Mathematics

8:00 PM

@Hippalectryon I assure you I attended a lot of matrices when I prepared myself to enter Polytechnic University (200/200 points).

Hippalectryon

200/200 lol. Those kind of scores would be so weird in France.

Chris's sis

@Hippalectryon Well, I'd like to see how those professors from France that give poor marks to students (as you probably suggested) try to solve a problem like this one.

14

Q: Calculate in closed form $\int_{0}^{1}\int_{0}^{1}\frac{dxdy}{1-xy(1-x)(1-y)}$

Can we possibly compute the following integral in terms of known constants? $$\displaystyle \int_{0}^{1}\int_{0}^{1}\frac{dxdy}{1-xy(1-x)(1-y)}$$ Some progress was already done here http://integralsandseries.prophpbb.com/topic279.html but still we have a hypergeometric function. What's your thou...

Balarka Sen

@Chris'ssis but have you done serious linear algebra (inner products, etc) and topology? if you want, you can do those after you finish writing your books.

Hippalectryon

@Chris'ssis It's not giving poor marks for poor mark's sake.

Balarka Sen

@Hippalectryon indeed, i agree.

"deep" is relative too. You'd expect that when a high school student first learns calculus, he'll call it "deep mathematics", but when he graduates, he'll call "topological quantum field theoretic conformality" or whatever more deeper than calculus :p

hi @Pedro

Chris's sis

8:08 PM

@Hippalectryon I was the only one in 400 students that reached the maximum number of points. Well, yeah, that might mean nothing as you suggested. But I wanna see how many professors in France manage to pass that test with 200/200 points. I turn them into my idols.

Pedro Tamaroff

@BalarkaSen Hey there.

Hippalectryon

@Chris'ssis I'm just saying that it's funny from me, who just passed competitive exams, which are not supposed to be totally do-able at all

Ramanewbie

@evinda Nothing gréât

@evinda Nothing great

Balarka Sen

@PedroTamaroff How's your day? What kind of mathematics have you been thinking about?

Pedro Tamaroff

@BalarkaSen Homological algebra yesterday, real analysis today.

Chris's sis

8:11 PM

mpt.upt.ro

@Hippalectryon ^^^

Balarka Sen

@PedroTamaroff nice. I have been doing some linear algebra (billinear forms, etc, the stuff I haven't thought about) to make up for my ignorance. Guess I'll do multivariable calculus afterwards.

Pedro Tamaroff

@BalarkaSen Sounds like a plan.

Chris's sis

@Hippalectryon I doubt those guys will ever forget me, one of the professors there said he was totally shocked for the score (after I finished the second test in a pretty short period of time).

Balarka Sen

@PedroTamaroff yeah, I have been planning to do differential topology sometime this year, so I gotta know those first thoroughly to make sure I understand difftop.

Chris's sis

Anyway, who cares? I dropped that uni ... (I actually dropped more)

Balarka Sen

8:16 PM

Can't study cohomology without knowing differential topology.

Pedro Tamaroff

@BalarkaSen Well, that depends on the cohomology theory you're studying, of course.

Balarka Sen

Well, Hatcher talks about singular cohomology, but I think I should get the geometric intuition behind before studying it.

Hippalectryon

@Chris'ssis why ?

Balarka Sen

i.e., de Rham stuff.

GBeau

The set $\{0\}\cup\{1,1/2,1/3,\ldots\}$ is closed and bounded, therefore compact. What kind of strategy can I use to show that every open cover of the set has a finite subcover?

Balarka Sen

8:19 PM

any nbhd of 0 of this set covers $X$ leaving finitely many points, @GBeau

and then you can use finitely many more open sets to cover the rest of the points.

the whole point is that the set clutters around $0$ to make things simple.

GBeau

That makes sense, thanks

Chris's sis

@Hippalectryon hard times that I wasn't prepare to manage.

r9m

@Chris'ssis corrected my calculations and put it up on my blog :) .. all my damn examinations are over now :D

GBeau

showing it for closed intervals was much more complex, but my professor suggested this was easier

Chris's sis

@r9m Hey! I was trying to write to you now. :-)

Balarka Sen

8:22 PM

@GBeau I don't think doing it for intervals is hard.

GBeau

I'd be interested in hearing your explanation of an outline of an approach

Chris's sis

@r9m Ooo, nice work! ::D

r9m

@Chris'ssis :) now I am dying to see your approach !!! :D ..

Balarka Sen

@GBeau It follows from Bolzano-Weierstrass, doesn't it?

Chris's sis

@r9m All is marvellous there too! I'm sure you have no doubt about that. :-)

Balarka Sen

8:26 PM

It implies [a, b] is sequentially compact, and note that sequential compactness means compact in R.

of course, this is ad-hoc, but uses less machinaries.

r9m

@Chris'ssis booahaan! :'( when do I get to see it? :-)

Balarka Sen

hi @Kaj. Done with the exams?

Kaj Hansen

Indeed @BalarkaSen

Chris's sis

@r9m I wanna add that to my book. So, you need to wait a bit. :-)

Balarka Sen

Cool, @Kaj

GBeau

8:28 PM

@BalarkaSen I'm reading back over the Bolzano section in my text

Balarka Sen

@KajHansen What kind of mathematics have you been planning to study, then?

r9m

@Chris'ssis _/_ @the BOOK!! bows twice with arms crossed on the back while replicating a cannibalistic dance from Central South American jungle :P

Chris's sis

@r9m :-))))))))))))))))))))))))))))

robjohn

@Incurrence: Do you still have a page with MathJax on Wordpress? I have slightly changed the bookmarklet and want to see if it works now. Let me know, please.

Chris's sis

@r9m There is a fascinating integral, not sure you saw it, but I won't tell you where you may find a proof to it.

Balarka Sen

8:30 PM

rehi @Ted

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$Mathematics$ Mathematics