Recent content by retrostate

Thank you Dick, I can't tell you how much I appreciate the time you have spent helping me.

That f(z) is constant if and only if g(z) is constant, and because g(z) is bounded and entire, by Liouvilles theorem it is constant, which implies f(z) is constant

Ahhh, no the denominator can't vanish because we are dividing 1000 by an inequality which is greater or equal to 1000, therefore, the maximum value g(z) can take is 1 if |1000i+f(z)|=1000. So, as the denominator does not vanish it must be analytic everywhere

I would say g(z) is differentiable on the whole C - {-1000i}, and so would be entire within the region {z:Imz > - 1000}. And is bounded above at g(z)=1,Therefore, by Liouvilles Theorem f(z) is a constant? i.e. if f(z)=0 then g(z)=i < 1…?

Homework Statement Show that if f is an entire function that satisfies |1000i + f(z)| ≥ 1000, for all z ∈ C, then f is constant. Homework Equations (Hint: Consider the function g(z) = 1000/1000i+f(z) , and apply Liouville’s Theorem.) The Attempt at a Solution Ok, so I assume that as f is...

Absolutely, I do a bit of tutoring on the side every now and again, and i find even being really enthusiastic and positive about the subject, especially on a one to one basis can really help. I listened to a brilliant podcast with the author of this book, here is the link. http://newbooksinmath.com

I'm looking for some light reading for this summer after my exams, and came across this book called "Zombies and Calculus"... looks brilliant. Just want to know if anyone has read it, or any other good math books out there for light reading. http://www.amazon.com/dp/0691161909/?tag=pfamazon01-20

Thanks Greg, Really cool site man, I've just spent nearly 2 hours reading threads on here...awesome collection of knowledge

Hi all from Sunny Reading in Berkshire UK, I've just started my final year undergraduate Maths, but will be taking 2 years over it as I'm a part timer, at the moment the 2 courses I'm doing are complex analysis, and fluid mechanics. Hopefully if I pass them, I will be starting QM and Probability...