8:00 PM
They state the result is..
$(-1+(-1+c)^2c)\infty /c^3$
Yeah, it will be $-\infty$!

Huh?

Do you guys know of any good resources on dimensional analysis (applied math). I'm mostly searching for problem sets and some explanation of how to reduce PDEs to ODEs?

@Chris'ssis He will find it tough to get married :P

@picaposo i know nothing about that

8:04 PM
@Sawarnik You refer to Maria Sokolovski? :-)

@Chris'ssis No, the girls of his country :D

@Sawarnik :D

I'm not a marriage material :P .. lol

@r9m: How so?

8:07 PM
@Huy nothing .. :P

@Teddy Yes, this is not a mathematics chat.
You've come to the wrong place.

@BalarkaSen lol

Disks, man, disks.

@Huy Hmm.

8:08 PM
oh ok^^

@Sawarnik: ?

i am a woman too :P

@Sawarnik That was meant as a pun. Beyond your understanding, as you haven't learned topology.

@Teddy: asl?

@Teddy Oh :D

8:08 PM
asl?

@Mike!

finally some peace for balarka...

^^

@Teddy asl = age / sex / location .. :)

8:10 PM
@Teddy There is your algebraic topologist extraordinaire points at @Mike

@Teddy Where are you from?

@Pedro Conway has a good number of exercises.

@r9m Oh, nice.

ok^^. Im 23, from germany
and my english is bad :(
and i have to do math now
byebye

bye :)
@Teddy get out of here then :)

8:32 PM
Hello @alizter. I am also waiting for Sarah's reply, lol.

Just found out my brother was playing the Don't stop me now by Queen some years ago on my piano
That's cool

@UserX Your piano is cool to tell you such stuff.

What?
Does SE have a piano SE?

There is a music SE.

Damn a piano SE would be awesome
But harmonic analysis(music) is fine on music SE so whatever

8:40 PM
@GTR: LOL, no. This is just a course about multivariable analysis and linear algebra. We don't even do Baire (usually) in our undergraduate analysis or topology courses, although I certainly have a few times.

@DanielFischer seems like the low-quality posts queue is flooded by Mhenni B's answers

oh, is that rascal back at work again? ... when René gets off suspension, he'll contribute again.

@Ted he's suspended until Christmas

what? I thought it was a month ...

It is so sad that Marsden and Weinstein's Caculus I, II, III are so seldom used today compared to Stewart's Calculus when the former costs a small fraction of the latter.

8:41 PM
How do you know that?

It says on his profile.

I utterly hate Stewart

Marsden and Weinstein were never used ... really ... Totally nonstandard. No one used it.

I'm with you on this one @JasperLoy

@TedShifrin Hehe, yeah. I guess except in Berkeley, lol.

8:42 PM
I am not fond of Stewart, but our university is probably switching back to it.
Even Berkeley didn't really use it, @Jasper.

@TedShifrin That makes me a real hipster, lol.
I like it that Marsden has lots of examples and pictures, good for an elementary calculus book, without the unneeded colour.

@GTR: Mhenni and I had several fights, too. I like to teach with answers, too, but not with wrong answers :P

Today, an angel gave me 5 upvotes. Who is the angel? Confess.

"who is we? i'm working also with a part of the IMO team in Leipzig – ** Dr. Sonnhard Graubner 1 hour ago**" Really ?

8:45 PM
That was alot of low quality posts

@G.T.R If he says so, it is probably true.

@GTR: As I thought, the suspension ends in 6 days. You can't wait.

@Alizter that was an awful lot of Graubner and B. I wonder who flagged all those

@TedShifrin My school uses a book by Rogawski. It's, in my opinion, the worst I've seen.

I rather like Rogawski, actually.

8:47 PM
@JasperLoy What? Me got it too!

How does Mhenni have a PhD?

@Sawarnik Really? Aww, now I am jealous. I thought the angel only upvoted me.

I see Mhenni was put on a 2 month probation... what'd he do now?

It's very well written, but has some nonstandard things which make some people not like it. Although they will probably be removed by the co-author in the third edition.

@JasperLoy :P

8:48 PM
I actually think Stewart is the best big hardcover calculus textbook with colourful pics.
That is, it is the best in that class.

Basically, all calculus books are isomorphic, some more hand-holding than others. Edwards and Penney was my favorite, but after the second edition it got worse, too.
Stewart basically copied Edwards and Penney.

