<p>I think Michigan is a no-brainer. If you can afford it, in-state, there are no other public schools that you should consider. None. Really. None. </p>
<p>Just to round out your perspective to see some private schools in the same league, I’d add</p>
<p>MIT
Stanford
Princeton
Cornell
CMU
Rice
Harvey Mudd
Cal Tech</p>
<p>Each has it’s particular appeal to a student like yourself. I think Cooper Union is a very different experience, but I don’t think I’d go there over Michigan. I think every other option is inferior for you. I think that you can skip AAA and make the majors. I think all of the private schools that I mentioned require SAT II’s in math and a physical science.</p>