gtsjiho, I think newjersey17 makes some outstanding points. Why would anyone want to attend a school like University of Michigan where math classes are held in huge lecture halls when you can attend a school like Rice with a one to six faculty/student ratio? I certainly don’t want to be in large lecture-size classes.
Also, I just came across this article and ranking of the top ten applied mathematics undergraduate programs in the country. Michigan is not on the list, but Rice is (in the tenth position):
http://college.usatoday.com/2016/04/29/top-schools-for-applied-mathematics/
Personally, I don’t put much stock in rankings; however, an earlier poster stated that Michigan was ranked higher than Rice—apparently not so at the undergraduate level.
Good luck. I think you’ve received a lot of good information to help you make your decision.