@robjohn

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

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)

hahaha

Feel free to take a look at my question

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?

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?

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*

Anyone up for some Romberg Integration?

@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

@JasperLoy How was your walk?

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

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

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

@JasperLoy Yep, but I'll not ignore your advice, I'll read it too.

@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

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

@GustavoBandeira Long time!

@JasperLoy What does Spivak and Apostol books have that others haven't?

@JayeshBadwaik Yep. How are things?

@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.

@JasperLoy As opposed to Unity Ubuntu?

@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?

@JasperLoy Thanks for the advice.

@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.

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

@JasperLoy Is this book distributed for free?

@JasperLoy Perfection requires some effort. (ArchLinux)

@JasperLoy Hmm. How often do you have to reinstall your distro?

Because in Debian, once you install stuff, basically, that's it.

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.

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

I solved one of the quals. Was able to solve 2/3 Analysis, 2/3 algebra. 1/3 complex analysis.

@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.

@JasperLoy Yeah, he told me so too.

@JasperLoy :P :P :P

@JasperLoy hmm.

@Jasper is this one?

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

@Jasper Ok. Thanks. =)

@JayeshBadwaik Thanks. =)

Really thanks.

Just be careful. ;-)

@JayeshBadwaik With what?

bye. goota run.

@Jayesh Oky, cya. =)

no 1 hour later today.

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

@JasperLoy "the look of the bookshelf"!!!! :-o

@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.

My International Edition Baby Rudin costed $7.5.

There are so many Rudin's sold and Walter Rudin is not even alive. It makes no sense to sell it for $100.

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.

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

@JasperLoy Hmm.

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

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 :-)

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

@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 :-)

@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 $x=\sinh t$.

@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.

@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 algebra tag makes me feel that I am doing something useful, when I procrastinate here at MSE.

@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

@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.

@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.

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...

@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?

@JayeshBadwaik Yups.

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.

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.

@JasperLoy Bwuhahaha. ArchLinux FTW.

@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

@JasperLoy :-) BTW. see this.

@JasperLoy there?

@JasperLoy I didn't

@JasperLoy Okay. Got it I think.

@JasperLoy BTW See this. (This would not have been a pedro ping. right?)

@JasperLoy Hmm.

hi @Aki

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

@JasperLoy Just started Ubuntu, dude!

@JasperLoy folder? folder? folder? We no want no folders.

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

@NickKidman Can I read some?

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!!!

@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

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?

I just had an idea:

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?

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.

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?

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)

Do you know what O(n) means?

the required memory goes linearly with the input length?

yes

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)

@JayeshBadwaik Jayesh,are you there?

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

@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

I don't understand

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

@Charlie Hii!!

@JayeshBadwaik How are you?

@Charlie Good.

@JayeshBadwaik :D

Hello this question is fascinating math.stackexchange.com/questions/213601/square-of-polynomial/…

does it have a connection to hasse-minkowski?

I understand his use of pell equation, that's really nice