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00:00
Random thought: My youngest sister studied at Trondheim for a year or so before she finished her PhD in Scandinavian archaeology.
Her life must be in ruins now
Why? @N3buchadnezzar
Joke: archaeologists look at ruins.
lol
$\spadesuit$ Just Curious $\spadesuit$
00:01
Ruins are the remains of human-made architecture: structures that were once complete, as time went by, have fallen into a state of partial or complete disrepair, due to lack of maintenance or deliberate acts of destruction. Natural disaster, war and depopulation are the most common root causes, with many structures becoming progressively derelict over time due to long-term weathering and scavenging. There are famous ruins all over the world, from ancient sites in China, the Indus valley and Judea to Zimbabwe in Africa, ancient Greek, Egyptian and Roman sites in the Mediterranean basin...
Actually, she ended up not being able to get a job in her field, so she was a bit unhappy with how things turned out.
A joke (or ) is a phrase or a paragraph with a humorous twist. It can be in many different forms, such as a question or short story. To achieve this end, jokes may employ irony, sarcasm, word play and other devices. Jokes may have a punchline that will end the sentence to make it humorous. A practical joke or prank differs from a spoken one in that the major component of the humour is physical rather than verbal (for example placing salt in the sugar bowl). Purpose Jokes are typically for the entertainment of friends and onlookers. The desired response is generally laughter; when t...
Scandinavian Archaelogy is too specialized to be of practical applications. Am I right @BrianMScott?
@BrianMScott That was also part of my joke, my sisters husband also never got a job in archeology. And it seems these jobs are quite rare
I guess all the dead vikings have alreade been dug up
@KannappanSampath She was well qualified to teach in any anthropology department, but academic jobs were in very short supply. In fact, she did teach as a part-time instructor for about five years before she gave up on finding a tenure-track position.
00:04
Sad then!
Sad even then!
Hi all :-)
hey robjohn
@N3buchadnezzar ?
*someone smart appeared*
*He uses wisdon, teaching and knowledge*
*it`s super effective*
00:10
@robjohn Hi
@anon I added a couple of auxiliary things to my answer to the question about integral with exponential function and logarithm
Let me know if they are unintelligible :-)
@KannappanSampath How has your night gone?
sleepless !! :)
I enjoy being at math.SE than sleeping I guess!
@KannappanSampath Where are you from, Germany?
India! @N3buchadnezzar
@KannappanSampath That sums up my last night. I've been doing something for work for several days pretty much non-stop
00:13
@KannappanSampath Oh, herro !
I guess I will stay up most of the night too, I have some hand ins that is due tommorow
That's great! @robjohn Work is passion for all of us! :)
I had to take a break, so I added a bit to a recent answer :-)
starts writing them in tex
Looks cool to me, rob
@anon Okay, I didn't want to confound the answer with confusing appendages :-)
00:33
Well, back to work for me :-(
see whoever is still here when I surface again.
have fun
@anon Oh, you bet :-p
Pete is around!
Of the L. Clark variety I presume?
Damn, that guy got 90 rep on an answer any of us could have made. In fact I would have had the same answer if I was around at the time.
Your assumption is right!
You mean the question about two dice?
@anon
00:38
Yes, zat wun.
Did you read my answer to that?
@anon
Don't believe so. let me look it up again
Oh
I just figured it out
all of us visit TheArtOfproblemsolving forums too!
I don't usually! @N3buchadnezzar
I just remember people who post amazing integral solutions ;=)
00:42
Here is one of that kind@N3buchadnezzar
I was thinking of creating a page that collected all the integrals floating around
and having a simple sorting and rating system
But I left it as a fun idea
@N3buchadnezzar My profile page has started it already.
I am willing to add some questions there if you wish!
May be I might take it to my blog, if really needed!
I already have collected a large pdf with hundreds of clever integrals
00:45
link please! Would love to see it man!
Although, only the problems.
Never mind. I'll solve; host it on my blog. How priviledged should you be?
