Mathematics - 2012-10-11 (page 1 of 4)

Jayesh Badwaik

12:00 AM

@Link stop guessing in the dark! You should have atleast some light to wander around!

Link

i get it not

sin3x = sin(x+2x)

user19161

@Link sin2A=sin(A+A) and sin3A=sin(2A+A). Use these together with the addition formula.

Link

= sin x cos 2x + sin 2x + cos x

is that right?

Jayesh Badwaik

@Bitrex Just a min. I am working on it. I do not guarantee a solution though.

user19161

The problem with math teachers these days is that they throw formulas around without explaining how they work so students are left confused.

Bitrex

12:01 AM

Supposedly, $\sum_{n=0}^{\infty}\frac{N!N!}{(2N)!} = \frac{4}{3} + \frac{2\pi}{9\sqrt{3}}.$

Link

yes

:C

user19161

Not all math teachers suck, but most of them do.

Peter Tamaroff

@Bitrex Do you wanna prove that?

Ian Mateus

$\sum_{n=0}^{\infty}\frac{N!N!}{(2N)!} = \sum_{n=0}^{\infty}\frac{N!(2N -N)!}{(2N)!} = \sum_{n=0}^{\infty}\frac{1}{2N \choose N}$ Maybe?

Bitrex

@PeterTamaroff I'm trying to think up an approach to think about proving it :)

user19161

12:02 AM

So @link first work out sin 2A from sin (A+A) and then use that to work out sin 3A.

Link

okay

sin(2x) = sin(x)cos(x) + cos(x)sin(x) = 2 sin(x)cos(x)

user19161

And you may ask where the addition formula for sine comes from. Well, from geometrical considerations, and that is a little difficult to prove.

Link

is that work right?

user19161

@Link Yes.

Link

yay

then i would do sin x + 2 sin(x) cos(x)?

user19161

12:06 AM

@Link Well, apply the addition formula to sin(2x+x).

Link

sin(3x)

Jayesh Badwaik

@Bitrex Probably this will help.

Bitrex

everything comes from euler's formula, geometry can get stuffed!

Link

or you mean the sum formula?

user19161

@Link Whatever you call it.

Link

12:07 AM

so sin (2x + x ) = sin 2x cos x + sin x cos 2x

user19161

@Link Yes. Now you need to know what is cos 2x. That can be found from cos (A+B)=cosAcosB-sinAsinB.

Link

okay

so then it comes out to sin 2x cos x + sin x (cos x cos x - sin x sin x)

like that?

user19161

@Link NO.

Link

hmm

user19161

cos 2x = cos (x+x)

Link

12:12 AM

arrgh

oh yea

:C

user19161

Like I said, read your textbook 9000 times first.

Link

sin 2x cos x + sin x (cos x cos x - sin x sin x)

:D

user19161

OK, now expand everything out.

Link

okay

user19161

Once this stupid teacher said she must "drill" the students. But drilling them with all the wrong things makes them learn the wrong things.

Link

12:15 AM

sin 2x + cos x + sin x cos^2 x - sin^3 x

i think i did tht right

user19161

So they can move symbols around, but without understanding the reason the movements all become wrong later on.

Link

i agree

i had to relearn deriatives the hard way

user19161

@Link How did the times become a plus?

Link

i could do them

just didn't know why

whuch one?

user19161

@Link Look carefully.

Link

12:17 AM

it goes sin2x cos x + sin x ( cos^2 x - sin^2 x) = sin 2x cos x + sin x cos^2 x - sin^3 x

user19161

@Link Exactly, which is not what you wrote.

Link

ooh

:c

do i expand the sin out now?

user19161

2 mins ago, by Link

sin 2x + cos x + sin x cos^2 x - sin^3 x

Link

oops

user19161

@Link You expand the sin 2x now.

Bitrex

12:19 AM

@JasperLoy 4.bp.blogspot.com/_iagsTXV5Xys/SvCVeHrV6pI/AAAAAAAACW8/…

Link

okay

i got it now

thanks

user19161

@Bitrex So true. I hate some of these teachers. I talked to them and they acted as if I know nothing about mathematics when it is they who know nothing.

user19161

@Link We are not done yet.

