Mathematics - 2014-02-20 (page 4 of 4)

Balarka Sen

21:00

correction : inside 10:45

except that, totally fine

i am sure you're thinking about how i keep my position in first bench if i come last, righto?

Sawarnik

Who will like to be in the first bench?

Go to last, and play.

Balarka Sen

i sit in 3rd.

the members of MASH sit there

Sawarnik

MASH?

Balarka Sen

Mathematical Association of Sodepur Highschool

Sawarnik

First time I m seeing that Indian schools are also quite in variety.

Balarka Sen

21:03

wat?

Sawarnik

Actually, your school, as I see, functions in ways I cannot parallel to mine.

Balarka Sen

like?

Sawarnik

Like:

i)Go anytime you wnat

ii)Things like MASH exsist

iii)Members of MASH sit at the nth bench [!]

iv)Nothing to do with studies, assignments

I can list many.

...

Balarka Sen

ii) was not before I came here. I am the president.

iv) it has something to do with studies, but with less assignments.

:13886408 picked up a couple of math geeks of my class the first day in library and named it MASH sometimes later. Done and done. We actually are referred to by "freak mathematicians" there =D

Sawarnik

@BalarkaSen So it is a useless organization? I mean, I thought it was something official.

Balarka Sen

21:08

Not really.

And not official no,

We do math for fun

but there are some extra privileges given to us by HM

Sawarnik

You know your school is really different, from the ones that exist here.

Balarka Sen

I didn't saw that.

What was it about?

The "removed"?

Sawarnik

Was about what does your organization do?

Balarka Sen

Do math, learn math, ask math.

That's it

Nothing officially sound

robjohn

@N3buchadnezzar: you around?

Sawarnik

21:11

Uhh..I thought it was something , you know..

N3buchadnezzar

@robjohn Just back

Balarka Sen

@Sawarnik Ah?

robjohn

@N3buchadnezzar I just posted an answer to that question. What I got look like what you got?

N3buchadnezzar

@robjohn Did you check your result numerically?

Sawarnik

@BalarkaSen Leave it.

Balarka Sen

21:13

Sure.

robjohn

@N3buchadnezzar I haven't. Does it look wrong?

I will now

N3buchadnezzar

@robjohn I think it should be $a^2$ in the denominator and not $a$.

@robjohn But again I got the same as you, but my numerical results says $a^2$

robjohn

@N3buchadnezzar I will try. Hang on.

Balarka Sen

:13886611 I didn't get anything, and when we got it wasn't even named anything. HM just observed that we go to library in off-periods and do mathematics.

Do not think mash is any official name, it's just what we call ourselves for fun.

Officiality destroys the goal of an organization.

Sawarnik

@BalarkaSen See that, off periods, does not exist in my school.

Balarka Sen

21:17

No lunch?

Sawarnik

So you do maths in place of food?

Balarka Sen

@Sawarnik Yeah.

Sawarnik

!

Balarka Sen

But we use off-periods too.

Sawarnik

Off periods, does not exist.

Balarka Sen

21:18

I don't do eating while in school.

And neither any of MASH members

Sawarnik

Yes 4 hrs of schools, not required

Balarka Sen

straight to library and open up books and things and do higher math.

Sawarnik

If anyone did this in my school, he would be ridiculed to death.

Balarka Sen

Maybe I am an exception since I am the only candidate of my school going to IISc

and people think I am representing the school (lol)

robjohn

@N3buchadnezzar I checked mine numerically for $n=3,m=2,a=2$ and got the same answer to 20 places

Sawarnik

21:21

I am in school from 6am to 2pm. We have to eat, otherwise I ll starve.

Wat? You are doing a graduate degree.

Balarka Sen

I don't starve so easily.

@Sawarnik Haha, no, no. absolute negatory.

Sawarnik

Then IIsc?

Balarka Sen

I am in for a special course.

on math

analysis and number theory mainly

they invited me

Sawarnik

Invited you? On what basis?