@anon That's 900 rep, if he didn't cap at 200 yesterday :-) he got 90 votes!
Actually 908 rep since it was 91 upvotes and 1 downvote
@KannappanSampath Although most of the soloutions are scattered over the internet. Having an integral database would be fun (Alas not suitable on a blog)
Why so? @N3buchadnezzar
00:48
@KannappanSampath It might be fine for a smal amount of problems, but for a larger part. One would need a more specialized design =)
The ability to search for specific problems using latex, the ability to rate problems and solutions, to be able to sort problems after difficulty, to have serveral persons writing problems and solutions, and so on =)
The ability to generate x numbers of problems in difficulty range y, for easy printing
ok! :( My blog is not SE!
artofproblemsolving.com/Forum/viewtopic.php?f=296&t=458410 a smal subset (integrals is somewhat of a strange hoby for me, hahaha)
@N3buchadnezzar $\int (1+2x^{2})e^{x^{2}}\,\text{d}x$?
00:58
@robjohn Yeah ?
closed form, not definite?
Huh?
It have a closed form, thats what I like about it
You want a closed form for the integral, not the evaluation from $-\infty$ to $\infty$
Then it is not so bad :-)
$xe^{x^2}$ I was thinking you were looking for the definite integral when I first looked at it.
Yeah, but obtaining that answer is not easy for most people =)
@N3buchadnezzar People who don't integrate by parts creatively :-)
01:02
Straight integration by parts fails ;)
I like the ones that work well with introducing a new variable and differentiating wrt it.
@anon I usually see that with definite integrals.
@anon $$ \int_{0}^{\infty} \frac{\text{d}x}{\left( x^2 + 3\right)^3} $$
What are you, a physicist? Put the dx at the end man!
@anon I like it that way sometimes
01:06
This one can be solved by letting
$$I(a) = \int_{0}^{\infty} \frac{\text{d}x}{x^2+a}$$
Wait, nvm that's a fraction. Need to put up that render bookmark again...
And look at $I''(a)$
That reminds me. This integral really bugs me. I even emailed the author of the paper - his aid emailed me back saying he was on vacation and would get back to me but I never got an answer. (Maybe it's too trivial?)
$x^{-3}(x+i2\sqrt{3})^{-3}=x^{-3}(-i24\sqrt{3})^{-1}(1+\frac{x}{i2\sqrt{3}})^{-3}=x^{-3}(-i24\sqrt{3})^{-1}(\dots+6\frac{x^2}{-12}+\dots)\to\frac{\pi}{48\sqrt{3}}$
@N3buchadnezzar by contour integration
If I didn't make any mistakes.
LEarning that next year ;)
01:18
Will Jagy is around!
I think I fail at online shopping.
Heh. What happened Henning?
@N3buchadnezzar I just checked in Mma, I was correct :-)
It even gives it in that exact form :-)
01:20
But, with my method I can easilly solve
I just spent an hour and a half searching for the cheapest source for a set of Rubik's cubes, comparing reviews and quality, etc. In the end I think I saved about half an hour's salary (pre-tax) compared to just buying the most expensive option at my first search result...
An entire set of Rubik's cubes?
@HenningMakholm but just think, you've kept that money out of the general circulation, helping to bring down the economy :-)
$$ \int_{0}^{\infty} \frac{\text{d}x}{\left( x^2 + a \right)^3} $$

where a is an arbitary constant. I suspect this is haarder with your method ?
Henning
I just got a cube at a garage sale I believe.
01:22
@robjohn Always a silver lining, I see.
Want some guidelines in where to buy cubes? I am a rather experienced cuber
Although nothing compared to the fastest guys
@N3buchadnezzar Nope. about the same
@N3buchadnezzar I used to be pretty good in grad school. Don't remember it at all now.
The cheapest I have found is 6dollars per cube, including shipping.
@N3buchadnezzar I did finally place an order, so now's too late.
