I'm graduating in two months (Pure Mathematics), and I'm planning to take 2019 to prepare for applying to PhD programs in the US (in Mathematics or Computer Science, depending on the program). I'm not applying this year because of time constraints. My interests lay within the broad area of logic. I particularly like (generally speaking) to design effective procedures that have a strong theoretical background.
My issue is the following: during the last few years, I have been exploring different research areas (ordered from oldest to newest: a little of BigData, cybersecurity, three full years in a software engineering research lab, and a research internship in Coding Theory. My MSc thesis was in ordinal notations and proof theory, a somewhat abstract logic subject - which I loved).
It's a complex story, but I can explain why I did it: I was exploring! I don't regret any of it, as it was really fun and I, as a human being, have many interests. Now I know I want to focus in logic. My questions are the following:
1) Does it have a negative impact that I tried so many different things?
I'm expecting the answer to be "it depends on how you tell the story". I like being passionate about more than one subject, but can it be a bad thing?
2) Should I focus 2019 on getting more research experience in logic?
I have no intentions in using my time just to apply to the US. I know the obvious answer to this question might seem to be "yes", but what I'm not sure about is whether I should put all my effort in more concrete experience in logic, or if I should round up the things I have already been doing - for example, I can continue the research I did in the Coding Theory internship, which was really interesting for me. Also, though I don't support hunting, 'a bird in the hand is worth two in the bush'. Anyway, of course it's not a binary decision.
Thank you very much for your time.