Q:

What is the closest mathematical area related to the Collatz Conjecture?

I want to study mathematics at university. But, it is extremely important that the area I have chosen is correct. I need to know this to deal with the Collatz Conjecture, which is famous in mathematics. I am extremely passionate about this problem. In short, my question is this:

Is the Collatz conjecture only about Number Theory?

What is the closest mathematical area related to the Collatz Conjecture?

A:

"I want to study mathematics at university. But, it is extremely important that the area I have chosen is correct."
When you start studying mathematics at a university you have not yet chosen a subject. You take courses in analysis, linear algebra, computer science, and then later in abstract algebra, topology,  mathematical physics, what have you. Only when you are through all of this you will "choose a subject". It may be that right now your dream is the "Collatz conjecture". You will learn many things that might have a bearing on this problem, and you may learn other things that you will then esteem of much greater importance to you.
The actual grounding of your decision to study mathematics should be a genral easiness with going about mathematical plays and a strong desire to understand better the secrets in the background of these plays.

