1:55 AM
@robjohn

2:06 AM
Hi @PeterTamaroff
Are you familiar with romberg integration?

@math101 Not really. What is it?

Well i find it quite difficult since you are not given the function but maybe you will find a lead

user19161
@PeterTamaroff Pedro! I am going out for a walk now. It is Sun morning here.

Romberg integration is used to approximate the integral from 2 to 3 f(x)dx. If f(2)=.51342 f(3)=.36788, R_3,1=.43687 and R_3,3=.43662. Find f(2.5)

user19161
@math101 Interestingly, I have never heard of Romberg until now.

user19161
2:13 AM
However, I have heard of Stromberg who wrote a few books.

hahaha

user19161
@skullpatrol Some humans are worse than animals.

4:04 AM
Feel free to take a look at my question

4:36 AM
I'm trying to prove a statement involving a countable set. Can I use induction if I'm showing the result is true for the entire set at once, or is induction only allowed when dealing with finite subsets? I'm asking because every time I've seen induction it has been to show that statement holds for "any n" but not that it actually holds for the whole set at the same time?

4:50 AM
When proving something about a countable set, is it ever not ok to say "WLOG, suppose the countable set is a subset of the natural numbers"

should be ok to just assume it's the natural numbers themselves in that case
i'm not sure what you mean by your earlier question. what is the difference between "P holds for any n in S" and "P holds for the whole set S"?

When I say countable, I include finite.

oh alright.

The former looks like it holds for numbers up to n, whereas the latter holds for all numbers n at the same time.

Are you guys familiar with romberg integration?

4:56 AM
No, I
typo: Never heard of Romberg.

with weak induction you prove P(1) and then prove $P(n)\Rightarrow P(n+1)$, so if you've proved that, you've got it for the whole set - otherwise there would exist an $n$ for which $\not P(n)$, which would then imply $\not P(n-1)$, and so on down to a contradiction of the base case

Of course. Thanks Alexander.

gup
yup*

5:59 AM
Anyone up for some Romberg Integration?

6:17 AM
@math101 I guess everybody is partying hard.

hahaha no one ever likes my questions. One more week of numerical methods and then its out the window
For some reason many people are not familiar with this topic. Its not a course that I would actually suggest. I found it quite boring

@math101 Quite boring = too abstract.

Well I agree on that point but in this case numerical methods was just plain and simply boring. It had no personality

@math101 Why did you take this course then?

I had to take it. And someone had told me that I should take this over Real Analysis. They said Real Analysis was boring but numerical methods was interesting

user19161
6:25 AM
Hi @jayesh. Did you sleep well last night?

@math101 I have a little conviction that it's easier for one to love real analysis. But it's baseless.

user19161
@math101 OK. I suddenly have a feeling I know you, hehe.

user19161
@math101 Well, different people like different things. To me, numerical methods is boring.

@JasperLoy Doubt you know me. I live on the other side of the world

user19161
6:28 AM
@math101 OK. Though I have close friends all over the world now.

user19161
@GustavoBandeira Any progress with Paul notes?

@GustavoBandeira I will end up taking Real Analysis sometime in the coming months anyways

@JasperLoy I'm finding my way through Stewart's book. =)

user19161
@GustavoBandeira OK, though I prefer Paul to Stewart.

user19161
6:32 AM
@GustavoBandeira No, I think if you like Stewart just use that. No need to read Paul again. It's all calculus after all.

@JasperLoy Yep. I got a doubt: People say that Apostol and Spivak are required for a deeper understand of calculus, what you think?

Are you talking about calculus textbooks?

@math101 Yep

user19161
@GustavoBandeira Yes, definitely. Use them if you can handle it. Alternatively read analysis books immediately if you can handle it.

@JasperLoy Hi man. Yup. I slept well. Will go to have lunch now in some time.
@GustavoBandeira Long time!

6:34 AM
@JasperLoy What does Spivak and Apostol books have that others haven't?

user19161
@JayeshBadwaik It was sunny when I was walking just now. I am home now and it is raining.

user19161
@GustavoBandeira Maybe more proofs?

