You should be more concerned with the education you can obtain than the degree you can earn. Princeton is a very small research university. Princeton does not offer as many majors as larger universities. However, the large number of certificate programs and the ability to conduct research on a topic of your interest in your junior and senior year provide the flexibility to concentrate in a field where Princeton does not offer a major.
The small size of the university does offer advantages. For example, in several freshman seminars freshman have been exposed to the functional MRI. See: Princeton University - Exploring the science and nuance of facial perception
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You should check to see if the larger universities that have a neuroscience major allow undergraduates to conduct research on advanced medical imaging devices.
If you are interested in both biology and applied math you should review the seminars and research done in the Center for Quantitative Biology. Center for Quantitative Biology at Princeton University
Graduate schools are primarily concern with the education you have obtained, your faculty recommendations, and your test scores, e.g. MCAT. Princeton students major in many fields for preparation for med school. Princeton students do not have to major in science to be accepted in med school.