Peter Tamaroff

@Bitrex I think I can help

Jayesh Badwaik

@PeterTamaroff I'm listening.

user19161

12:22 AM

@JayeshBadwaik Hehe.

Peter Tamaroff

@JayeshBadwaik No, you're not.

Jayesh Badwaik

@PeterTamaroff I am. Serious.

user19161

@JayeshBadwaik I think we usually don't abbreviate that.

Jayesh Badwaik

@JasperLoy Thanks.

user19161

@link Have you been kidnapped?

Peter Tamaroff

12:24 AM

@JayeshBadwaik OK

user19161

@PeterTamaroff Wrong line.

Peter Tamaroff

@JayeshBadwaik Consider $a_n=4^n {2n\choose n}^{-1}$

Jayesh Badwaik

Okay.

Peter Tamaroff

Now, express $a_{n+1}$ in terms of $a_n$.

You'll need just a little manipulation.

hhh

Am I understanding the term "positively definite" correctly?

Peter Tamaroff

12:27 AM

$${a_{n + 1}} = \frac{{2n + 2}}{{2n + 1}}{a_n}$$

Jayesh Badwaik

Well $a_{n+1} = 4\frac{(n+1)^2} {(2n+2)(2n+1)}$

Peter Tamaroff

@JayeshBadwaik Whuuuu?

hhh

img [i.stack.imgur.com/NTRYZ.jpg]

Jayesh Badwaik

@PeterTamaroff $a_{n+1} = 4^{n+1} {2n+2 \choose n+1}^{-1}$

Peter Tamaroff

Yes.

hhh

12:29 AM

(the arbitrary $\bar x$ is defined inside an unit ball, can the norm be arbitrary?)

@PeterTamaroff To me?

Jayesh Badwaik

@hhh Please do not post long images in between conversations? It destroys the continuity for other people.

hhh

-

Jayesh Badwaik

@hhh Yup.

Peter Tamaroff

@hhh Nope, sorry.

@JayeshBadwaik $$\frac{{2\left( {n + 1} \right)}}{{\left( {2n + 1} \right)}}{a_n} = {a_{n + 1}}$$

This can be written as:

Jayesh Badwaik

@PeterTamaroff yup, we have written the same thing.

Except I did not write $a_{n}$

Anyway, I agree with you.

Peter Tamaroff

12:32 AM

@JayeshBadwaik OK, now we write that as

$$2\left( {n + 1} \right){a_{n + 1}} - {a_{n + 1}} = 2n{a_n} +2 {a_n}$$

Jayesh Badwaik

Okay.

user19161

I think Link has been kidnapped. Send in the special force!

Peter Tamaroff

@JayeshBadwaik Now consider the generating function $A(x)$ of $a_n$

This means

Jayesh Badwaik

@PeterTamaroff Ahh.

Peter Tamaroff

@JayeshBadwaik You'll get a diff eqn

Jayesh Badwaik

12:33 AM

Hmm. Yup.

Peter Tamaroff

@JayeshBadwaik I leart that easy case from this here

Jayesh Badwaik

okay.

Yup, so we solve for the function and then put in the appropriate value of $x$ to get the summation of $a_{n}$. Neat.

Peter Tamaroff

@JayeshBadwaik Yeah =)

Jayesh Badwaik

@PeterTamaroff I somehow got stuck in the ratio and was trying out convergence tests to first determine whether the sequence actually converges or what.

It obviously does though. Since the term decreases exponentially fast.

Peter Tamaroff

@JayeshBadwaik Hmmm. I want to prove that if $a_n$ is Cauchy then it converges. Should it be too long of a proof??

user19161

12:40 AM

@PeterTamaroff You need completeness of course.

Jayesh Badwaik

@PeterTamaroff It actually depends on completeness of the space.

