Choosing full time vs part time on a PhD application, is one necessarily better than the other for increasing chances of admission? Don't know if relevant, but I'm applying for PhD programs in math. 

In general for grad school apps*, if I'm asked if I want full time or part time, I choose both if I am allowed to do that.

Is there necessarily a better choice if I am not allowed to tick both or pick either?

I mean:


Does part time indicate I'm open to working at the university as a grad/teaching assistant (and hence full time indicates not being open to such work?) ?
Or does part time indicate that I would have other commitments and so would not be seen as a whole hearted student (and hence full time means that I would be a whole hearted student)?


There may be some other things I'm not considering. Please answer in general. Which option, if I have to choose only one, gives an applicant a better chance of getting in the university?

If this depends on the program, please give examples of programs where indicating full time is a better choice and examples of programs where indicating part time is a better choice

To make this clear, I'm not asking if it's better to take a PhD full time instead of part time or vice-versa. I'm asking which is better in applications assuming I am open to either and am allowed to pick only one.

*or for example databases in ETS or QS Grad School Tours
Or does part time indicate that I would have other commitments and so would not be seen as a whole hearted student (and hence full time means that I would be a whole hearted student)?


Yes, this is my understanding of how it would be interpreted.  It would definitely not mean working as a TA or RA.

Unless you have a job you'd like to keep, or other comparable responsibilities outside of studying, I'd recommend checking only the full-time box.  I don't think expressing an openness to part-time study would help get admitted to a math PhD program, while it might look odd or worrisome.

In particular, in the math PhD programs I've studied or taught in, there have been essentially no part-time students.  (It might have been a theoretical option, but I can't think of any actual part-time students.)  For programs like this, the application might ask about it, but the expectation would be that everyone is a full-time student.

I think this is standard in U.S. math PhD programs, but some programs may run differently, so I can't say this advice is necessarily universal.  (The biggest variance would be that some applied math programs may be more open to having part-time students.)