matt N.

07:56

Ah so you did do something wrong rather than just messing up the sums.

Skullpatrol

@MattN "A Brief History of Time" is only 1:19:43 and it gives an inspiring insight into a modern day Newton/Einstein....

Kannappan Sampath

@MattN Yes, I did it wrongly. I miscomputed that integral! : ( But you would not want to penalise me by slashing down 18 grade points out of 20.

Matt N.

@Skullpatrol Yes, thanks skullpatrol but I don't have enough patience. I really need to read the book. You see I've also had a brief look at video lectures but I just can't listen. I need a book : )

@KannappanSampath Minus 18 out of 20 total for the entire exam for making 1 mistake? What the...

Kannappan Sampath

@MattN Yes. This is exactly what pains me!

Anyway, shall I be back after lunch?

Matt N.

Ok! Enjoy!

Skullpatrol

08:03

Ahhh!!! the audio on youtube is terrible

I think @MattN is right and I'll get the book ;-)

or sign out the DVD at the library

again ...

Kannappan Sampath

Back....

Skullpatrol

08:20

"A Brief History of Time" is more of an autobiography than about Time ...

Kannappan Sampath

08:46

Will someone tell me a good place to learn about eigen vectors and eigen values?

anon

what about them?

Kannappan Sampath

I'd like to get the geometric idea behind them.

Skullpatrol

09:02

The audio and visual qualities of "A Brief History of Time" are more than offset by the video's incredible content.

Kannappan Sampath

Is it true that people interested in algebra have the same kind of gravatars? Hint: Dylan

Hi @NadimRustom

(I feel sorry that you'd not be able to reply because you need 20 rep points. Looking forward to your joining the room soon.)

Hello @MattN. I have a question to ask. Mind it now?

Matt N.

No, shoot.

Kannappan Sampath

Where did you learn linear algebra from? (You can assume I have had a first look at most of the concepts. Now I am interested in getting the connections and geometric ideas right.)

Matt N.

The notes I took during the linear algebra course.

Kannappan Sampath

Hmph, I have no access to them. : )

Matt N.

09:10

I know that's not helpful.

Kannappan Sampath

What I find is there are a plenty of connections with matrices which become particularly helpful while doing finite field arithmetic.

(Apart from this, I am looking for a place to learn linear algebra in general, eigen vectors and invariant subspaces in particular.)

Matt N.

I think that's a good idea. Maybe someone else can recommend a good book to you.

Skullpatrol

@MattN Did you know that youtube has a feature in it that if you move your mouse pointer over the "time line" of a video you will get small images of what happened there?

Matt N.

No. I think that's new.

Skullpatrol

Too cool.

Check it out

Matt N.

09:23

Yes cool.

Skullpatrol

;-)

BTW when I use the symbol ";-)" I am not winking @ you ... the one closed eye is also on my gravatar.

Daniil

09:36

@MattN pfffft, youporn had this feature for ages

Matt N.

@Daniil I never noticed.

: )

@Daniil Just checking. It's not true: on youtube you can mouse over in the timeline of the player. Youporn only has the feature on the preview icon.

Skullpatrol

@Daniil Porn is basically the same throughout, so why would you need this feature?

Daniil

@MattN hm, maybe mixed it with some other streaming site

anon

tube sites all over the internet have had this feature for ages. skull you must watch boring stuff.

Daniil

@Skullpatrol I think it's quite different

Matt N.

09:40

What Daniil said.

Daniil

guardian.co.uk/society/datablog/video/2012/mar/15/…

Skullpatrol

BTW not all videos on YOU tube have this feature.

Kannappan Sampath

@Skullpatrol Link to some video where such a feature does exist?

Matt N.

@Daniil Heh. : )

Daniil

Yeah, I have nothing against drug use, but that's quite silly. I mean, you wouldn't be a "mystery pint of alcohol" would you?

Matt N.

09:48

Well I wouldn't. : )

Skullpatrol

@KannappanSampath Link to video where the feature does exist

►

anon

The scrollover feature works fine for me on that video, skull

Kannappan Sampath

For me as well.

anon

@Daniil: How would one be a "mystery pint" of something? Get cremated and have one's ashes mixed in with an unknown liquid?

Skullpatrol

@KannappanSampath Indeed, didn't you ask for a " Link to some video where such a feature does exist?"

anon

09:51

I think he forgot the "not," because otherwise his comment makes no sense.

Skullpatrol

@anon Maybe

anon

you said not all videos have that feature, and then he asks for a video with the feature. you don't find that odd?

Skullpatrol

Yes.

@anon Have you seen "A Brief History of Time," and if so what did you think of it?

anon

I read the book by Hawking. Is that related?

Skullpatrol

Yes, I think. But I haven't read the book, to be honest.