N3buchadnezzar

@robjohn Probably a mistake in maple then

Balarka Sen

21:23

Interview

Sawarnik

Oh! Distance course?

Balarka Sen

Nah.

Going there physically

on May

Sawarnik

And skip the school?

So lucky!

Balarka Sen

Yeah, permission granted by HM.

Sawarnik

[Should I go? Am wasting your time?]

Balarka Sen

21:25

No.

Sawarnik

Thanks! You will get tired of my inquisitiveness, sure.

Balarka Sen

okay, true

Sawarnik

Are the other freaks also kind of specialized like you?

Or like me?

robjohn

@N3buchadnezzar I've checked it for several other values of $a$ and $n$ (and the corresponding value of $m$), and my formula gives the correct numerical answer.

Balarka Sen

@Sawarnik Not exactly like me, but yes.

in MASH

N3buchadnezzar

21:27

@robjohn It sure is correct then, I got the same as you!

Sawarnik

Quite a talented school!

N3buchadnezzar

Silly computers

Sawarnik

Well, maybe due to you.

Balarka Sen

Yes

@Sawarnik I came here just a couple of months ago

So no.

Sawarnik

You organized that talent.

We kind of had a similar group in 7th, but very small, 3 to 4 members.

Balarka Sen

21:29

We have 6 members, I think, let me count

Yep, 6 for sure.

...or no. 5

Sawarnik

But more social like you all, did maths in the periods [actual periods], play cricket until the teacher comes, and go on.

Stupid?

Balarka Sen

Okay, that came out wrong.

Sawarnik

Re energizing

After maths.

Balarka Sen

We don't re energize.

Sawarnik

We are humans.

Balarka Sen

21:31

Whoops.

Sawarnik

Actually that was group, generated my interest in maths.

Balarka Sen

I see.

Sawarnik

Told you, a year before I knew nothing, but I accelerated then after.

Balarka Sen

What happened to it, then?

Sawarnik

One went to Delhi, the others, in different sections.

We do share questions, but on phone.

Balarka Sen

21:34

Phufooot.

@Sawarnik Don't you have school today?

it's 3:03

Sawarnik

2:02?

3:02!

Balarka Sen

Ignore

It

Sawarnik

Today? Or tomorrow? Oh no, today. Yes, the last day before the exams. But do nt worry, will sleep a longgg .. after coming from school.

I think you are feeling sleepy now.

Balarka Sen

Last day?! And you're chatting?

Sawarnik

Why? Any problem?

Balarka Sen

21:37

@Ian

@IanMateus

Copy command, captain.

Do you copy?

@Ian

Flight lead's gone and shoot's jammed.

I think.

Nevermind

Sawarnik

Ah, yes you are bored now. And I mean exams are not tomorrow, probably from Monday.

Balarka Sen

Oh, I see.

Take a break from school tomorrow as it's the last day then.

Sawarnik

I took one today.

Balarka Sen

Take another. I do that always

Sawarnik

My mother wont allow.

Pedro Tamaroff

21:41

@Mike This is gorgeous analysis. Just sayin'.

Ian Mateus

@BalarkaSen sorry :-(

Balarka Sen

@IanMateus Any nice problem at hand? I am bored outta my mind.

Sawarnik

@BalarkaSen What made you specifically choose number theory?

Ian Mateus

@BalarkaSen wait a bit, I'll try to remember

Balarka Sen

@Sawarnik Godknows.

Perhaps because there is much to discover there.

It's quite an undeveloped branch compared to the others, you know.

Sawarnik

21:45

IC

Balarka Sen

Integrated Circuit

skullpatrol

Hi @Charlie

Balarka Sen

OK, no math here, I think I will go and sleep now.

Bye guys.

Sawarnik

@BalarkaSen Is this true that if f(f(x) has an fixed point then f(x) has one?

Balarka Sen

@Sawarnik Not really.

Sawarnik

21:51

Its continous

Balarka Sen

I stick to my argument.

Sawarnik

Then whats with this:

f(f(k)=k

let m=f(k)

Balarka Sen

Yes?

