UChicago only uses custodial parent income and would be free to apply; if you enjoy truly original essay prompts, you’ll love their application supplements (and if you don’t, it’s probably a sign UChicago isn’t a good fit for you).
I’d include UChicago, HarveyMudd, and Northwestern*, even if they’re big reaches.
Are you involved on your university’s campus, with a professor, in a lab, with mathematical research? If not, look into it tomorrwo and pursue it seriously.
- You'll probably be interested in the MENU sequence http://www.math.northwestern.edu/undergraduate/first-year-focus/