@GustavoBandeira They are more "analysis" than calculus. More proofs rather than techniques. Though solid proofs lead to more powerful techniques, but still.
@GustavoBandeira Things are good.
@JasperLoy Hmm. It is sunny here now. However, it is winter sun now, so kind of warm and fuzzy rather than hot and unbearable.

user19161
@JayeshBadwaik I am going to try out gnomebuntu which should be out on 18 Oct. It will be the first release.

6:37 AM
@JasperLoy As opposed to Unity Ubuntu?

user19161

@JasperLoy Just install gnome shell by yourself.

@JasperLoy I didn't know it was possible to jump into analysis like this.
Any requirements for that?

user19161
@JayeshBadwaik I know, but still it is nice to have something like that.

user19161
@GustavoBandeira Well, any book you read will have things missing. You can even read Rudin's Mathematical Analysis immediately without losing too much info.

6:41 AM

user19161
@GustavoBandeira But I think they will be hard for you, so use what you like.

user19161
@JayeshBadwaik I am a little tired of Debian. Must install wireless firmware separately, must install firefox separately etc.

@JasperLoy Yup. That is always there. If you install Ubuntu, install the LTS version.
Else you will have to clean upgrade every 1 year I think.

user19161
@JayeshBadwaik Yes, I know, but I hate unity.

@JasperLoy You can just install GNOME Shell and then remove Unity.

6:45 AM

user19161
@JayeshBadwaik Yes, tired of that. I am a "perfectionist", always on the lookout for the "perfect" distro.

@JasperLoy Perfection requires some effort. (ArchLinux)

user19161
@GustavoBandeira No, but for any book there are always people who scan their copies online.

user19161
@JayeshBadwaik Too difficult, so not perfect. Linux is not math.

@JasperLoy Hmm. How often do you have to reinstall your distro?
Because in Debian, once you install stuff, basically, that's it.

6:47 AM
I've searched it on google look, and the link ends in edu.tr - I thought it was some university who had the rights to give it for free.

user19161
@JayeshBadwaik Well, you are right. But like I said, I like the "perfect" distro.

Even in Ubuntu LTS. I installed Ubuntu LTS on my dad's computer and haven't touched it since then.
@JasperLoy There cannot be 7 billion perfect distros. :P :P

user19161
@JayeshBadwaik The three J's should make the perfect distro, Jinux, one distro to rule them all.

@JasperLoy Harvard wants its graduate students to be proficient in six subjects.
Algebra, Algebraic Geometry, Algebraic Topology, Differential Geometry, Real Analysis and Complex Analysis. I right now can only be sure of three topics in the above six, that too not grad level for sure. I am not sure if I can learn all the above topics in less than three years. Or can I?
I solved one of the quals. Was able to solve 2/3 Analysis, 2/3 algebra. 1/3 complex analysis.

user19161
@JayeshBadwaik Jayesh, if you read 6 of the nine books in my holy list, you more or less have covered them all.

user19161
6:50 AM
Of course, there is not too much AG per se, but it's better to do more CA first.

@JasperLoy hmm. I am not saying how to approach. I am asking about the time availability.
CA = commutative algebra? hmm.
@JasperLoy Perfect distro is a gone problem. It is like writing a good comprehensive book on the freshman calculus. Has been done too many times.

user19161
@JayeshBadwaik Yes. No need to jump into AG too quickly. Harvard recommends Hatcher, it's a terrible book to me. It is just very hand waving at parts. Benja thinks so too.

@JasperLoy Yeah, he told me so too.

user19161
@JayeshBadwaik Why do you think I am going to write all my books in future?

@JasperLoy :P :P :P

user19161
6:52 AM
@JayeshBadwaik The nine holy books will be used as my base for writing my three holy books.

@JasperLoy hmm.

@Jasper is this one?

Anyway, lunch. BBL. Too much to read, too less time.

user19161
@GustavoBandeira Yes.