I don't agree that it's well-written. It's very frustrating that they frequently make claims they don't even do a proof by vigorous handwaving.

I recommend Apostol, Courant and John, and Lang's calculus books, other than Marsden.

You're recommending books for math majors, not for the usual student, @Jasper.
3

8:49 PM
6 mins ago, by G.T.R
LOL http://math.stackexchange.com/a/900668/66096

@G.T.R "who is we? i'm working also with a part of the IMO team in Leipzig – ** Dr. Sonnhard Graubner 1 hour ago**" Really ? Where is that?

@TedShifrin Do many non-math majors take calculus in the US?

Apostol is a text for the math majors at MIT or the students at Cal Tech. No one else can manage it.

@UserX Will flagging work?

8:50 PM
@Jasper, are you kidding?
All science and engineering majors ... plus a number of business majors.

(In particular, this frustrated my students in a section he has on integrating things of the form $\int sin^{2n} \cos^{2m}$; despite having the entire section be about a reduction formula for this, he doesn't give any indication as to how one might do it. The integration by parts involved isn't trivial, either!)

@TedShifrin I don't know the US system, lol. I am not lucky enough to be born there. I am still stuck on my shit island.

I'm betting that sort of thing will get fixed by Colin Adams (or has been).
@Jasper: Even in your shit island, what I said is true.

@TedShifrin If such things are fixed in the next edition my complaints will be gone.

@TedShifrin Hmm, I guess the engineering students take calculus, but I think they have a different course.

8:51 PM
@G.T.R lol

In the US some schools have special courses for the brightest kids who want a super-hard course. But that does not mean all math majors.
@GTR, did you see what I said? The suspension ends in 6 days.

@UserX Perhaps @Alitzer.

I wonder why a bunch of Mhenni's old posts are showing up in the low-quality review queue.

@Ted how do you know ? it says Christmas on his profile though

@MikeMiller Did someone flag them?

8:53 PM
@MikeMiller Maybe the script has got to do something with recent bans..

@Jasper, FYI, at this point a lot of schools (e.g., UC San Diego and Georgia) have a math degree (called applied) which require students to write hardly a single proof.

@G.T.R holy shit is Graubner really doing anything olympiad-level related?

No, @GTR, it says 6 days.

@Sawarnik This makes sense.

The script has not restored all my crazy downvotes.

8:54 PM
@TedShifrin how do you know when someone's suspension ends?

:P

@TedShifrin Have you spoken to robjohn about it lately? Perhaps he can escalate.

@TedShifrin Wow. I did not know that applied math does not require proofs, lol. I thought applied math means math applied, lol.

@UserX On their profile? :/

I mentioned it to him, and he implied he had noticed something odd, but I don't know what happened.

8:55 PM
@EclipseSun Excellent reaction... :-) — Did Oct 19 at 11:36

Well, @Jasper, yes, and certainly at the graduate level they still do plenty of pure math, but not so much at the undergraduate.

@Ted I read "The suspension period ends on Dec 25 at 9:15" here math.stackexchange.com/users/35472/…

@Alizter :D

Oh, @GTR, we're talking about two different people.

8:55 PM
@TedShifrin I must say that after my time and before my time, the math course I took was much more rigorous, so basically it was a shit time for me, lol.

ah ;P

Oh it got deleted.

@TedShifrin Perhaps mention it again... this is clearly a consistent change that's not due to a change in your answers

At UGA, I now have approximately 20 students in my super-hard multivariable math class, and I won't have quite that many in the second semester. All the other hundreds of math students take the standard course.

How do you write LaTeX in latex?

8:57 PM
I don't want to pester him, @Mike, and it's only a dozen or a few more at most.

In that fancy font

@TedShifrin Your multivariable book is very popular. I hope you write a single variable book one day. Make it complete.

\LaTeX :P
It's not popular at all, @Jasper. Hardly used.
No, I won't ever write a single variable book. I have no interest. Spivak wrote the book analogous to mine.

@UserX You can right click at the latex piece and then show math as ..

@TedShifrin I find such downvotes offensive because they make correct answers look incorrect. (This is also, apparently, Mhenni's objection, but his answers suck.)

8:58 PM
@TedShifrin Unfortunately, Spivak wrote a multivariable book that is too thin, lol.

Spivak wrote THE book

$\LaTeX$
$\no$

Anyway, I'm out for friday night.
Cya all

I agree, @Jasper. My book is better for students than Spivak's ... unless they already know the subject. Munkres rewrote Spivak's Calculus on Manifolds to make it a bit more readable.

