<p>a) Princeton prepares you extremely well for graduate schools in all subjects, but their math and physics departments are among the best in the world. The amount of independent work that you are required to do prepares you extremely well for graduate school and makes you an extremely attractive applicant. Grad courses are also accessible in both departments.</p>
<p>b) the professors are very accessible. The math department has weekly (daily?) teas at the top of fine hall. Many professors come and its an informal way to meet them. All professors have office hours, and it is very easy to schedule a meeting with them.</p>
<p>c) because you are required to do research at princeton, you do not need to be proactive about seeking out opportunities, they are expected of you and you are helped in choosing jp and thesis advisors. Because the thesis is expected, there is definitely support for the summer between junior and senior years. There is support for the other summers, but you may have to be slightly more proactive about that. Either way, I think that due to the required nature of the thesis, Princeton makes the most research opportunities available (and easily available, you do not need seek them out) of possibly any school.</p>