<p>There is also the Honors Summer Math Camp at Texas State (it’s free). And SuMaC at Stanford is also fairly good.</p>
<p>I agree with shushugah - MathCamp is the best because there are a variety of topics you can explore, whereas in ROSS you have to learn number theory. It is also the hardest one to get in (<25% admit rate).</p>
<p>Ross, PROMYS, HCSSIM, and AwesomeMath are also great programs. Look through their websites and pick the one whose topics most interest you.</p>