Peter Tamaroff

@JayeshBadwaik You should use Wallis' approximation.

@JayeshBadwaik I'm on $\mathbb R$.

Jayesh Badwaik

@PeterTamaroff Yup. I used that.

Peter Tamaroff

@JayeshBadwaik Oh, OK.

Jayesh Badwaik

@PeterTamaroff It is not a long proof. Quiet simple actually.

user19161

12:41 AM

@PeterTamaroff Depends on what theorems you already have.

Peter Tamaroff

@JasperLoy Bolzano Weierstrass, Monotone Conv.

user19161

@PeterTamaroff Did we do this before? We can just use the fact that every sequence in R has a monotone subsequence. That leads to a neat proof.

Jayesh Badwaik

@PeterTamaroff You should be able to do it on your own then. Its quiet concise then.

user19161

@JayeshBadwaik See my above remark. It is the most beautiful proof ever.

Peter Tamaroff

@JasperLoy Ever?

Jayesh Badwaik

12:45 AM

@JasperLoy Yup. That is how I did it.

user19161

@PeterTamaroff Yes, to me. Beauty is in the eye of the beholder.

Jayesh Badwaik

@PeterTamaroff By now you should have realized that @JasperLoy talks in hyperbole.

user19161

@JayeshBadwaik Yes, for instance, 9000.

Peter Tamaroff

@JasperLoy Well, Spivak does this: Proves every Cauchy sequences is bounded, then prove it has a conv subsequence. Then he asks me to prove that if a subsequence of a Cauchy sequence converges, the original sequence does. I think I can do it. At least, I can picture the idea.

user19161

@PeterTamaroff Well, the convergent subsequence can just be taken as the monotone one I speak of. Alternatively, use the ones that go to limsup or liminf.

Peter Tamaroff

12:52 AM

@JasperLoy Yeah. Now I'm thinking: Say $\{a_{n_j}\}$ is the subseq.

user19161

@PeterTamaroff I will give you the hint for the monotone proof.

Peter Tamaroff

Then there is an $\ell$ such that for every $\epsilon >0$, there is an $N$ such that $$|a_{n_j}-\ell|<\epsilon$$ whenever $n_j >N$

@JasperLoy Shhhuuuuuuush!

2

skullpatrol

hi @Charlie

Charlie

@skullpatrol Hello!

Peter Tamaroff

$$\left| {{a_n} - \ell } \right| < \left| {{a_n} - {a_{{n_j}}}} \right| + \left| {{a_{{n_j}}} - \ell } \right| < \frac{\epsilon}{2} + \frac{\epsilon}{2}$$

@JasperLoy Done!

user19161

12:56 AM

@PeterTamaroff Yes, that is the idea and where the Cauchiness comes in. Now do you know how to get the monotone subsequence?

Peter Tamaroff

@JasperLoy I already got it.

user19161

@PeterTamaroff OK, well done. Can I befriend you?

Peter Tamaroff

@JasperLoy Maybe.

Jayesh Badwaik

@JasperLoy You have to be on fb first.

user19161

Hey guys, do you know why you will never find me on FB now?

user19161

12:57 AM

Because I have no FB account! QED.

user19161

@peter What is your proof of the existence of the monotone subsequence?

Peter Tamaroff

@JasperLoy I show the Cauchy sequence is bounded. Not monotone subsequence, but CONVERGENT subsequence.

user19161

@PeterTamaroff Ah OK. Want to hear the other proof?

Peter Tamaroff

@JasperLoy The more the merrier.

user19161

@PeterTamaroff OK, now we want to show that every real sequence has a monotone subsequence. Call a term in the sequence a peak if it is greater than or equals preceding terms. If a sequence has infinitely many peaks, we have an increasing sequence. If it only has finitely many, we have a decreasing sequence.

Peter Tamaroff

1:01 AM

@JasperLoy That is how Spivak does it!

@JasperLoy But it is a little informal for my taste.

=O

user19161

@PeterTamaroff Wonderful. And of course, you know that a monotone sequence converges if and only if it is bounded!

Peter Tamaroff

@JasperLoy Yeah.

Charlie

@jayesh you're in my ears and in my eyes

user19161

@PeterTamaroff Now I can be your friend. =)

Jayesh Badwaik

@Charlie I am not penny lane! :-)

user19161

1:02 AM

@Charlie OMG.

Charlie

@JayeshBadwaik \o/

user19161

Is Jayesh and Charlie getting married soon?

skullpatrol

Do you wanna go to the wedding?

user19161

Maybe.

skullpatrol

Why?

user19161

1:04 AM

Why? Why not?

skullpatrol

I'm not going because I'll start crying :(

user19161

@skullpatrol Why? Is it because you want to marry one of them instead?

skullpatrol

Why? Why not?

Charlie

@jayesh are you reading this???

Jayesh Badwaik

@Charlie yeah.

user19161

1:07 AM

I think skullpatrol and anon should get married. It will be an anonymous wedding. =)

4

Charlie

@JayeshBadwaik did you rest?

Jayesh Badwaik

@Charlie 3.5 hours. No worries, will sleep later.

skullpatrol

@JasperLoy I think Jasper Loy and Good Will Hunting should get married. It will be a match made in heaven :-D

Charlie

@JayeshBadwaik ok.i may sleep...

soon

user19161

@skullpatrol Now that is just rubbish!

Jayesh Badwaik

1:09 AM

@Charlie Okay. good night!

user19161

I hate it when people star and then unstar my message.

Charlie

@JayeshBadwaik i listened to 4 Beatles album

skullpatrol

@JasperLoy You once said you're here to take out the garbage.

user19161

@skullpatrol That is because I am Will Hunting. How can I marry myself? Duh.

Charlie

@JayeshBadwaik Night!

Jayesh Badwaik

1:11 AM

@Charlie Nice. I got your octopus. Same here.

@Charlie good night.

skullpatrol

@JasperLoy You are?

Charlie

@JayeshBadwaik :DDDD

@JayeshBadwaik It will be a good night!

user19161

@skullpatrol Yes, I am. I am not Matt Damon. I am Will Hunting. QED.

Jayesh Badwaik

@JasperLoy I thought you were Ben Affleck.

skullpatrol

@JasperLoy Thanks for the information.

user19161

1:12 AM

Wait. Who is sleeping, Jay or Charlie?

Jayesh Badwaik

@JasperLoy Charlie. It is morning here.

user19161

@JayeshBadwaik Do you celebrate Deepavali?

Jayesh Badwaik

@JasperLoy Yup. It is one of the two of the festivals I always look forward to.

user19161

@JayeshBadwaik And the other one?

Jayesh Badwaik

The other is Holi.

user19161

1:17 AM

Not heard of here.

user19161

Is that like Thaipusam?

Jayesh Badwaik

No.

It is more like Baisakhi.

It is the the occasion of crop harvesting.

user19161

It's quite scary to see people piercing themselves.

skullpatrol

@JayeshBadwaik What festival do you not look forward to?

user19161

I would not even want to wear an ear ring if I were a girl.

Jayesh Badwaik

1:19 AM

@skullpatrol We have around 30-50 festivals in here. I cannot look forward to everyone of them!

user19161

I always look forward to Christmas and New Year's Day, just because of the mood.

Jayesh Badwaik

There are three or four which I observed diligently. Rest, I do not pay much attention.

@JasperLoy Festivals are always about the moods.

skullpatrol

I don't like Halloween.

user19161

I think I will skip all horror movies now.

skullpatrol

But you like vampire movies.

Jayesh Badwaik

1:21 AM

@JasperLoy Okay, so power is gone, I might sign out soon. Bye. Good day!

user19161

@JayeshBadwaik See you.

Jayesh Badwaik

Or hope the power comes back in less than 10 minutes.

skullpatrol

@JayeshBadwaik Do you have anything similar to Halloween?

Jayesh Badwaik

@skullpatrol We have a festival for the dead, but it is quite formal and all. No funny stuff and not a big deal actually.