Aww shoey
Anyways, orders can often easilly be canced. I just bought myself two new cubes =)
01:24
If I interpreted the websites correctly I'll end up with Eastsheen 4³ and 5³'s. Hope that is not too shabby.
"Not too shabby" - my brain thinks you're quoting Legend of Zelda there.
They are avreage, much better than the rubiks brands. They are also sturdy, and last a long time.
Although, they require quite havy modifications and breaking in, if one intends to speedcube with them =)
@anon Almost certainly not. I know (?) that "Legend of Zelda" is a series of video games, but that's about all.
@N3buchadnezzar I'm not aiming for speed anyway, just some interesting idle fiddlework.
Exactly, like I said. They are good cubes =)
When buying, the only thing to remember is to stay away from rubiks brands, and get some that fit your hands. Oh and, I am not that concerned about price, more about shipping
01:39
hi all
hi @Srivatsan
I am reading one the speedsolving.com forums
It`s a forum for people who enjoy solving various puzzles, 90% rubiks cubes.
These guys turns everything into a speedcompetition!
Right now I am looking at a 12 page long thread about speed banana eating...
02:12
That's one of the saddest things I've seen online :/
2
02:23
What do the $s$-Catalan numbers (below) count? $$C_s(n)=\frac{1}{(s-1)n+1} {sn\choose n}$$
is tex supposed to work here?
Tex does work here, with a user written javascript I belive
@anon, \choose is essentially deprecated: you are supposed to write \binom{n}{m} nowadays...
It is? Oh. I always liked \choose :( ... Also, math.ucla.edu/~robjohn/math/mathjax.html
there are technical reasons, which I do not remember
02:25
No non no
Clearly they must be pretty important then ;)
Much better below
$$ \left( \stackrel{\large a}{b} \right) $$
:p
if you do that in public, your TeX rights are going to be suspended, @N3buchadnezzar
2
I thought using latex in public would sendme to jail!
@anon Could you show that the s-Catalans are integers?
02:28
if you pick the public correctly, wearing latex in public can get you a date, in fact!
leo
leo
@MarianoSuárezAlvarez see this
and hi all
Hi Mariano & leo.
@Sri: Not off the top of my head, no. I was pilfering through .edu directories when I cam across this, so...
@N3buchadnezzar I prefer \left( \begin{array} a \\ b \end{array} \right) :)
Perhaps binom is internally implemented this way; who knows?
@Srivatsan For binomial expressions?
leo
leo
02:35
consider $E_1$ and $E_2$ subsets of $\mathbb{R}$ with positive measure. Show that $E_1-E_2=\{x_1-x_2:x_1\in E_1,\ x_2\in E_2\}$ contains an interval
@N3buchadnezzar Yep. For \binom{a}{b}
Well i only see a $b$ rendered in LaTex, and I cant read non latex mathtyping!
leo
leo
have you seen that problem before?
seems classic
@leo This is (almost) a theorem of Steinhaus
leo
leo
@Srivatsan i see
leo
leo
@Srivatsan thanks :)
@leo You are welcome.
Does $\displaystyle \exp(x)=\lim\limits_{n\to\infty}\left(1+\frac{x}{n}\right)^n$ have a $q$-analog?
leo
leo
02:55
:) the problem is a theorem in the Steinhaus's original paper
Doesn't look quite like an anolog to me
The powers get replaced by the pochhammer symbol, just as in one of the sides of the equality of the Cauchy binomial theorem.
03:14
@leo Yesterday's theorem, today's problem.
5
leo
leo
Indeed!
MaX
MaX
Nicely said Sri :)
I have one problem
If A be a nonsingular matrix. Then how to prove that if B is row-equivalent to A then B is also non singular
Could anyone explain to me in simple terms, if I wanted to study abstract algebra in a university, what would be the order I would take subjects in. ? Galois theory, Introductory to algebra, groups, rings. Manifolds, field theory etc
@MaX What does nonsingular mean for you?
