yes, hcssim is the greatest summer program ever! I have went there during both of the last two summers. It provides not just mathematical experience but also chances to meet great people and make friends with professors!

In year 2002, the 30th program, I took the following classes:

Rob's workshop (Wing, Josh, Jeff were the junior staffs)

Kelly's maxi on dynamics ( Matt and Ari were the junior staffs)

Josh's mini on combinatorial graph theory

Tom's mini on generating funtion

In year 2003, the 31st program, I was in these classes:

Sarah-marie's workshop (Wing, Leathan)

Tom's maxi on origami math (Anna)

Sarah-maie's mini of recent papers

Ari's mini of ramanujan

The program is much more than just these math, I made many good friends in hcssim, and had more fun activities than any of the school years. Don't be intimidated by 8 hours of math a day, u can do it if u are at hcssim!

You can get a more detailed description of the program on hcssim official page. While applying early doesn't give u a easier admission, it does give u chance to apply other programs if u didn't get in, and saves the hassle of doing tests for other programs if u did.