For children's fun, we have other festivals like Kojagiri among others.

skullpatrol

@JayeshBadwaik So there is a festival for every mood?

Jayesh Badwaik

1:27 AM

@skullpatrol Yes.

skullpatrol

@JayeshBadwaik Combined with each age group?

Jayesh Badwaik

There is a festival for appreciating the eldest sibling in the family since he has to deal with first-time and hence inexperienced parents etc etc.

@skullpatrol yup.

Most of them are not big deal. You would not find people stopping their work on every one of them.

skullpatrol

Are there festivals for men only or women only?

Jayesh Badwaik

There are some important ones, but others are taken in stride.

@skullpatrol Hmm. Not really. There are special festival(s) (I am not sure if there are more than one) for women, but men are included there too.

skullpatrol

hi @jeighjoans

leo

1:38 AM

@PeterTamaroff hola!

Peter Tamaroff

Te perdiste la diversion @leo

un poquito de secuencias de cauchy por aqii y por alla

leo

@PeterTamaroff estaba viendo tu pregunta en el main

que, ya salió?

Peter Tamaroff

ahh la de la aritmetica de la secuencia?

leo

si

Peter Tamaroff

si salio que??

leo

1:52 AM

@PeterTamaroff que si ya pudiste demostrarlo

Peter Tamaroff

ahh... no esta casi twrminada la demostracion? Que crees?

leo

@PeterTamaroff I'm not sure that you always con choose the $N$ and $n_0$ properly. However I don't know how to explain why

Peter Tamaroff

Hmmm

leo

@PeterTamaroff perhaps I'm wrong

Peter Tamaroff

Como lo harias vos?

leo

2:02 AM

@PeterTamaroff igual que tu. Llegaría al punto en que está el post y entonces no sabría como seguir

Peter Tamaroff

@leo =P

leo

@PeterTamaroff tengo otra forma, pero solo sirve para $a_n$ monótonas

skullpatrol

@anon Is there anyway to format your link:
5 Main Chatroom Etiquette Rules | Latex Support for Chat - 5h ago by anon ▼
into the title description:
Associated with Math.SE; for both general discussion & math questions alike. Please see meta.math.stackexchange.com/questions/3890/… for the rules ("ChatJax" link contained therein).

anon

My answer is the same as last time: I don't know how to format links in the chatroom description. (I still haven't even looked into it.)

Peter Tamaroff

@anon Hey

anon

2:04 AM

also I had no idea that triangle was copypastable

Peter Tamaroff

Maybe you can help?

anon

ah, cesaro sums

pretty sure I have an answer for that over $\Bbb C$ somewhere

Peter Tamaroff

@anon No, Cesàro sums are different.

anon

how so?

leo

How

Peter Tamaroff

2:07 AM

They are $$\frac{s_1+s_2+\cdots+s_n}{n}$$ where $s_n=\sum_{k=1}^na_k$

anon

oh right

Peter Tamaroff

This is just the arithmetic mean.

One is the average of the terms, the ohter is the average of the partial sums =)

That's a nice way to remember it.

leo

@PeterTamaroff you can take $a_k=b_{k+1}-b_k$ with $b_1=0$ and then it is a Cesàro sum

Peter Tamaroff

@leo Well, yeah.

anon

@PeterTamaroff I have to back AD's approach, it's more or less what I had in my answer I'm not going to bother finding.

Peter Tamaroff

2:10 AM

@leo But it is not the original sequence =P

anon

You can of course rephrase it without limsups if you want.

leo

@PeterTamaroff you can fix it

:-)

anon

n(n+1)(2n+1)/6

leo

that one

Peter Tamaroff

@leo LAWL =P

user19161

2:14 AM

Hmm, I am trying to think of a really short proof for Pedro.

user19161

I seem to have dreamed about this 9000 years ago.

skullpatrol

Maybe you're dreaming about this right now.

Peter Tamaroff

I have to sleep now! @leo I'm almost finishing with Spivak's book!

