Hey, I’m a Purdue IE with a son who is at UChicago.
If you want at great well rounded education that teaches you how to think, you can’t go wrong with UChicago (all things considered and if cost isn’t an issue). However, as an IE, I don’t think you would be prepared much for that career at UChicago. Very, very, very rarely would you need to understand the level of Stats, Math or Physics that you would learn there, and I suspect your career may shift once you were there.
When I entered Purdue 30+ years ago, I wanted to be an engineer. I had no idea what an engineer did, just knew that my parents said that “It was a really good career.” I was the first to go to college in my family, both my parents were factory workers, and they knew 3 types of careers that required a college education. A teacher, a doctor, and an engineer. I knew I really didn’t want to do the first two so I went for the third. I arrived on campus with very little understanding what an engineer did. Freshman engineering helped me figure it out, but really you don’t know what an engineer does until you start working as an engineer. You find out very quickly that little engineering you do in college is “what a real life engineer actually does” or at least that was my experience.
I love my job now, have few regrets, but my life experience and a couple grad school degrees later make me ask questions like “What if?” When I see the breadth of things my son at UChicago is experiencing, I have to tell you I’m a little jealous. The whole Chicago experience is more what I think of when I think of traditional college. You get exposed to a very broad cross section of natural science, math, social sciences, physical sciences, and foriegn language. You read the classics and discuss what they mean with your classmates and teachers. It just seems much more “scholastic.” There is a reason that many, many, many graduates go onto grad school and do things like win Nobel Prizes.
However, not a place to go if you want to design process flows, put together quality plans, develop logistical framworks. IF you are absolutely sure that is what you want, then your options at Purdue are your best bet. If you are set on being an engineer and especially if you are in state, you’d be foolish to consider anywhere else for an engineering undergraduate degree.