Sawarnik

then f(m) - m = k-m

Balarka Sen

Fine

Sawarnik

21:54

and f(k) - k = m - k = -(m-k)

Balarka Sen

okay

Sawarnik

intermediate value theorem?

Balarka Sen

Good. Well done.

Ian Mateus

@BalarkaSen no luck for finding interesting problems today

Balarka Sen

Okay, now I am off to sleep.

Well done, btw, @Sawarnik.

Kasper

21:57

is this correct ?

Im not so good with complex numbers

Ian Mateus

@Kasper the cube roots of complex numbers are rarely unique.

Kasper

Ah. I remeber it already. $-8i$ is also $7\pi/2$

etfc.

Ok thanks :0

:)

skullpatrol

Hi @MarianoSuárez-Alvarez nice to see you back again.

Mike

22:15

@TedShifrin Hello

Ted Shifrin

Hi, @Mike, @skull ... How do you always descend right when I do, @Mike? :D

Mike

@TedShifrin Luck, I guess

I just got back from filling out forms.

Ted Shifrin

Ah, I hope you filled wisely.

Mike

It was a form to take $C^*$-algebras next quarter. Fun stuff.

Ted Shifrin

As well as Hodge theory?

Mike

22:17

That's the other class.

This is from an analyst... I'm keeping @Pedro happy

Ted Shifrin

I'm amazed the faculty have the time to do so many independent study classes.

skullpatrol

Hello Professor @TedShifrin

Mike

Now you see why they're ready to get me out of here :)

Ted Shifrin

Well, knowing analysis better will help with passing quals, regardless. Yeah, unfortunately, we seem to have some undergrads who aren't so strong who request reading classes to avoid taking classes from professors (ahem) they'd rather not take.

We really shouldn't allow it, but people are pushovers.

Mike

Well, $C^*$ algebras is more topics in analysis than the foundations. But it should be interesting nonetheless.

I remember a proof in my topology course in the Fall that apparently could have been vastly simplified with the basic theory of $C^*$ algebras...

Ted Shifrin

22:20

Yeah, I've heard lectures on the stuff, @Mike, but never taken a course.

Well, $C^*$ algebras won't hurt for reading some of the analysis in that book you won.

Mike

Haha, exactly.

Now I just have to find the time.

Ted Shifrin

Stop wasting time here!

Whoa ... five people just left.

skullpatrol

well said^

Mike

I definitely should... but that time wouldn't end up going to index theory ;)

Ted Shifrin

It would if you made it do so.

skullpatrol

22:22

they don't call it a "discipline" for nothing

Ted Shifrin

A guy sent me an email asking me to write out details of a solution I gave someone else almost a year ago. I really don't want to waste the time. Sigh.

Meanwhile, my 30 diff geo students are downstairs taking an exam at 5 pm to make up for one of our ice-age days.

Daniel Fischer

Heya, @skullpatrol! Who's the tough-looking dude in you new picture?

Mike

Then don't

Ted Shifrin

You don't think it's @skull, do you, @Daniel? :D

Mike

@DanielFischer Ruben Cortada

Daniel Fischer

22:24

Hi, @TedShifrin, how's things? (No, I don't think it's him)

skullpatrol

@DanielFischer @TedShifrin :D

Daniel Fischer

@Mike Is that somebody whose name I should recognise?

Ted Shifrin

I think if @skull were such a deadly handsome guy, he wouldn't have any need for math.

skullpatrol

lol

Mike

@DanielFischer Tennis player

Ted Shifrin

22:25

No, @Mike, I don't think so.

Daniel Fischer

@Mike Can't be. Tennis players are named Connors, Borg, McEnroe, Lendl.

Ted Shifrin

Oh, as a youth ...

Don't forget Rafa, @Daniel. And plenty of other Spaniards and South Americans.

Mike

You forgot Sampras on that list, the only one that matters.

Ted Shifrin

I was listing Spanish ... or Latin.