Then I'll go on with Algebra, maybe.

user19161

@PeterTamaroff Well done!

leo

@PeterTamaroff that's great!

user19161

2:17 AM

@peter Is the converse true?

Peter Tamaroff

@JasperLoy Too late for mindgames!

user19161

@PeterTamaroff OK, I will see you in your dreams.

skullpatrol

welcome back @JayeshBadwaik

Peter Tamaroff

I need to get the cymbals monkey going in my head now..

►

Jayesh Badwaik

@PeterTamaroff you solved every problem from the book?

Peter Tamaroff

2:19 AM

@JayeshBadwaik Nah, but I usually worked out the relevant ones.

I still have lots of exercises to solve, though!

LOTS OF THEM!

user19161

@PeterTamaroff Good, good!

user19161

@PeterTamaroff That monkey looks a little like you.

skullpatrol

How can you say you're finished with the book?

Jayesh Badwaik

@PeterTamaroff Hmm. I thought you solved every one of them. Then I would have given you the title of superperspicacious.

Peter Tamaroff

@JayeshBadwaik I'll let you know when I do

@skullpatrol " I'm almost finishing with Spivak's book!"

user19161

2:22 AM

@PeterTamaroff Almost means except for a finite number of pages.

Jayesh Badwaik

@PeterTamaroff about your cesaro sums thing, I think you have got it correct, the stolz cesaro thing.

Do you want verification for the upper part?

Peter Tamaroff

@JayeshBadwaik Yes! Please!

@JayeshBadwaik It is an awesome theorem to have at handy, like LH-

Jayesh Badwaik

@PeterTamaroff Yup! Totally agree.

user19161

@JayeshBadwaik Also very beautiful.

user19161

Ah, I think I am going to bed as well. Over and out!

Jayesh Badwaik

2:27 AM

@JasperLoy dude, self-study is hard. You not only have to study, you also have to find out what to study (which is infinitely difficult). You can study single books and get stuff from one direction (mainstream stuff), but so many things are not given in a single book! And things which are not mainstream fall through the cracks.

user19161

@JayeshBadwaik Better than studying at crap places under crap lecturers and syllabi. You know what I am thinking of...

Jayesh Badwaik

@JasperLoy Hmm. Prolly.

user19161

@JayeshBadwaik Hehe. But if you stick to my nine holy books, you can't go wrong.

Jayesh Badwaik

@JasperLoy Blah. I think even they would miss something or the other. Rudin already misses some stuff. Point is you cannot focus on a single book.

user19161

@JayeshBadwaik Actually, self study to me is not hard. Solving my life problems is hard. Like I said, if not for them I might have won the Fields Medal by now. =)

Peter Tamaroff

2:30 AM

Sanity check please! It is too late...

user19161

@JayeshBadwaik Yes. My point is, every book will leave out something important.

user19161

@PeterTamaroff You should be in bed now dude.

Jayesh Badwaik

@JasperLoy Self-study is not hard to me either. But you lose out important stuff, which it is not possible for you to know is important or even to know it exists.

Peter Tamaroff

@JasperLoy Yeah. Bye.

user19161

@JayeshBadwaik I knew important stuff precisely because I ignored the lectures and lecturers...

Peter Tamaroff

2:32 AM

@JayeshBadwaik That's why we need to research!

Jayesh Badwaik

@PeterTamaroff research? as in?

user19161

@JayeshBadwaik Meaning read up on your own dude.

Jayesh Badwaik

@JasperLoy hmm. Okay. like that. Yup! You are correct.

user19161

@JayeshBadwaik I have looked through 9000 course syllabuses and 9000 books. Even though I don't know the math now, I know about the math.

Jayesh Badwaik

@JasperLoy Hmm.

user19161

2:34 AM

@JayeshBadwaik But your Artin book is a great choice. In particular it covers geometrical aspects not treated elsewhere.

Jayesh Badwaik

@JasperLoy Yup, that i observed. It is really nice in that aspect.