MaX
MaX
@Dylan: $\det(A) \neq 0 $
leo
leo
03:22
groups first
@MaX I see. Can you use that $\det(CD) = \det(C)\det(D)$?
MaX
MaX
@Dylan: Yes, A is square matrix so that holds.
leo
leo
also an elementary row operation just affect the sign of the determinat
That's a good point too. That's better.
The determinant is an alternating multilinear map on the rows.
MaX
MaX
leo's approach is better :) Thanks guys
leo
leo
03:27
glad to help
It's not just the sign, however. You can multiply a row by a unit, and the determinant is multiplied by that constant.
But it definitely preserves the determinant being non-zero.
leo
leo
What happened when we add two rows?
@DylanMoreland?
To the determinant? Nothing.
leo
leo
yes. I miss that
If I have an alternating multilinear $f$ (let me just write two variables for the two rows involved) $f(a, b)$ then $f(a, a + b) = f(a, a) + f(a, b) = f(a, b)$, since $f(a, a) = 0$.
leo
leo
03:32
I see. Thanks
04:22
05:22 AM
leo
leo
10:22 pm
I might go bed now.
leo
leo
@N3buchadnezzar sleep well
But I do have to get up at around 07 to prepare for uni
leo
leo
go to rest. Avoid late nights
that's destructive
04:28
SLEEP IS FOR THE WEAK
leo
leo
uh. I see
so...
sup ?
Arturo is really close to 100k.
leo
leo
who has the record?
04:36
Certainly he. I don't think anyone else is close.
leo
leo
one year 5 months and up to 2000 answers!
that's amazing
 
1 hour later…
05:45
Well this is bizarre.
@DylanMoreland 929.3111872344565678798794. Wonder if the upper bound is correct to so many decimal places. =)
leo
leo
Good night all
good night, leo.
@DylanMoreland Did you see that user's comment in the other question? math.stackexchange.com/questions/101507/…
06:07
Hah.
If we had a tiff every time two people posted the same answer... yikes.
@DylanMoreland Yikes, indeed. Check the same post now.
E-POINTS
I am wondering why I was pinged by the latest comment addressed to Patrick.
06:29
Hello there
@AkramHassan Heya.
hey Dylan , what's up ?
Trying to remember group cohomology for tomorrow. You?
I an just a beginer in mathematics and my interest emerged later than i wish , now i am working on Rosen's book in discrete structures
Ah, different Rosen.
I thought it might be the same fellow who wrote this nice book.
06:40
aha , so you're into Algebra ?
I do number theory. At least, I try.
Number theory is interesting and full of questions i guess
It certainly is. And you get to use everything.
you mean every other branchof mathematics ?
Hi guys
06:45
Hi @robjohn.
Hi @robjohn.
Has it been a good night so far?
@AkramHassan I guess it is morning there :-)
yes , it's 10 AM
what have you been up to @robjohn ?
@AkramHassan work. It's been a heck of a weekend.
@AkramHassan How about you?
i am a beginner and amateur , working on Rosen's discrete structure book
on and off though
06:52
I'm not familiar with that book.
are you professional mathematician or student ?
Discrete Math and Its Applications
yes that's the title
I used to be an assistant prof at UCLA, but that was a couple of jobs ago.
I taught discrete math at UCLA when I was there.
@AkramHassan I hope that's going well. I don't really know what "discrete math" means, I must admit. I got the impression that there is combinatorics involved.
06:55
@DylanMoreland Combinatorics, algorithms, small bits of graph theory
@Dylan it does include combinatorics
more algorithms applied to graphs than real graph theory
@DylanMoreland . discrete math deals with stuff that has a "discrete" nature , which is the opposite of continuous
Going to read Silverman in bed. Goodnight all.
Good night @Dylan
so @robjohn what are you interested in currently ?
06:59
@AkramHassan That's a good slogan, but I wonder whether people call themselves "discrete mathematicians". It seems like the term serves to bundle up these areas for course titles.
@AkramHassan I've been broadening my interests, but I am interested in Harmonic Analysis, Combinatorics, some Analytic Number Theory.
@Dylan , never heard of "discrete mathematicians" as a discipline , so i think it's more about the subject
@DylanMoreland It is. It is not a branch of mathematics, but you could call it "basic math for computer programmers" for what it teaches.
@robjohn , nice areas , i am wondering about something , do you see beauty in Mathematics ?
@AkramHassan I do. Many of the results fit beautifully together. Sometimes I am really taken by completely different proofs of the same result.
07:06
@robjohn , do you think some areas more beautiful than others ?
or do you "find" some areas more beautiful than others ?
I can't comment on the areas I don't know, but I think each topic has its own attraction.
you wanna give any example ?
I don't know, but some of the ways that things fit together. Are you familiar with the Euler-Maclaurin Sum Formula?
no , but it looks "beautiful"
For functions that are smooth enough, it gives a way to compute sums of the function over 1...n for large n
07:15
okay
@AkramHassan Do you have the MathJax bookmark installed?
not yet :( , why ?
If you want to read what people write here, you should install it.
yeah , i have been told so
$\frac{D}{e^D-1}$
Things like that.
07:16
aha
i have some impressions about the beauty of mathematics
important link , thanks
when you install the bookmark in your bookmark bar, it will allow you to read the LaTeX formulas that people write here.
$\frac{D}{e^D-1}$
Does it look better now?
07:20
still can not see it , i will try later
you have to click on the bookmark in your bookmark bar
wow
that's helpful , thanks
Now you can see it :-)
Are you familiar with Maclaurin series?
07:22
i took it in college
i guess
yes i did , it's elegant too
you mean those are examples of beauty ? or you have some other point ?
So you know that $f(x) = f(0)+xf'(0)+\frac{x^2}{2}f''(0)+\dots$
i remember i took it before , but i need to review calculus
or more particularly, $f(x+1)=f(x)+f'(x)+\frac12f''(x)+\frac16f'''(x)+\dots+\frac{1}{n!}f^{(n)}(x)+ \dots$
i have taken a lot of math courses in college , " computer engineering " , i remember we had those stuff in second year
Now writing the derivative as $D^nf=f^{(n)}$, that becomes...
07:28
Nice taylor series there
Sup guys
$f(x+1)=(1+D+\frac{D^2}{2}+\frac{D^3}{6}+ \dots+\frac{D^n}{n!}+ \dots)f(x)$
hi @Daniil
Does $1+D+\frac{D^2}{2}+\frac{D^3}{6}+ \dots+\frac{D^n}{n!}+ \dots$ look familiar?
so @robjohn i have some impressions about beauty of mathematics . first i think abstract algebra is less beautiful than analysis and number theory for example , what do you think ?
07:32
I know much more about analysis and analytic number theory than algebra, but I don't assume that there are not things just as beautiful there.
Do you know the power series for $e^x$?
how much "abstract algebra" do you know, @AkramHassan?
unfortunately i need to review a lot of subject
@MarianoSuárezAlvarez he speaks! Hello Mariano.
not much @MarianoSuárezAlvarez , how about you ?
07:35
bits here and there
Top of the morrow to you, and whatnot.
@AsafKaragila I'm glad you're not out of whatnot. You seem to use a lot of it :-)
Hello Asaf and Mariano :)
@AkramHassan, "thinking XXX is less beautiful than YYY" is best done when one does have a profound knowledge of both XXX and YYY
:)
@robjohn You know that I have that bottomless jar of whatnots.
Hi Daniil
07:36
agreed @MarianoSuárezAlvarez , that's why i am asking what do you guys think
@MarianoSuárezAlvarez Indeed! That was sort of what I was trying to say. I don't know enough Algebra to compare with what I know of Analysis.
