Advice for a confused math/engineering guy.

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IttyBittyBit
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Hi everyone. I'm having a bit of a crisis here and I'd appreciate any help.

I'm 24 years old, I have a bachelor's degree in math, specializing in computer science and logic, and right now I'm doing a graduate diploma in engineering science at the University of Auckland. My grades in math weren't great, but my grades in engineering are not bad (I have straight A's so far). The reason I chose to do a graduate diploma in engineering was, to be honest, I don't think of myself as smart enough to continue my education in mathematics, despite the fact that I love math.

I'm pretty sure I want to continue my education in some form, preferably a (research) master's degree (I hate coursework at this point).

Projects I've worked on in the past:
AI (neural networks, machine learning, ...)
Image processing (feature recognition, ...)
Algorithms (complexity theory, implementation, ...)
Operations Research
Programming (mobile database applications, data mining, etc...)

I have not yet had a job requiring any of these skills, the reason being that I finished my bachelor's in a third-world country, and right now I'm in New Zealand and I have no work visa (and furthermore, for now I am expressly forbidden to have one).

I want to apply to an American university, but I'm really confused as to what program I should be considering, and (given my background) what Universities will accept my application. Do you guys think I have a shot at the top universities? My advisor told me that it was worth a shot, but I don't want to be wasting my time if it's hopeless.
 
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Sorry for the late reply.

Yes I would like to continue in computer science, but the downside is that it would involve a change of departments.

Right now I'm focusing on computational techniques, mathematical modeling (partial differential equations, perturbation theory, signal processing, etc.) and operations research. I can safely say I don't want to continue the operations research stuff (the only reason I'm doing it right now is because I was stuck with it and it's too late to turn back - it's only for a single term anyway).
 
I am not very familiar with the system in New Zealand, what is a "graduate diploma"? Is it the equivalent of a Master of Science degree in USA?

When you say you want to continue in computer science, do you mean you like theoretical computer science (logic/computation theory/complexity etc) rather than computational stuffs you are doing?
 
A graduate diploma is just two semesters of high-level coursework in the subject. It's basically what a master's degree student would take at the very beginning of their study, or an undergraduate would take at the very end.

While I love theory, I'm thinking of the more applied side of things.