<p>If you want the best engineering and the best pure math, the strongest schools on your list would be MIT, Stanford, UC Berkeley, Caltech, and Michigan, which are among the very best in both. I guess I’d also place Harvey Mudd somewhere in that group, but it’s a very different kind of school. Cornell is definitely in that group on the engineering side, maybe just a shade lower in math. UT Austin is very strong but a shade below the top group in both math and engineering. Harvard is among the best in math, a bit less well regarded in engineering (US News ranks it #26 for undergrad engineering, the same as NC State and RPI). Carnegie Mellon, Georgia Tech, and UIUC are the opposite, among the very best in engineering but not quite as strong in math; still very good, though. Duke and Rice are great schools but not among the very best in either engineering or math; but they have good, strong programs in both fields. RPI’s good but another notch down. NC State is a good option as an in-state safety, pretty strong in engineering, less so in math. (I assume it’s a safety; I don’t know your stats, but if they’re not high enough to make NC State a safety then you have little chance of getting into most of these schools).</p>
<p>Given your family income I think financial aid needs to be a serious consideration. MIT, Harvey Mudd, Stanford, Caltech, Harvard, Cornell, Duke and Rice all met 100% of need, though they may define your need somewhat differently, and some will include loans and work-study in your FA package. Carnegie Mellon and RPI don’t meet 100% of need, and the out-of-state publics (UC Berkeley, Michigan, UIUC, Georgia Tech, UT Austin) don’t meet 100% of need for OOS students (that means you). That’s not to say you shouldn’t apply to some of these schools; some people do get a lot of aid at some of these schools, and you won’t know until you see the FA package they offer.</p>
<p>Problem: the only schools on your list that meet 100% of need are “reaches”; they’re so selective that they’re reaches for pretty much everyone. So what should you do? Well, definitely apply to NC State, a very respectable engineering school, in-state (i.e., cheap), and the easiest to get into. Maybe also RPI as probably the next easiest to get into; FA there is a crapshoot, see what happens. Definitely apply to some of your private reaches that meet 100% of need, but I’d say not more than 3 or 4. Apply to 1 or 2 OOS publics and see what happens; I’d suggest Michigan (stats say it gives more OOS FA than Berkeley, the other public in the top group in both math and engineering, though lots of OOS students at Michigan complain about FA) and maybe Georgia Tech or Texas; see what happens. But I really think you need more schools in the “match” range that meet 100% of need, or as close to it as you can get. One thought: UVA. It’s not as good an engineering school as NC State or Va Tech, but it’s one of the few public universities that meets 100% of need for all students, in-state or OOS (NC State and Va Tech don’t come close to meeting 100% of need, so your FA award from UVA might actually make it more affordable than your in-state option). Another thought: Johns Hopkins, quite strong in both math and engineering. Their 27% acceptance rate is low, but not as low as the other top privates on your list, and their ED acceptance rate is 50%, if you’re willing to go that route. They also meet virtually 100% of need; actually 99% is what they report, but they’re probably just being more honest than other schools. </p>
<p>Good luck.</p>