@Rememberme: There is no space $X$ other than the point for which every space $Y$ has a quotient homeomorphic to $X$. Even if you throw out special $eY$ you will get no interesting $X$. You might be interested to know that any compact, connected, locally connected metric space can be described as a quotient of $[0,1]$.
I never said only $[0,1]$. You can describe $[0,1]$ as the quotient of a lot of spaces $X$, so compact connected locally connected metric spaces are automatically quotients of $X$. $[0,1]$ is just a nice space to work with.
@Balarka: You seriously annoyed me a couple weeks ago. I don't remember why anymore so I'm unignoring you. On the other hand I didn't have an aneurysm the past two weeks...
I find myself forgetting lots of things that aren't facts or proofs/theorems. I can spout off the Heegner numbers but I can't tell you what I had for breakfast two days ago.
ok. just to let you know, I have found an analog for points, fibers over a point in a field extension, an analog for nbhds. hunting for a formal evenly covered nbhd defn of separable extensions right now
What are your thoughts on this series?
$$\sum _{k=1}^{\infty } \sum _{n=1}^{\infty } \frac{\Gamma (k)^2 \Gamma (n) }{\Gamma (2 k+n)}((\psi ^{(0)}(n)-\psi ^{(0)}(2 k+n)) (\psi ^{(0)}(k)-\psi ^{(0)}(2 k+n))-\psi ^{(1)}(2 k+n))$$
No need for partial/full solutions, but just some thoughts of yours....
@Gato C'est un language utilisé au delà des maths. Tu as toutes les fonctionalités d'un language normal (C, Java, ...) + des libraries de calcul formel (SAGE)
@Gato Je conseille de l'apprendre comme un language de programmation, car il est largement utilisé. J'ai même fait un programme rapidement pour aider Owatch il y a à peu près une semaine qui permet de simuler des planètes dans l'espace :D
@Gato The way to success in mathematics is not that easy, and it depends on how we define it. In my case, the success in the area I like is producing stuff like Ramanujan, not for the sake of producing such similarity, no, but it should happen naturally. It's about the profound views he had on the stuff and that one can easily figure out reading his notebooks.
@Chris'ssistheartist sure, but to find what is "naturally" (in mathematics) for us is a bit tedious, I am not sure I will be good at it, I like it but it's not my natural attraction.
How not to love such series? :D $$\sum _{k=1}^{\infty } \sum _{n=1}^{\infty } \frac{\Gamma (k)^2 \Gamma (n) }{\Gamma (2 k+n)}((\psi ^{(0)}(n)-\psi ^{(0)}(2 k+n)) (\psi ^{(0)}(k)-\psi ^{(0)}(2 k+n))-\psi ^{(1)}(2 k+n))$$ It's brilliant and full of meaning in every way.
@Hippalectryon It depends on how you look at this series, because when I look at it a see a lot of marvellous connections with other fantastic results.
@Gato @Hippalectryon Isn't the beauty of mathematics produced by the mathematical connections finally? For instance, you wanna calculate a series or an integral and all you need to do is to be able to make those connections that together make up the marvellous picture of mathematical beauty.
@Hippalectryon Mathematics is also about very much courage, trying to do things that no one tried before, no one dared to do before, dreaming and reaching what most of us consider to be impossible.
Yes, @Ted, and I signed up for time warner the day I should have gotten the modem, and I only got one. They screw with your service if you don't have it set up within 2 days of signing up. Call me the fool, sure, but still.
@iluso Yes, I think it should be like that. I just exposed the view of a self-educated in mathematics, that's me. Some might not agree though, but it's OK.
Oh, weird that that modem would go to UCLA. ... I'm having my own hassles regarding cable/internet. My landlord doesn't have the time to call them up to terminate his service so I can call and start mine :(
If I develop, say, a theory on a mathematical basis of Darwinism by inspection of random walks in the Euclidean space, that's not really considered to be much of an achievement. It's silly, that they want us to learn Darwinism but not understand it.
I had a few good English teachers in high school, one superb science teacher, one excellent French teacher, and one excellent history teacher. The math teachers were mostly mediocre.
I survived fine, as did many of my good friends. The less motivated and/or less talented students perhaps weren't so lucky.
My geometry teacher had a PhD in math but had a horrible attitude. She punished me for asking questions out of genuine interest. My teacher who taught calculus didn't know it. I resigned from the class and taught it to myself and two friends.
How does a differential topologist end up teaching high school? @Balarka
It seems to be common that high school math teachers don't know anything more than, at best, multivariable calculus and linear algebra. It's hard to inspire joy when you only understand the bare minimum of inspiration yourself.
Well, to get certified, they are required to have a course in abstract algebra as well, @MikeM, and one in geometry (for teachers). But the average such student is mediocre.
No idea. We have quite a bit of PhD's in our school. The chemistry teacher is awesome, for one, and the history one talks too much but seems to know a great deal.
Well, in this country, one doesn't have to be that incredibly gifted or interested to get a Ph.D. But very few end up teaching high school. Those people generally truly love teaching, which is NOT true of most Ph.D.'s here.
OK, @MikeM, I apologize. Locksmith on his way? I've always taken keys to a hardware store or Lowe's or something.
You manage to make the English language particularly ambiguous. That's a useful skill :D
It's only googleable if you know what to google. Even I don't know such things. But I'm surprised he'd be working on what he's working on and not have encountered Sard.
What are your thoughts on this series?
$$\sum _{k=1}^{\infty } \sum _{n=1}^{\infty } \frac{\Gamma (k)^2 \Gamma (n) }{\Gamma (2 k+n)}((\psi ^{(0)}(n)-\psi ^{(0)}(2 k+n)) (\psi ^{(0)}(k)-\psi ^{(0)}(2 k+n))-\psi ^{(1)}(2 k+n))$$
No need for partial/full solutions, but just some thoughts of yours....
