Also, someone tried to teach a bunch of us Stokes's theorem. But that was before I studied any differential forms at all, so that went right over my head.
I think that $\int uv^\prime dx = uv - \int u^\prime v dx$ can be more error prone. A point in evidence is that Matt got the integration by parts wrong :-)
I must admitt, i feel writing $dx$ looks better than $\mathrm{d}x$. But thats perhaps only becuase I have seen the former notation used more frequently.
@tb Apart from aesthetics, why do you hate it? My physics prof wrote integrals consistently like this, and it caught on to me for some time. I am back to the old style. =)
What does this notation mean? I know it can mean the forth derivative, but because of the parenthesis, does not $f^{(n)}(x)$ also have a different meaning?
I write the fourth power as $f(x)^4$. Of course, when we're working points-free then I just write $f^4$, but this is not so good when the ring in question is also a composition ring...
@tb I actually tried to read Categories and Sheaves recently. It was not very helpful. I may come back to it after I learn much more homological algebra/abelian category theory.
I used some basic functional analysis, yes. My point was that it was possible to get rid of most of it and treat the theory purely algebraically after verifying a few simple things.
Is it unfair to conclude from this thread that there are no serious applications of category theory? :p
@tb Would you happen to know if there's an English translation of Les débuts de la théorie des faisceaux appearing in Sheaves on manifolds? It looks interesting.
Even the first sentence escapes me... "Pendant qu'il était prisonnier de guerre à l'Oflag XVIII en Autriche, Jean Leray a fait un cours de topologie algébrique à l'Université de captivité qu'il avait contribué à organiser."
I'm feeling overwhelmed by a feeling of autmn-ness. I saw a kite stuck on a tree that's lost all its leaves and there is a harsh cold wind going on up here.
@JonasTeuwen I guess things like using « » instead of double quotes...
I picked a random sentence from wikipedia: Enfin, si la progression du récit est l'élément central dans l'écriture de Kirby, la construction des cases n'est pas abandonnée et Kirby peut être caractérisé comme un « maître de la forme et de la composition des vignettes ».
Wikipédia dit, « les signes de ponctuation doubles (« ; », « : », « ? » et « ! ») doivent être précédés d’une espace insécable et suivis d’une autre espace (à l’exception du deux-points quand il est utilisé pour exprimer une heure) »
When generalisation has gone perhaps a little too far... "The affine line is the functor $\mathfrak{O}$ which associates with every ring $R$ its underlying set."
The incredible thing is, it's actually a completely reasonable definition!
Why not? It indicates that it is a borderline question :) If you insist to remove one, I'd remove the elementary set theory tag because I'd assume that many first year courses on set theory won't mention ACC.
I do not claim the tag [tag:fixed-point-theorems] is necessary, but here are few questions that would fit the tag nicely: http://math.stackexchange.com/questions/16146/ http://math.stackexchange.com/questions/89268/ http://math.stackexchange.com/questions/90261/ http://math.stackexchange.com/questions/52111/ http://math.stackexchange.com/questions/41964/ http://math.stackexchange.com/questions/11634/ http://math.stackexchange.com/questions/90309/
@ZhenLin Do you happen to still have the link of that blog you mentioned on "I found a blog post a while ago discussing the rules for ſ in the old typography of various European languages." I was unable to find it.
@ZhenLin Ryll-Nardzewski and Bruhat-Tits are two more that immediately come to mind.
"Continuing on, it is useful to appreciate that the set of polynomials over a finite number of variables with coefficients in a finite field is itself finite." ... Confusing polynomials and polynomial functions ...
There is not a single mention of recursion theory or proof theory... and though the words ‘syntax’ and ‘semantics’ do make an appearance, I suspect that there has been some confusion about what Gödel's incompleteness theorem is about, especially the definition of the provability predicate.
Slightly annoyed that reinstalling OS X has not helped with my laptop freezing problem, and that reinstalling OS X forces me to have to reinstall TeX and the Developer Tools...
I thought that too (some are crap, and some are "open problem"-hard), but I wonder how many are note being touched just because they've been entombed? I don't think I've seen the bot bump a question without answers lately... and it seems not everybody looks through the "Unanswered" tab.
Looking at the "featured" tab recently showed me three questions (a fourth) that would've been of interest to me, but which I simply missed because of the high influx rate. This makes me wonder how many questions I missed because they weren't tagged properly (or unexpectedly). Still -- I think that having over 90% of the questions answered is pretty good, given the humungous number of questions.
I definitely agree with "I think that having over 90% of the questions answered is pretty good, given the humongous number of questions." Most of the answerers here are too damn helpful... :D
I am rather active on another site answering questions ranging from higschool to college. And a girl asked how to solve $$ \int \frac{dx}{(x^2+1)^2}\,dx $$ as they had only learned substitution, integration by parts, and simple integrals.
Now there`s an "easy" question, that is hard to answer.
To reduce work, we should bug a mod to do the rename. Since there aren't as many graph theory questions as there are integer partitions, those can be manually retagged.
So I have a homogeneous 2nd order linear differential equation: y''-3y'-10y=0. I determined (and verified with Woflram) that the general solution is: c_1e^(5x)-2c_2e^(-2x). However, I am given initial conditions: y=1 and y'=10 at x=0. How do I find the constants given only y=1? Don't I need a value of x for which this is true? Help?
Some write stuff like, we have convergence in $L^2$ on a finite measure space, then by Cauchy-Schwarz (they often don't mention that either) we have convergence in $L^1$. Hence pointwise convergence. Then I am like:
