I'm not sure about student loans being eligible for graduate programs. I've never taken any loans before, so if Federal loans are available to Masters students, then yes, I think I would be eligible but I'd have to double-check.
I did directly apply to a PhD program straight out of undergrad. I did the Masters when I didn't get accepted into any of them. From what I saw from other applicants, I don't feel like a 3.6 is very impressive at all, especially from a no-name school. I did also apply to REUs my last summer...
I just assumed the competition in any field for a PhD is competitive, regardless of the area, since more funding means more applicants and I was not a strong applicant for a pure math PhD program, so I wouldn't believe I have any more advantage applying to an applied math program. Besides, I...
I have a Masters in pure mathematics and wanted to do my PhD in the areas of category theory, homotopy theory, and related fields, but I was not accepted into any programs despite not trying to attempt at all for the "brand name" schools and aiming for what I believed were the less competitive...
Sorry, don't have much to say about myself since I actually don't have any background in physics. Came on here at the advice of a colleague to inquire in regards to career advice (which I will be posting about soon). I do have a math degree, though