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my parents are willing to pay or at least work something out if the school is worth the extra cost **over the education I would receive at A&M or UT. **
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That’s just it. You’re not going to get a ChemE education that is “over” (better) than you will at TAMU or UT at those other schools. Those rankings aren’t an indication of more superior classroom education.
You live in Texas which is blessed with several schools that have quality ChemE progams. You also have related-internships and co-ops in your state. To pay more to go to UMinn or UDel or elsewhere is just wasting money.
I hate to see kids look at these silly rankings and think, “oh, I can’t go to my instate school because that other school has a higher ranking.”
Your future employer is not going to pay you more for going to UDel or UMinn or elsewhere. That employer is going to pay the new Texas Tech grad, UMinn grad, and UDel grad the SAME salary.