<p>This is exactly what I had, except throw in Multivariable and independent study in Complex Analysis. It’s absolutely no guarantee of getting into either of these schools, although I suspect it substantially helps. Personally I got into Caltech but not MIT or Princeton. There was another kid in my school that took Calc BC/Linear/Multi/Diff-EQ and graduated early after junior year, and the best school he got into was Carnegie Mellon (granted he had crappy grades and horrid essay-writing skills). I think my Caltech acceptance had more to do with my research at Penn than my advanced math classes, although I don’t think I would have gotten accepted without both. Also, I had mid to high A’s in these classes and all my other classes.</p>