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?