@Jasper Ok. Thanks. =)
Really thanks.

6:56 AM
Just be careful. ;-)

bye. goota run.

@Jayesh Oky, cya. =)

7:51 AM
no 1 hour later today.

user19161
8:14 AM
@JayeshBadwaik I see I missed some secrets!

@JasperLoy hmm. yup and no. nothing really secret.

user19161
@JayeshBadwaik OIC, well I look for books now and then online, but eventually I will get a cheap copy of it.

user19161
Different countries also have different copyright laws.

user19161
I think as long as I don't print an entire book and bind it myself it is fine.

user19161
Printing an entire book is also silly as it costs money as well and it ruins the look of your bookshelf.

8:20 AM
@JasperLoy "the look of the bookshelf"!!!! :-o

user19161
@JayeshBadwaik Yeah, I like everything to be perfect.

@JasperLoy I buy a lot of books. But many times, I simply want to read a small portion of the book, or just try out some book. Not necessarily keep it forever. And there are no libraries. So, I use this as a kind of library.

user19161
@JayeshBadwaik Hmm, I think that's alright.

user19161
One can copy a chapter for self study for example, that is considered fair use. =)

My International Edition Baby Rudin costed $7.5. user19161 8:24 AM Mine is a little more than that, also IE. There are so many Rudin's sold and Walter Rudin is not even alive. It makes no sense to sell it for$100.

user19161
It makes sense to the publisher.

user19161
Publishers just want to make money.

user19161
Authors may not make much.

user19161
And many expensive books today are crap, I won't name them, you know which kind.

8:26 AM
But...... but....... copyright is for the authors and helping authors improve creativity in the society. :P :P (I know what you are talking about.)
Its a temporary legal monopoly designed to benefit authors to help bring creative works into the world.

user19161
Creative works? Or 800 page differential equations texts with lots of pictures and no proofs!

@JasperLoy Hahaha. I think I know which book are you talking about.

user19161
@JayeshBadwaik There are many such books.

@JasperLoy Hmm.

user19161
@JayeshBadwaik I am going to take a nap now, see you.

8:29 AM
bye.

integral of $\frac{({1+x^2})^{0.5}}{x}$ ?

Do you mean $\int \frac{\sqrt{1+x^2}}x \, dx$?

yes
finally thanks @MartinSleziak

What about $t=\sqrt{1+x^2}$ and $dt=\frac{x}{\sqrt{1+x^2}}\, dx$?
$$\int \frac{\sqrt{1+x^2}}x \, dx= \int \frac{1+x^2}{x^2} \cdot \frac{x}{\sqrt{1+x^2}}\, dx = \int \frac{t^2}{t^2-1} \, dt$$
The last integrand is a rational function.

1 sec I'll come back
I'll solve it
and be back

8:44 AM
I hope I did not make a mistake there...
In fact, the last integrand is a rather simple rational function: $\frac{t^2}{t^2-1}=1+\frac1{t^2-1}$.

I am on a Ubuntu system now @JayeshBadwaik
@Rajesh, @Martin Long time since we spoke. How are you?

@kan Hi. Long time. Good (about Ubuntu)

Hi, kan

Hi @kan
good to c u after long time

Hey all :-)

8:52 AM
Hi @robjohn. :)

@robjohn Hi.

@MartinSleziak substitution I should use for the last integral $\frac{1}{t^2-1}$ ?

Anything interesting today?

