Columbia is the right place to learn finance, and Umich's 2nd is on the area related to mechanical engineering, which is more called manufacturing engineering. Now Detroit is dead. you know industrial engineering has to be based on some specific engineering area. Columbia is private school which means elite education, Umich is a huge state university.
So, ivy >> state, new york >> detroit, I do not see any reason to choose UMich. I am on the waiting list of Columbia, if you do choose Umich finally I have to thank you for leaving that space for us.
by the way, are you from ZJU? If you do my email is rocksun at hotmail dot com