There is a narration of the book on youtube, but I don't like being read to.

@anon The video has lots of autobiographical info in it and appearances by famous scientists of today, you should check it out, when you get a chance, and let me know how it compares to the book ;-)

anon

10:01

I don't even remember the book, I was like in middle school.

I'm more interested in watching Archer and reading very slowly about number theory than bio stuff on scientists right now.

Skullpatrol

@anon In my opinion, it is a truely inspiring story about a present day Newton/Einstein.

t.b.

@Skullpatrol That's the thing that is truly annoying about the book.

Skullpatrol

@tb What is "the thing" that annoys you t.b.?

Matt N.

Many things...

Skullpatrol

@tb...for example? please.

Kannappan Sampath

10:09

Well, I read the transcript and don't get some of the comments related to "For me as well". Let me clarify: Skull said it does not work on all videos. So, I asked for one where it works. Anon said, the feature worked for him and I said it worked for me as well.

t.b.

@Skullpatrol That Hawking sells himself this way. He's neither an Einstein nor a Newton. And he doesn't tire of mentioning the fact that he has the Lucasian chair, etc... It's not like he's a bad scientist (as his almost namesake Dawkins is) but he's selling highly controversial interpretations as "the truth".

Skullpatrol

@tb These are all very good points.

@tb Now look what you did. You scared off Matt...

@t.b.You've gone from teddy bear to Grizzly bear in less than a week ;-)

Ilya

10:35

Let me try Safari now...

Kannappan Sampath

Hi @Ilya

Skullpatrol

@Ilya Where are you going on your Safari? ;-)

Africa.

t.b.

@anon: pulling a Dubuque, eh?

anon

Precisely.

Ilya

Safari is crappy :)

Kannappan Sampath

10:39

@tb Thinking of which even I have started write answers with Hint but a series of logically ordered bullets, (starting today!).

Daniil

hey @Ilya, what's up?

Ilya

@Dan: opening new tabs in new windows is just ridiculous

Kannappan Sampath

I don't see how this comment is of some help to OP

anon

I think it's just inefficient.

Who uses capital $I$ for an integer? Eww!

Kannappan Sampath

I !! :-)

(Looks like I'll break 5k this week!)

BTW, Did people see that your drop down summary has not reset after yesterday?

anon

10:48

that has also affected me

Matt N.

Is there a better way to show $p$ prime element, $p \mid x^n$ then $p \mid x$ than applying the definition: if $p \mid x^n$ then either $p \mid x$ or $p \mid x^{n-1}$ etc. until $p \mid x^2$?

Benjamin Lim

@MattN I think you need to be in a UFD.

Matt N.

Then it's broken because the rings in Atiyah aren't necessarily UFDs...

Benjamin Lim

Where is this in AM?

@KannappanSampath Have you seen this? math.stackexchange.com/questions/120429/…

anon

You don't need unique factorization.

Matt N.

10:52

It's a question that came up when I read the proof that $n = \bigcap_{p \text{ prime ideal } } p$ on page 5. (where $n$ is the nilradical)

anon

What's wrong with the inductive proof?

Matt N.

I think induction is fugly.

Kannappan Sampath

@BenjaminLim Yes, I have.

Matt N.

So I thought I might see if someone knows a slick proof.

: )

And I'm not sure that that's induction. It goes down rather than up...?

anon

Induction seems to be the most natural explanation to me.

Benjamin Lim

10:54

no you do not need to know anything about division :D

@anon Don't you need to be in at least a factorisation domain?

anon

Oh yes. The proof just goes through $n$ steps with $n$ indefinite. That's not induction.

Matt N.

: )

Benjamin Lim

Every non-zero non-unit can be written as the product of finitely many powers of irreducibles

Skullpatrol

I'm getting a "[Math Processing Error]" message when I click MathJax 2.0

Matt N.

@BenjaminLim I think the proof I gave doesn't use factorisation.

anon

10:55

@Skull: Try Ctrl+F5 ... maybe...

Matt N.

Thanks : )

Benjamin Lim

@MattN Yeah what problems do you have with the proof?

Matt N.

I think it's ugly. I thought I might be missing something and someone might know something less clumsy.

Benjamin Lim

what is this?? math.stackexchange.com/questions/120453/…

t.b.

@anon How is that not induction?

Benjamin Lim

10:57

It's beautiful

Skullpatrol

@anon Thanks, that worked!

anon

@t.b. I was being sarcastic :) @Skull: No prob.

Benjamin Lim

Where is the induction in that??

t.b.

@anon oh, yet another instance where I could have used a sarky emoticon...

Kannappan Sampath

@BenjaminLim I think people might down vote, Ben. So, add a line or two about how the question is imprecise.

Transcript for

$Mathematics$ Mathematics