Mike

That was @DanielFischer

Daniel Fischer

22:27

@TedShifrin I'm showing my age here.

Ted Shifrin

You're younger than I, @Daniel, so hush up.

Going to check on my kidlets in their test ...

Daniel Fischer

@TedShifrin Yes, but you play tennis.

Julien

Hi, Someone have never seen this exercise before : I have $n$ sugars,length L,we place on top pieces of sugar by shifting each piece on the right. What is the maximum distance to stay in balance? I know that there is a relationship with the Harmonic series.

Mike

@TedShifrin So, looks like the official course title is going to be "More Algebraic Topology"

Ted Shifrin

Ah, yes, @Julien, great classic question. Here's a hint: Try to balance from the last one down.

@Mike: Yes, you told me that.

Julien

22:42

@TedShifrin I will try. thanks

Mike

@Ted No, the 'more' was just added.

Ted Shifrin

Oh, I thought I berembered it.

Mike

I like to be cute with official titles when I can.

Alex Gruber is doing a course too... he's teaching the theory of associative loops

Ted Shifrin

teaching? I'm confuzled.

OK, I emailed the guy about the area of a sector of an ellipse from the focus. Done. Letter of recommendation mostly done. Waiting for exams to finish ...

Mike

Well, loops are just not necessarily associative groups.

Ted Shifrin

22:49

But he's teaching? I thought he was a student.

Mike

I don't see the issue with that...

Ted Shifrin

Teaching whom?

Oh great, after our ice age and 5 days of school canceled, now they're threatening tornados for tonight and tomorrow. Sigh.

skullpatrol

Great, more time to watch the Olympics :-)

Ted Shifrin

More likely to lose power/TV if there's really a tornado ... or even my house :D

skullpatrol

:-O

Ted Shifrin

22:53

Actually, I've been totally boycotting the Olympics, but I never watch very much anyhow.

skullpatrol

why?

Ted Shifrin

the nature of Putin's stance on human rights ... Not that I'm happy with much of America, either.

3

skullpatrol

ic ic

they say that Moscow has the most billionaires out of any city in the world

skullpatrol

23:12

Total Number of Billionaires from Russia: 110
Total Number of Billionaires from the U.S.: 442

Astrum

@skullpatrol IMO a high number of billionaires is a consequence of an unfair economic system. Not exactly a positive

skullpatrol

@Astrum I totally agree.

Astrum

I remember a video from some cable news channel of a rich goon saying that it was great that the top 100 or so richest people hold more wealth than the lowest 50%

skullpatrol

It is only "great" for those that ARE rich.

Astrum

Politics suck

skullpatrol

23:18

yep

Astrum

Holy crap, Spivak's Calculus on Manifolds is super dense

and crappy print quality

5space

Can anyone help me out with external direct sums of modules with arbitrary index?

@Astrum, what is your background? (maybe I can recommend book other than spivak?)

Astrum

@5space I just finished Axler's LA (although I'm still a bit shaky on some of the later chapters) and Spivak's single variable book. That's really it for pure math. I'm using Calculus on Manifolds along side Hubbard's multi-variable text

5space

23:33

Ah. That's a good pairing.

Astrum

not sure if Spivak will be too much for me right now, the first chapter is really just a review of inner-products

5space

That's what I did.

Astrum

I'm just a little bit worried about how much mathematical maturity he expects from the reader

5space

I used Spivak as a reference for a class that used Hubbard. Worked really well.

It's spivak, so a decent amount :-). But that's how you obtain the maturity, anyways.

Astrum

@5space I found most of the problems in his single-variable book doable, but I'm afraid I might have forgotten some of it O.o

5space

23:35

I think calc on manifolds is notoriously terse and challenging.

Others have suggested Munkres' Analysis on Manifolds.

Astrum

I'll probably be making a lot of posts here for help, but I think I'll make it through in one piece

5space

I think so!

Astrum

I've heard Munkres is a bit hand-wavy

5space

Looking at Munkres preview on Amazon looks pretty good.

I haven't heard that. I heard it was just more computational than Spivak.

(And likely less terse)

But, Hubbard is a really cool book!

Astrum

Yeah, I think Hubbard will come in handy

I skimmed his treatment of LA, and I already see how much more difficult Spivak is in comparison

5space

23:39

Hubbard has varying degrees of difficult.

It starts out pretty easy (especially the linear algebra)

But once you get to manifolds and forms... it is pretty challenging.

Astrum

That's all I've looked at so far

I can tell you that the book itself is much better quality, Spivak is trash

5space

If you get to forms and are having no problems, you should start reading the appendix too. And read Spivak thoroughly.

Do you mean quality of the actual text?

Astrum

yeah, printing quality

5space

I only have the pdf of Spivak.

But my copy of Hubbard is falling apart.

But, I did use it for 9 months and covered it front to back.

Astrum

I can't work off of pdfs, sadly

5space

23:41

Yeah, I hate it.

Astrum

they start to hurt my eyes after 30 minutes, and it's so easy to get distracted online

5space

I agree.

Astrum

"ooh, look, cat pictures"

5space

I didn't go through spivak very thoroughly. Just when Hubbard confused me.

I also like Pugh's analysis book.

But he doesn't get to the forms and manifolds until 3/4 of the way through.

And it's rather terse, again.

But better than Spivak :-)

Astrum

We'll see how this goes

"Subsets on Euclidean Space"

usukidoll

23:44

Prove that $f: X \rightarrow Y$ is an injection if and only if the equation $\bar f^{-1}(\bar f)(A)=A$ holds that for all $A \in P(X)$. Use this to prove that $f: X \rightarrow Y$ is an injection if and only if $\bar f^{-1}: P(Y) \rightarrow X$ is a surjective. .__.

Astrum

@5space how much (aside from the basic theorems and principles) of single variable ana is used in these texts? As I said, I think I'm a bit foggy on the details, it's been a couple months since I last worked with analysis (other than to review limits and cont.)

usukidoll

any hints to this thing * points uP*

Pedro Tamaroff

@usukidoll Hello.

Astrum

@usukidoll try shouting

usukidoll

bunny help me give hints pleaseeeeee T___T

5space

23:48

When I took the class, I was taking calculus 2 at the same time.

Pedro Tamaroff

What the hell is $\bar f$?

Astrum

@5space O.o

5space

Really, all you need is basics of differentiation.

usukidoll

isn't that preimage?!

5space

If you know $\delta$-$\epsilon$ arguments, then you will be solid.

Pedro Tamaroff

23:49

@usukidoll Why do you put the bar on it?

That's unnecessary.

$\bar f$ is usually used for extensions of $f$ or something of the sort7.

Astrum

@5space So I think I'm good!

5space

You're more than prepared if you did the majority of Spivak.

Pedro Tamaroff

@usukidoll So.

Suppose $f$ is injective.

usukidoll

meaning one to one

Pedro Tamaroff

You want to show $f^{-1}f(A)=A$ for each $A\subseteq X$.

usukidoll

23:53

yes...

isn't there a formula for that? I mean the definition of the inverse

Pedro Tamaroff

One inclusion always holds.

Which one?

usukidoll

hang on

Definition 5.5.10 states that we let $X$ and $Y$ be sets and let $f: X \rightarrow Y$ be a function. If $g: Y \rightarrow X$ satisfies the two conditions $g \circ f = i_x$ and $f \circ g = i_y$, then $g$ is an inverse function of f (or more briefly, and inverse of f).\\

Pedro Tamaroff

Yeah, that is slightly irrelephant here.

I am simply asking this.

Let $f(A)=\{f(x):x\in A\}$.

For $B\subseteq Y$, let $f^{-1}(Y)=\{x\in X:f(x)\in Y\}$.

Then there is an inclusion between $A$ and $f^{-1}f(A)$ that always holds.

Regardless of $f$ being one one or not.

Which one is it?

Transcript for

$Mathematics$ Mathematics