Recent content by michael.wes

I'm from Canada This is generally my feeling as well; I simply am a bit taken aback by some of the 'FAQ' and admissions information on the web pages for some/most of these schools. Agreed, and I have thought about this for some time. I was coming close to the point where I thought I...

Hello, I am writing to ask for some academic career guidance. I am interested in doing research in cryptography at the PhD level. At present, I do not have much in the way of formal computer science, but I have programmed during internships/co-op positions and during a few undergraduate...

LaTeX is neither necessary nor sufficient for doing well, but it looks nice and can help you later if you plan on doing a USRA. In terms of CS courses, I would recommend knowing the bash shell and basic c/c++ before going in. That means the kind of stuff you can easily find online. You will...

Waterloo pure math and mathematical finance (which falls under the pure math department) are strong programs. If you get a chance, check out the professors' CVs and current/past grad students. Many students come from or go to study at so-called 'ivy league' institutions. This is neither...

Waterloo pure math co-op student in 4B here. Co-op is an unusual choice for pure math majors. I am only in it because I internally transferred from electrical engineering (co-op only). That being said, if you start out in it, then you have many great opportunities. If you plan on majoring in...

I can't seem to come up with much after you pointed out the flaw in this argument. Could you give me a hint on how to proceed? The assignment itself says: 'hint: circles are compact sets'. The only use I can think of for this is that f_n converges on closed disks to e^z, and hence uniformly and...

Homework Statement Let f_n(z)=\sum_{k=0}^n\frac{1}{k!}z^n. Show that for sufficiently large n the polynomial f_n(z) has no roots in D_0(100), i.e. the disk of radius 100 centered at 0. Homework Equations This is a sequence of analytic functions which converges uniformly to e^z on C...

Thanks, I got it now :)

Homework Statement If f,g are entire functions and |f(z)| <= |g(z)| for all z, draw some conclusions about the relationship between f and g Homework Equations none The Attempt at a Solution I just need a push in the right direction.. thanks for any and all help!

Ok, I think I know how to do it now. But there is a follow-up question, which seems a lot harder, but "looks" similar: Suppose f\in L^1(\mathbb{T}) and \int_0^{2\pi}f(x)x^n=0 for all n=0,1,2,... Show that f is 0 almost everywhere. The hint is again to use the density of continuous...

Homework Statement Suppose f\in L^2[0,1] and \int_0^1f(x)x^n=0 for every n=0,1,2... Show that f = 0 almost everywhere. Homework Equations My friend hinted that he used the fact that continuous functions are dense in L^2[0,1], but I'm still stuck. The Attempt at a Solution I need...

I got that e^{g(z)}=cf(z), for some complex constant c and some analytic function g. It's usually easy in these problems to show that the constant is 1, but this is not a concrete function, so I'm not sure how to do that.

Homework Statement Suppose that f is analytic on a convex set omega and that f never vanishes on omega. Prove that f(z)=e^(g(z)) for some analytic function g defined on omega. Hint: does f'/f have a primitive on omega? Homework Equations f(z)=\sum_{k=0}^\infty a_k(z-p)^k The...

Homework Statement Prove that the power series for e^z does not converge uniformly on C. Homework Equations e^z=\sum_{k=0}^\infty z^k/k! The Attempt at a Solution The hint in the problem is to prove a proposition first: If f_n is a sequence of entire functions that converges...

I feel kind of relieved that I'm not the only one who experiences this..