@AkramHassan, as a good rule that's served me a good long time now, every time I come to suspect some area is not beautiful, the only conclusion is I don't know anything about it :D
@AsafKaragila how do you keep things in a bottomless jar?
even subjects like numerical analysis, which are generally viewed with something close to contempt, are filled with beauty
Things seem to fall out of mine all the time.
07:38
@MarianoSuárezAlvarez and when you know about it you find it more beautiful ?
@robjohn Oh it's fine, it's one of those things without the axiom of choice that are bottomless but every decreasing sequence is finite.
either that, or infomedly decide that I don't like it
beauty is not an objective thing
@Mariano I saw somewhere that you maintain gnome-terminal?
I used to
(One of my new year resolutions is to update my webpage :) )
Prior to the gnome3 horror?
@MarianoSuárezAlvarez too busy maintaining other things? :-)
Two weeks after gnome3 was out I moved to awesome. The name is proper, it is awesome.
it does take time, and I did not want to do it badly, so I retired
@robjohn , @MarianoSuárezAlvarez . Another impression i have is that modern mathematics is less beautiful . for example Euler , Gauss and Cauchy's work seem more beautiful than modern stuff , what do you guys think ?
@AsafKaragila Are you on Linux?
07:41
that you need to learn more modern math
@robjohn For the past six years, at least.
@AkramHassan What Mariano said.
@AkramHassan Sometimes the overview has a beauty that is lost in all the detail that is given these days, but once you have gotten the details down, you can see the overall beauty.
extraordinary things have happened in the, say, last 10 years
Modern mathematics may seem more technical than "old old school mathematics" but it's only because it's less accessible to the layman. You have to really put an effort and study it to truly appreciate it.
things that Gauss would not have dreamt of
he'd be jealeous of you, really!
07:43
@AkramHassan and the details have a beauty of their own
Like a series of tubes connecting people from all over the globe in a chat about nonsense and mathematics.
@AsafKaragila and whatnot
The whatnots are mine, Bob.
07:45
Right, you're not very Silent ;-)
@MarianoSuárezAlvarez Is that the smile that we see when the rest of you disappears?
well , i studies alot of undergraduate math in college "Computer Engineering" such as linear Algebra , caclulus , PDE , complex analysis , generating functions ... etc but i was interested in using math just as tool and i wasn't interested in "doing" mathematics . some time after graduation i started to find mathematics more interesting and beautiful , that's why i am wondering :)
@AkramHassan You definitely seem to be far more interested in analysis. That's okay, so am I, but I don't assume that that means algebra and other areas are less beautiful, just that I have not seen it yet.
Math in movies... I watched Good Will Hunting recently and the math was abysmal.
07:50
@AsafKaragila 99% of the movie-going public wouldn't know.
@AsafKaragila, yeah
there is a note in the AMS Notices from that year written by the guy/guys who got asked by the writers about math and &c
they were not pleased with what had ended up in the movie :)
@robjohn Of course. The first time I watched Pi it seemed almost reasonable (though still far-far fetched), with each Pi Day that I watch the movie again... yikes.
@AsafKaragila :-)
I do like the parts of the old man in Pi. I find him the one true diamond in that Sierra Leone of a film.
"As soon as you discard scientific rigor you are no longer a mathematician, you're a numerologist."
@robjohn i watched Pi movie and i liked the old professor advices about rigor
07:54
And the story about Archimedes, and such...
I have to watch that movie now (Pi)
It's a long standing tradition, to bake a pie with the letter Pi on the top, and eat the said pi on the pie, and the pie, while watching Pi.
@robjohn , and @MarianoSuárezAlvarez , good talk , thanks
@AsafKaragila on March 14 :-)
@robjohn Better known as Pi Day.
07:58
Then there is June 28...
@robjohn You mean July 22.
@AsafKaragila I was thinking of Tau Day
@robjohn Oh :-D
But that is 1/Pi day in the US :-p
7/22
22/7 is Pi Approximation day here.

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