I am trying to construct an example

@RajeshD partial fractions

8:53 AM
@RajeshD Partial fractions

no break through just tryin some integrals
ok
ok wait i'll be back

People, what do you type with? fingers? MUCH faster than me! frets

@kan Well, I am proud of my typing speed, if not the accuracy. :P

@RajeshD partial fractions
$$\frac1{(t-1)(t+1)} = \frac12 \frac{(t+1)-(t-1)}{(t-1)(t+1)} = \frac12 \left[ \frac1{t-1}-\frac1{t+1}\right]$$

@MartinSleziak It looks like $u=\frac1{x^2}$ should work pretty well, too
@MartinSleziak That'd do it :-)

8:56 AM
@robjohn Well, I tried the first one, which seemed reasonable. No doubt there is plenty of others.
$x=\sinh t$ is another reasonable possibility.
I'd say that whenever there is $\sqrt{1+x^2}$, one of things worth trying is $x=\sinh t$.
yesterday, by Martin Sleziak
We have not heard anything from any of the mods in the discussion about blacklisting algebra tag. I believe that after the point that the issue is discussed by MSE users, the rest is up to moderators and their communication with SE. Is that correct?
@robjohn I tried to ask this yesterday, but no of the mods answered to that. (I saw you and Mariano here in chat.)

@MartinSleziak I have been away for a few days with some unavoidable personal issues. Sorry

Well, the only think I'd like to know is whether there is something else I should do. (I feel kind of responsible for that since I started the thread, also I am not in favor of blacklisting.) Or whether at this point I can leave the issue to the mods.
@robjohn You've mentioned that here in chat. I am sorry to hear about that.

@MartinSleziak I'd much rather see some diambiguation solution. It's more helpful.

You mean implementing that feature request from the other thread?
That would be nice.

@MartinSleziak Of course that is up to the developers, not the mods.

9:05 AM
@robjohn Now you're talking about blacklisting or feature request?

The mods can present that thread to the devs and hope for the best :-)
The disambiguation

I guess SE team checks other metas for feature-request, too.

@Jayesh Up for a chat about Linux, Ubuntu, TeX?

they do, but it helps if we prod them :-)

ok. We will see what happens.
At least removing tag makes me feel that I am doing something useful, when I procrastinate here at MSE.

9:14 AM
@MartinSleziak It's not something that will happen overnight. code changes take a while.

I wonder there is a expression for arc length parameterization for Hyperbolic spiral

9:33 AM
@kan Sorry, was afk. If you are still there, then yes.

@JayeshBadwaik Just a few minutes. I will be here...

@kan okay.
@MartinSleziak algebra can be synonnymed to mean algebra-precalculus. This way, people who know the difference in the level of algebra-precalculus and other forms of algebra would not use that tag (undergraduate and above) and people for whom the only algebra is algebra-precalculus (high school level) will not have to learn new terminology by default (although it is a small job of looking up algebra-precalculus but still.)

Perhaps it could be good to suggest this at meat, so that we know what other people think about this?

@MartinSleziak Hmm. I will post it as a comment to your question?

Algebra disambiguation tag or The use of the algebra tag seem to me a reasonable places, where this could be mentioned.
I think it's better than opening a new thread. (There are already many threads on algebra tag.)
@JayeshBadwaik My opinion is that posting an answer would be better than posting a comment.

9:41 AM
@MartinSleziak Okay. I will post an answer on the use of algebra tag question.

More people will notice an answer than a comment and they can upvote/downvote/comment to show what they think about it.

@MartinSleziak Yup.

There.

@kan I am here too.

OK. I want a couple of software suggestions.

9:43 AM
Okay.

How do you organise your files?
Esp. whispers pdf files...

@kan Hmm. Recently I have started using mendeley. Before that, I used tellico. Even before that I decided on using a naming scheme as follows <title>-<author>-<edition>. Everything was in small case, spaces in titles replaced by underscores and using only author's surnames separated by underscores again.
All books, papers etc were in a single folder, and I would use the filter functionality of dolphin to get the book I want. Also, I used recoll full text search engine to search what I wanted to search inside the books.

Hmm. I need to google everything there. :(

@kan dolphin is a simple file browse like nautilus.

OK. And, the math support we get with note takers are awful...

9:51 AM
@kan Yup, that is very very true.

Zim... Aweful.
Have you tried Instiki?

Yup.
I have tried every damn wiki on the planet and zim and everything! :P :P
You have a laptop?