@UserX Cya :)
bye. me goes too...

8:59 PM
Yeah, when I've tangled with Mhenni, his answers have been either misleading or wrong, or just pompous.

The one thing I dislike about Spivaks book is the shape.

Yeah, I never asked him why he made it the odd shape ...

I think Spivak has written a book on mechanics. He might write more physics books.

I think he uses the wide margins for occasional figures ... Maybe that was easier to typeset in the old days.
His second physics book is almost done, he told me.

Arnold also wrote a book on mechanics. :)

9:01 PM
Arnold's book is quite nice. Not elementary ... :)

What's odd about the shape of Spivak's book?

@TedShifrin I always put it at the end of my bookshelf or it bugs me.

Have you ever seen it, @Mike?

No, hence the question :)

@MikeMiller It is ... square.

9:02 PM
It's 9 x 10 1/4.

Ah, so Alizter lies.

close enough

well, in the bigger scheme of things, @Alizter is right :P

@Alizter Oh. That could be odd, yes.

9:02 PM
squares, circles all the same

Well, keeping height fixed, one can write more per page in a square book.

@TedShifrin haha :D

Not perfectly square, so there will still be an unstable axis of rotation :P

Why don't they make books round instead of square, lol.

@Alizter lol, circular books :D

9:03 PM
I think we all know why.

@Ted That's a good argument for round calculus books; keep with the theme!

Who else got the upvotes, other than Sawarnik and me?

prof @Ted's on fire !! :D

huh?

9:04 PM
yeah. huh?

@TedShifrin chain of humour !

@TedShifrin After reading more, Hatcher's notes/book on characteristic classes is quite good. But it's probably written more towards the homotopy theory-minded than Hirzebruch's or Milnor's.

use arrows people.
$\to @Ted$

@TedShifrin: "Apostol is a text for the math majors at MIT or the students at Cal Tech. No one else can manage it." Why would you say that?

9:05 PM
I've never looked at Hatcher's, @Mike. I actually rather like Hirzebruch, although it's probably gone from my library.
I meant in the US, @Huy. We don't teach calculus with proofs, except to very small audiences of exceptionally motivated students.

@TedShifrin: What do you teach in calculus then? O_o

And these days because of the proliferation of advanced placement calculus in the high schools, most of the brighter students start in multivariable.
Computations, hopefully some problem solving. I get depressed about how our students can't do basic max/min problems on the uniform final exam.

@TedShifrin: And which year of university is that final exam being taken in?

I see someone finally removed Hippa's fake profile of me.
First, mostly, @Huy.

@TedShifrin I read that as Hippa's fake profile.

9:08 PM
well, it was

@TedShifrin: And what do you exactly mean by uniform? Uniform across the whole country? Across all students, no matter whether they are studying maths or engineering or CS?

But Hippa is real right?
Like Santa?
right?

no, no, no ... just for some of our Calculus I classes last spring, Huy.
at my university ... and not even all of them. Some faculty refused.

@TedShifrin: Okay.

But I spent about 8 hours writing the exam, @Huy.

9:09 PM
@TedShifrin: Over here, even most of the non-math majors have proof-based math courses.

@TedShifrin Solution: Make it an 8 hour exam

Not at all the sort of exam I would ordinarily write ... much easier and almost too fair ... :)

The longest exams I took were 3 hours, in high school.

I know you haven't, @Ted, hence the review :D I'm going to read Hirzebruch afterwards. You said it's a differential viewpoint? i.e., I'll be integrating characteristic classes and such? (I'm thinking of the first chern class of a line bundle, which I remember being equal to some integral that I've forgotten.)

Yes, @Huy, I know. We've dumbed down ridiculously in the US.

9:10 PM
@TedShifrin: It usually takes me a day to write an exam for my high school students. The most previous one I wrote today and it is really easy, I hope. :)

No, no integrals in Hirzebruch. @Mike ...

Hmm

mmH

I asked Hatcher when the second edition of his AT will be out, he said not anytime soon.

come one somebody add $mHm$ so we have Z_3

9:11 PM
@TedShifrin: I'm sorry to hear. But still a good reputation of the top-universities. Some friend of mine will go to MIT soon. I'm eager to hear whether he thought that he learnt more or less than over here.

Chern's original curvature definition is not prominent in the literature, although Milnor talks about it. But the proofs that you get duality to Schubert cycles by actually integrating curvature forms are not to be found in the literature other than in Chern's papers (or my courses) :P

Too much time in chat. Back to work.

Well, I'm interested in it, but pressed by time; so if nobody much uses that perspective anymore, I won't pursue it for now.

@MikeMiller Maybe pursuing things nobody uses will lead to breakthroughs?

@Huy: MIT's standard calculus course for the masses is the same as everyone else's, but just much faster. There is a Calculus with Theory course that uses Apostol. Most great schools have a super course for freshmen that does my book or Hubbard-Hubbard or something harder (e.g., at Chicago or Harvard) ... no one does a rigorous single-variable calculus course any more other than the tiny class at MIT, and a few schools — few — that still have a Spivak course.
They "use" it in the sense that they define things that way. But no one proves things that way, other than me :P

9:13 PM
@TedShifrin: He's a non-math major and he'll do a part of his MSc over there, so I doubt he'll learn any calculus. :P

I love the moving frames proofs with integrals over Schubert cycles.
oh, for the MSc, all the math is more advanced if he takes any.

@Alizter Bye.

@TedShifrin: Have you been around the world?

I have not travelled anywhere, but I have surveyed the universe with my mind.

Prof. @Ted, @Mike \o

9:17 PM
Not remotely, @Huy.

@Studentmath Hello. Did you see me in your dreams?

@Studentmath!! I finished writing my exam.

@TedShifrin: Do you intend to make up for some of it after you retire?

@Jasper I'm afraid not

maybe, @Huy ... Hope to go to Australia and New Zealand, and some parts of Europe I've never been.

9:18 PM
@Jasper I am afraid full stop.,

@TedShifrin: I hope you can do that. You would miss out on so much if you couldn't.

helli

@Ted ! Think they will manage?

@TedShifrin: To which parts of Europe have you been?

Yeah, @Studentmath, I made it easy. Well, some of them will manage too well, others probably not. I've decided to put a few "proofs"/derivations on the final.
@Huy: France, Italy, Switzerland, England
Oh, and, @Studentmath, I did put your expectation of exponential of linear normal r.v. on the next problem set.

9:21 PM
@Ted I was disappointed when my test had none, it made the course feel more technical even though it wasn't that technical
@Ted :)!
It's a nice question, it brought me back to basic algebra techniques
Not sure Algebra Techniques is the right way to call it..

Well, I think I want to make the A students write me some sort of derivation/proof, so I'll eventually announce that. But it won't be anything too hard (I did prove weak law of large numbers yesterday, modulo the assumption of finite variance).
basic high school algebra, yes, @Studentmath, and working with indices in summations, etc.

Indeed
Funny, I've been doing that just a year and a half ago in high-school, and now it feels 'basic'

@TedShifrin: I did not expect Germany to be missing in that list. Is there a particular reason for that? Where exactly in France, Switzerland and England have you been?

Haven't been to Germany since I was 7 years old, so I didn't list it.
I'm not going to list all the places, @Huy ... :P

I hope to be born in Germany my next life, lol.

9:24 PM
@TedShifrin: Okay, then, your favourite cities in those three countries? :D
@JasperLoy: If you're my child in your next life, I'll have to disappoint you. I'm staying in Switzerland.

other than Paris and London and Florence, not that much time in big cities (I guess I spent one day in Geneva). Particularly love the south of France.

I am annoyed with what I am trying to prove. I think I managed to prove the result I need to use in the proof itself, but I can't bring myself to formulate it. There are so many 'bad scenarios' that I need to explain why they don't matter, I fear I will end up with as complex proof as the usual proofs..

@Huy OK. I won't be dying so soon, so I doubt I will be your child. But I think Switzerland is a great place too.

Even that paragraph was torture to read, @Studentmath :P

@TedShifrin: I see. Most parts of France are really nice to be at for a holiday, I think. Did you like London?

9:26 PM
yes, like London a lot.

@TedShifrin: Really? How so?

@Ted too many variations of the same word in three sentences

Didn't do that much touristy there, though ... I was visiting friends.

@JasperLoy: I hope so too but I'm not counting on it. :P

@Huy Yeah, anything can happen. Two of my friends have committed suicide.

9:28 PM
@TedShifrin If I have the homology groups with $\Bbb Z$-coefficients of a space I can easily compute the homology groups with different coefficients via the UCT. Given the cohomology groups, can I "change coefficients" easily in some similar manner?

@TedShifrin: I really disliked the amount of people in London. I think on holidays I am the kind of person who likes to relax and that doesn't work for me in London.

sure, @Mike. There's a UCT for cohomology, too.
I love walking around cities ... I actually walked 5-15 miles a day in Paris, @Huy.

@JasperLoy: Don't do that.

Not that I know of. The cohomology UCT I know describes $H^n(X;A)$ in terms of the $H_i(X;A)$s.

@TedShifrin: But Paris, too, is so busy. And it smells, everywhere ._.

9:29 PM
nah, it does not.

mm?

well, @Mike, you can deduce it from that, of course.

@TedShifrin How do you propose going back to $H_i$ from $H^i$?

my "nah" was to Huy, not you, @Mike.
I haven't thought about it in years, @Mike.

If $H_n(X;\Bbb Z)$ is finitely generated, then I can do this by a silly computation by this same theorem (since $\text{Hom}$ and $\text{Ext}$ behave nicely in this case). But if $H_n(X)$ is bad I see no way.
e.g., take $X = K(\Bbb Q, 1)$ :P

9:32 PM
@TedShifrin: Maybe I have an abnormally sensitive nose, but basically, most of the times I I had found a quiet place, it was a bit spoiled by the smell.

@Mike ... I dunno.

When $n\to \infty$, is there anything in size between $\Theta (n^{2/3})$ and $\Theta (n^{\frac{2-\epsilon}{3}})$? $\epsilon$ anything bigger than 0.
Can be taken as low as we want, as long as it's bigger than 0, that's it.

Time for bed for me. I hear I'll get an extra hour this night. Looking forward to it. Good night, everyone!

@Huy See you in your dreams!

9:38 PM
@Studentmath You could say that $\Theta(n^{2/3})">"\Theta(n^{\frac{2-\varepsilon}{3}})$ maybe.

bonne nuit, @Huy

@Alizter yeah, question is whether there is anything inbetween

@Studentmath I think there is. Depends on $\epsilon$

I.e. some $x$ so that $\Theta (n^{2/3}) > x > \Theta (n^{\frac{2-\epsilon}{3}})$

because if $\epsilon = 2$ it is trivially true.

9:42 PM
@Alizter $\epsilon$ can be taken as small as we want it, as long as it is greater than 0.

$\epsilon$ has no restriction on size as long as it is greater than zero.

Yeah

@Studentmath I guess using the archemedian property of the real numbers

basically you could try $\epsilon/2$ always and get an inbetween

9:44 PM
Of course -
I lost my line of thought..
Not sure why I wanted this anymore
Okay, different question.
I prove that $x>k/c$, for all $c>1$ a constant. I can't say from that that $x\ge k$, obviously
But if I take $c>1$ to be anything - could also be dependent on $k$ and so on, than then can I state it?

I don't understand, you're saying that $x>k/c$ for all $c>1$?

For any value of $c$ that I will take, as long as it is strictly greater than 1.
Also $x$ is discrete, so is $k$.

district?

No, still false...

9:51 PM
oh, are these random variables or something?
@Studentmath discrete

How do you spell i-
Thanks.
That was embarassing. They aren't exactly random variables, but they are values among a set of answers in binomial rv

@G.T.R Sigh. Fairness be done, he has some good answers.

So they can only be natural numbers

@DanielFischer True :/
@TedShifrin Mhenni.

9:53 PM
oh, a set of small measure.

I think if I can take $c$ to be anything I want as long as it is greater than $1$, than that statement is true.

@Sawarnik It's likely referencing an infamous shock picture.

He also has really really sucky ones. A few less than this morning now.

@MikeMiller Still don't get it, fine.

@Daniel any counterexample for $x,k\in \Bbb N$, so that $x>k/c$ for every $c>1$ not necesseraly a constant, and yet $x<k$?

9:55 PM
no, @Studentmath, but you can have $x=k$.
And you can have $x<k$ if $c$ can be only integers.

@Ted that'll be just fine. And if $c$ is not necesserily a constant, but $x,k\in \Bbb N$ are arbitiraly large?
$c\in \Bbb R$

If it's true for all $c\in\Bbb R$, $c>1$, then you can have $x=k$.

But you certainly know that $x<k$ is impossible?

Don't you?

@Studentmath If $x<k$, let $c = k/x$.

9:58 PM
Because then you could mark $x=k-y$, and $k-y=k/c$ has a solution for $k,y \in \Bbb N$ and $c \in \Bbb R$
Or that.