If you say math is your strongest area on your college application, what kind of math achievement do they generally look for (schools like Harvey Mudd and Caltech), besides competition math (and given you want to have a "good" chance, however ambiguous that is)? Summer camps? Research? Advanced math (how advanced)? On that note, what are some excellent schools for pure math that are relatively much less competitive (compared to Caltech, Harvard, and the others in that acceptance range)? I know of Harvey Mudd. Others?