Should I be a visiting student rather than a non-degree seeking graduate student?

Question

Princeton has two nice options called "visiting student" and "qualifying student". UCB and MIT also have the same options, but their policies and names are slightly different. The former is for undergrads from other college who want to take courses in Princeton, and the latter is for those who graduated from their colleges who are not qualified for Princeton but would like to take courses in Princeton as a non-degree seeking graduate student. The cost is roughly the same (no stipend) as my current college, and both are a year only, but the only difference is whether the student is undergrad or grad. As a junior undergrad, I have exhausted courses on mathematical physics and relevant pure math courses offered in my university, so I would like to take courses, attend seminars and do research under professors of Princeton. Although my school's math PhD program is great, it's not comparable to Princeton, since they have Y. Sinai and professors in IAS for mathematical physics.

I can graduate this year (as a junior) and become a "qualifying student", or become a "visiting student" and I can graduate a year later. Which option is better? Or are both options bad? This is for the case that I will not get into PhD program of my choice this year, so please assume that situation. According to the following question, being a non-degree seeking grad student is waste of money. Does it apply to my case, too?

How will study as a non-degree student affect my graduate admissions chances later?

Answer 1

Enrolling as a non-degree-seeking graduate student in a U.S. mathematics graduate program is almost never a good idea, and this is in no way a mainstream option. (I'm talking about not seeking a degree anywhere. For comparison, it's not uncommon to be officially seeking a degree at University X but visiting University Y while your advisor visits there.)

It's easy to get the wrong impression from course catalogs, since they give short descriptions of options that may not reflect how they are used in practice. For example, I doubt the Princeton math department ever admits anyone as a qualifying student; if it happens at all, it is exceptionally rare. I can imagine it might happen for a clearly brilliant student from a deprived background, but not for the vast majority of applicants. There's just too much competition for admission.

If you are accepted as a non-degree-seeking graduate student:

1. You won't be treated in any way like an ordinary graduate student. To the extent anyone in the department is aware of you, you'll be in a special category of "person who wasn't admitted to the graduate program but is paying a lot of money to take courses anyway", which is not a flattering description. In particular, you should not expect faculty to supervise your research or interact with you any more or differently than they treat the undergraduates in these classes. (It could happen, but I'd guess it probably won't.)

2. It won't help with admission, compared with doing equally well in similar courses elsewhere. Specifically, any admissions committee will have members who want to make sure this isn't used as an easier back door to admission, and they will be sure to enforce strict standards.

I can graduate this year (as a junior) and become a "qualifying student", or become a "visiting student" and I can graduate a year later.

Are you sure you're interpreting these programs right? In this listing of the categories, visiting students are enrolled in graduate programs elsewhere, while qualifying students are non-degree-seeking students who are trying to make up for weak backgrounds in the hope of future admission. I'm not aware of any option for undergraduates to spend a year at Princeton, except for some international exchange programs. However, I might well be missing some possibility.

Answer 2

If you want to learn something in an academic environment, without earning credits (which I strongly support you to do while you are treading water), there is a low-cost option at most schools: auditing!

Besides enrolling as an auditor (for a fraction of the cost), you should also contact the instructor directly. You'll want his or her blessing. You should include an informal transcript and a little description of your experience and interests. And an explanation of why you are treading water for a semester (or two).