<p>Look at the US News and World Reports rankings of grad schools in comp sci, math and other subjects. Consider the top twenty schools and research those schools’ websites. Then consider other factors such as climate, atmosphere, activities et al to narrow the list. Do not let prestige misguide you.</p>
<p>Add the University of Wisconsin-Madison to the list for a public U in these fields. Many college freshmen will change their major. UW has a good Honors program with opportunities to take grad level courses in several fields, work in labs…</p>