In any event, thanks for trying. Your time is appreciated. At least you had the courtesy and dignity to tackle this problem. BTW, I'm not in grad school yet. I'm trying to solve every problem out of Palka's Complex Analysis book. There is no grade involved here. I leave here in sorrow not...
Nevermind. I have figured out all my other problems. This one is not meant to be. I dare say that only a few mathematician in the world could solve this one. No one online knows, lol. Anyhow, about your hint, (x-1)(x+1)*x = x^3-x. But I have already tried x-x^3 = y+y^3. It does not work...
I am aware of that identity, but I do not see how that will help me here. What you said makes perfect sense, but it does not help me construct the polynomial. I do know that, with a0 + a1*z + a2*z^2 +..., we would certainly have a1 =1. But otherwise, I'm stumped.
Find a (complex) polynomial function f of x and y that is differentiable at the origin, with
df/dz = 1 at the point z=0, and differentiable at all points on the unit circle x^2 + y^2=1, but is not differentiable at any other point in the complex plane. (Bruce Palka, Page 101)
I think we use...
Hi everyone. I want to get into an okay PhD program for pure math (analysis or algebra). I don't care if it is a lowly university, just so it is accredited. What are my chances of getting into such a program with funding? To how many universities should I apply? My background is as follows...