Recent content by some_dude

Wait... There are quant jobs in the Cayman Islands?

Why not just post your questions here? Or your misunderstandings are more general than specific questions, explain them here. It's unlikely someone will go through the trouble of exchanging contacting info with you if they have no idea whether or not they'll be able to address your unknown...

Show the function g(x) = d(x,E) is continuous for any set E, then the sum of such functions must be continuous, and the quotient as well, where it is defined. And use the disjointness and closedness to show your function is defined everywhere (the denominator is non-zero).

It's simpler if you just do it directly: y in X\{x} => d(x, y) > 0 Then use that to show X\{x} is open.

Ohhh, stupid me, you want the image of the function to be R^n I bet... Why map P to the origin, and then for ray originating at p approaching a point on the boundary of U, map that to a corresponding ray originating at 0 (= f(p)) approaching infinity. Apply the MVT to projections of the line...

I don't get it. If U isn't required to be open, then I don't think it's true. And if it is open, then wouldn't the identity function satisfy this?

Thanks for that. I'll point out relaxing path-connectedness would fail if you didn't assume Y were compact. E.g., Y = "Topologist's Sine Curve" (see wikipedia), and X = [0, 1]. Then if y_1 = (0,0), y_2 = some other arb pt in Y, and x_1 = 0, x_2 = 1. You'd be unable to extend that to a...

Perhaps you need to add the hypothesis f is dffble?

By "monotone" do you mean strictly monotone? (x < y implies f(x) < f(y))? If so it's trivial, but if not then I don't think you'll be able to prove this. E.g. f(x) = 0 for x in [0, 1/2) and = 2(x - 1/2) otherwise.

Hi, try speaking to someone in the one of the physics departments you may be interested about what the core courses they require for acceptence into their grad program. I think a better option, time-wise, is to avoid doing a new BS from scratch and instead self study to the point where you...

How good of a programmer can one become just from the required numerical calculations for a physics PhD? Presumably a lot of such people would have been good programmers before hand, but ignoring that, I'm wondering how much I'll miss out in terms of skill development if I do a very theoretical...

Write f(z) = \sum_{m=0}^{\infty} a_m\ z^{m} (which you can do since it's entire). Show that |f(z)| < |z|^n implies for some natural number N, a_m = 0 for any m >= N.

Move at a really, really slow pace. I've been burned many times trying to rush through difficult (for me) texts. I know the feeling so well I can't stress that enough. If you rush through proofs or just trying to "get through it", you'll miss all these little insights and it will compound, and...

Since f is continuous, the preimage A = f^{-1}((f(1), +\infty)) must be open in (0, 1]. Ditto for B = f^{-1}((-\infty, f(1)). Then (0, 1) \subset A \cup B and the surjectivity assures neither A nor B are empty. And this along with their openness implies A \cap B \ne \emptyset, which implies...

jfreezz, for possible graduate work, maybe check out Case Western university. I read a category theory book, and was surprised to find out the author was actually the head of their philosophy department (as well as being a mathematician). Also - you'll need to learn a lot to understand his...