Also, it has really good miscellanous questions which are like exploration to other areas sometimes not covered in book.

user19161

The Fraleigh book I really dislike, even though it is very popular too. I dislike Herstein too.

user19161

I do like the Artin book but I don't have a copy nor am I gonna read it now.

Jayesh Badwaik

@PeterTamaroff Seems correct to me. your solution. of that DE.

@JasperLoy hmm. It is noon at your place right? You sleep at this time? Don't you feel uncomfortable due to excessive body heat?

user19161

@JayeshBadwaik Well, when the mind is troubled, the body is immune...

Jayesh Badwaik

2:39 AM

@JasperLoy I would have thought otherwise. When the body is healthy, it stabilizes your mind and makes it less troubled.

user19161

@JayeshBadwaik I am weird. Nature's laws do not apply.

leo

@PeterTamaroff what is asked in your post follows from a theorem by Toeplitz. No Wikipedia link to that theorem

Jayesh Badwaik

@JasperLoy :P

@leo which question I mean?

leo

2

Q: If $a_n\to \ell $ then $\hat a_n\to \ell$

I need some help to finish this proof: THEOREM Let $\{a_n\}$ be such that $\lim a_n=\ell$ and set $$\hat a_n=\frac 1 n \sum_{k=1}^na_k$$ Then $\lim\hat a_n=\ell$ PROOF Let $\epsilon >0 $ be given. Since $\lim a_n=\ell$ , there exists an $N$ for which $$\left| {{a_n} - \ell } \right| <...

user19161

@jayesh I am planning to study six of the nine books next year as mentioned, and also aiming for complete recovery by end of next year. But these are just plans. I don't know what is gonna happen to me...

Jayesh Badwaik

2:44 AM

@JasperLoy You will succeed in your recovery and consequently mathematics.

@leo this one?

user19161

@JayeshBadwaik Yeah, we might even meet in grad school one day...

Jayesh Badwaik

@JasperLoy Hopefully!

user19161

@JayeshBadwaik Anyway, with regard to Indian food, I think I like masala tosai.

Jayesh Badwaik

@JasperLoy It is my favorite too. Masala dosa and idli sambhar.

Peter Tamaroff

@leo interesante! Toeplitz??

user19161

2:50 AM

@JayeshBadwaik There is another book that treats the geometry of algebra, online for free. It is Goodman's Algebra.

user19161

At this rate, Pedro will never go to bed.

Jayesh Badwaik

@JasperLoy okay. thanks!

leo

@JayeshBadwaik almost. It something similar. The one I say changes the first hypothesis by the boundedness of $(a_{nm})_n$ for each $m=0,1,\ldots$

@PeterTamaroff yep

Peter Tamaroff

@leo link??

user19161

@peter Check out Goodman's Algebra too. It is very good and it is online.

leo

2:53 AM

boundedness of columns

@PeterTamaroff let me see

@PeterTamaroff follows from this one

@PeterTamaroff can you see it?

John Smith

3:18 AM

achh

skullpatrol

5:53 AM

Can anyone believe Einstein's "God Letter" is being sold on ebay?

What's next, Gauss's unpublished theorems on Craig's List?

Jonas Teuwen

@skullpatrol I hope so!

skullpatrol

@JonasTeuwen Me too :-D

The opening bid for the letter was $3 million...

@JonasTeuwen I was just reading Gauss's diary was only 19 pages long.

Jonas Teuwen

6:14 AM

"Did maths today"

skullpatrol

"Discovered something."

That's roughly 1/3 of a page for every year or 1 paragraph/year.

Jayesh Badwaik

6:42 AM

@JonasTeuwen Silly question, but how can I update an information of file from google books etc by just entering the ISBN of the book in Mendeley?

Jayesh Badwaik

6:57 AM

@JonasTeuwen Look at Tellico. It probably does everything that mendeley does and does it better. Except for syncing though. However, I do not use syncing as of now, so its no bigggie. And I guess, if I want to, I will just sync a git repo for the library.