I just had a fleeting thought of whether it is possible to equip primes with additional operations to give groups or something. It's pretty far-fetched, but I think an interesting question to ask.
Aren't all people who don't have a mind of their own easy targets?
I mean, if you think at least some of time you can't possibly believe in God, your horoscope, ghosts, homeopathy, anti-wrinkle creams and whatever I can't think of right now.
That said, sometimes I do think my life would be more exciting if I had an imaginary friend following me around wherever I went and if I had to check under my bed for monsters before I went to sleep.
@MattN. As areligious as one gets. But that doesn't mean I've never read the Torah, it's after all an important cultural cornerstone. And occasionally good poetry.
@Hippalectryon Yes, hilarious. But my favourite part is where he points out that the other guy is not allowed to call himself school chaplain and then the other guy suddenly completely changes tone.
@MattN. Well, surely Jane Austen wrote better. But before you read Tollkien or so, the bible, even in mediocre translations, is far better literature. And if you read it, you can shake your head in disbelief about what the believers don't know ever after.
@DanielFischer Good point but I have already read the LOTR unfortunately. But now I can at least have countless arguments about how boring the book is and how even more terrible the films are. Worst films ever. Nearly walked out half way through.
@BalarkaSen After I evaluated the integral you showed me I came up with this version ... $$\int_0^{\infty} \frac{\cos(x)}{x} \left(\int_0^x \frac{\sin(t)}{t} \ dt\right)^3\ dx=-\frac{7}{8}\pi \zeta(3)$$
@DanielFischer I forced myself. I chose it for my English Abitur and the goal was to punish my teacher for being a teacher. You could choose 5 books or so and they ask you questions about them. So ideally the teacher has to have read them all.
@DanielFischer I'm missing something here. Prove or disprove the existence of a 2 by 2 real matrix $A$ such that $\exp A=-I_2$. I'd definitely say no, but I can't find a proof
Hrm, I've to find the surface area of a torus, $r(u,v)=(a+b*cosv)cosu*i+(a+b*cosv)*sinu*j+b*sinv*k$, when $0<b\le a$ and $0\le v,u \le 2\pi$. Now I used the obvious vector obvious attempt of double integral over the normal of the cross vector product. After abusing all possible algebric tricks I got this beast:
Better :). Still, though, no idea even how to approach it.. should I try some kind of subsitution? Or just lose fear and head to it by sheer force? It scares me..
Hi all. I posted this question yesterday but it didn't receive much attention. I'm sure I'm missing something simple. Could someone take a look at it please?
@G.T.R something similar happened when he answered one of my Qs some time ago (he 'trivialized' my entire $\mathbb{C}$-analysis assignment problems :-) :D
@r9m Not really, it's a LOT of work, and for the fields I would be capable of writing a decent book about, there are already a lot of good books, so ...
@DanielFischer No, it's more conceptual. It was originally made to train the German team for international olympiads. It's like a compilation of techniques to solve most olympiad-like problems. So it's basically teaching nice tricks to high school students
@JasperLoy, yes, one can. But it will be boring,I mean, Hartshorne compress 5 page material into a single sentence, and you have to sit down and write every thing down. Which will be relatively easy if you know some AG first. As my guide says, to learn some AG you should know some AG first.
@EnjoysMath, that is hard to say. Most books are unique in their own way. There might be better books to Lee, but I like lee because Topology looked interesting only after I read it.
@JasperLoy, yes. I have to read it some time in coming two years.But that is not a good introduction to Pointset Topology.
@Ram They told me Munkres spends too little time on nets, has a terrible proof of Tychonoff, ugly proof that completions can be done, no counterexamples, etc.