A solution is to host wordpress and mathjax on your laptop and then write in the blog on your laptop. However, previewing sucks.
I write notes in LaTeX, and store them in PDF. I have a folder named writing-desk in my home folder. For every note, I create a folder named as <year>-<month>-<date>-<title> inside that folder, and start writing my notes. When it is finished, I have a script which moves the folder as it is to a folder named completed-notes. And the copy resultant pdf file to a notes folder in the home folder. Then, I use mendeley to organize my notes.
I use recoll to search everything.

Oh, OK. Let me try instiki... It is what underlies ncatlab they say.

10:01 AM
One of the biggest problem personally with all the other software is, they would not have my custom packages. So, for example I cannot type \rob{} which I normally do to get well-sized round brackets. Instead, I would have to type \left( \right) which is much more tedious. Also, using a native LaTeX editor enables you to get advantage of all those tools like great context-based auto-completion from brackets to environment names to simple commands to even custom-defined commands.

Thanks. This chat helped. I'll be back with more questions.

Yup. No problem.

user19161
10:43 AM
@kan I read the TeX transcript and figured out. You should never install TeX from a distro's repositories as it is almost surely outdated.

@JasperLoy Bwuhahaha. ArchLinux FTW.

user19161
@JayeshBadwaik Not going to depend on that...

user19161
No offence, but I think Ubuntu has become one of the worst distros now.

@JasperLoy Hmmm. I too think so, but my friend says it is the best disto now, and it was not good before. Where I see degradation, they see improvement. :-o

user19161
@JayeshBadwaik OK, now we have something in common. =)

10:51 AM
@JasperLoy :-) BTW. see this.
@JasperLoy there?

user19161
@JayeshBadwaik Yes. You just did a Pedro.

@JasperLoy I didn't

user19161
@JayeshBadwaik A Pedro ping has two meanings. I even defined it in this chat.

@JasperLoy Okay. Got it I think.

user19161
@JayeshBadwaik I think Marilia does the same.

11:02 AM
@JasperLoy BTW See this. (This would not have been a pedro ping. right?)
@JasperLoy Hmm.

user19161

11:31 AM
hi @Aki

user19161
12:01 PM
Hmm, my sunburn is starting to show up.

user19161
@JayeshBadwaik FTW seems to have many meanings from Urban Dictionary.

user19161
@kan Just label everything by author title and dump everything into the right folder. What's there to organise?

user19161

@JasperLoy Hello. Thanks for your suggestion. :-)

user19161
@kan You like Unity? I prefer GNOME shell. It is cleaner.

12:11 PM
@JasperLoy Just started Ubuntu, dude!

12:57 PM
@JasperLoy folder? folder? folder? We no want no folders.
We want tags, and in its absence will deal in rags.
But we want no folders, we want to be bolder. :P :P

Hi!

@NickKidman hello.

hey, rimes
I LOVE rimes
the path of love is never smooth, etc.

hahaha. I like writing limericks. My writings are crappy though, so I don't record them.

question: Who was the first to come up with a set theoretic universe?
I actually write poems, some are about math/physics
and I inspire others to do so too

1:00 PM

problem is, they are not in english
and usually contain lots of insiders

@NickKidman ohh. :-( Hmm.

I got sick and my mom came to me with a medicine which I believe she received from the Curiosity in Mars: Milk with Kale, at first, I looked at her face with this music in mind, but when I proved it, it was amazing! I felt like 0:45 of the same music!!!

1:27 PM
@JayeshBadwaik: That's from a friend. It will make not too much sense to you though... i.imgur.com/D6fBH.jpg

@NickKidman Does the last stanza it have something to do with the observation of quantum phenomenon leaving a changed state while the first one describes the finite matrices that should be used instead of the logically correct infinite dimensions matrices?

@JayeshBadwaik: Well ya, I just realize that that text was actually her answer to a version of some lines I came up with in the PhysicsStackExchange chat, where the weekly discussion ended up being shorter than expected. The moderator was expressing his disappointment and then I wrote
Some chats are long and some are short, but all are of finite cardinality
I'm okay with that, because in the end, I think what counts is just the quality
Some chats are odd, but like my mother said: life's like a box with a cat
The axiom of choice is probably false, and so you never know, what you gonna get

Ohh! now it makes sense.

as a side note, I don't believe/disbelieve in a factual truth of axioms
that was just so it works with the rime
can one shortly say how the Gödel, von Neumann and Grothendieck universes are different? They were introduced in this order right? I guess they differ in what one wants to acchieve. Which is the "best" one? Is the Grothendieck one made up to work with categories?
say there is a function, which can only be evaluated in exponential time (the algorithm is in Exp)
can it be that there are certain values x_i in the domain, so that if I know them (say I compute them once and store them in a library), then I can compute all the functions other values in shorter time?
say the domain is 100 values and my function is f. Can it be that it's such that if I know a (special) subset of 10 values of these 100, so that all the other 90 are easy to compute?
some people
some people seem not to like set theory. But I mean something like category theory is not an alternative, is it? Category theory in itself is about nothing. Are there any computations/results, which don't involve any set at all and you still have something besides a structural result? How can it be a foundational theory, if it doesn't contain say differential forms before you introduce some set for a category to work with it?

2:27 PM
bump

@NickKidman Sorry, I cannot help you there. However, just found this when searching.

can the cubes of three consecutive positive integers be divisible by 27 if the sum is odd?

$3^3\mid n^3$ $\Leftrightarrow$ $3\mid n$

How do i solve this?
should i write* all the coungruence classes?

$n=3k$ implies $n^3=27k^3$ is divisible by 27
If $n=(3k\pm 1)$ then you can rewrite $n^3=(3k\pm 1)^3$ using binomial theorem to see that it is not even divisible by 3.
If it's no divisible by 3, it is not divisible by 27.
I hope I understood your original question correctly.

2:42 PM
sorry I wrote the problem wrong

@JayeshBadwaik: I don't think that the paper relates to my questions very much...

can the sum of three consecutive cubes be divisible by 27
if it is odd

new question: With a program written in a functional programming language, where the program is a huge function - where am I to imagine the running memory?
should I view the fuction as devided into several function, and at every evaluation, the big blog called working memory gets changed?4
I feel then this isn't very different from other paradigms

new question
can $3n(n^2+6)$ be an odd perfect cube?

3:15 PM
what is the closure of a poset? Like what is cl({4,9}) in the natural numbers?

@jayesh hi god of victory!!!

@NickKidman, you don't need to think about memory layout - just asymptotic volume.

@spernerslemma: What is this volume?

O(n) O(n^2) etc

the total volume of the biggest intermediate dataset?
but where is the memory?
f is the program, x is the input, where is the intermediate memory?
if "x -> f(x)" is all there is, how do I analyse the need for memory from that?
given f, how to read it off (it must be somewhere in there, but imagining a tape is easier)

3:22 PM
Do you know what O(n) means?

the required memory goes linearly with the input length?

My problem is just this: If I write a procedural program, there I hardcode where to write which memory, produce and read intermediate values etc. But if I have a functional program (just one function), then where is this memory tape? How to find out e.g. that f needs O(n)

just estimate the memory usage (in a strict language) as all the sum of the memory usage of all the objects (including functions) that need to be alive (not garbage collectable) at one time
@NickKidman, You can use category theory as a foundation of mathematics by postulating the existence of categories with things like induction (for example) in them

3:46 PM
@Argon Hey Aaron!

@Charlie Hi

@Argon wassup?studying for your n-th test?

@Charlie Physics tomorrow :)

@Argon again?I thought I was the only one who had a test per week...
@Jayesh !!!!

@spernerslemma: You mean certain categories? But then you still need classes, i.e. you postulated some sets after all. The only difference might be you don't need logic axioms, is that it?
brb

3:53 PM
I don't understand

@NickKidman naah it doesn't just thought it was interesting. and somewhat related.
@Charlie Hii!!