See  Math Dept. Letter re: Summer Programs  for an overview of the math programs listed below: 

(please note that although NYC Math Circle is not listed in the above overview, it has been attended by Stuyvesant students and the teachers are highly experienced and well-respected math teachers and math team coaches).

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see  Summer 2011 NYC Math Programs- Information

Macaulay Honors College The Summer Scholars Academy in Mathematics and Science at CCNY https://summerscholarsacademy.theschoolsystem.net/ssa.html

New York City Math Circle        Summer High School Math Circle

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Hampshire College Summer Studies in Mathematics  http://www.hcssim.org/ 
PROMYS      http://www.promys.org/
Ross Mathematics                              http://www.math.osu.edu/ross/

Awesome Math Summer Program       http://awesomemath.org/
Canada/USA Math Camp                    http://www.mathcamp.org/
The Texas Mathworks Honors Summer Math Camp   
 http://www.txstate.edu/mathworks/camps/hsmc.html

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The following program is very prestigious and is actually more of a science program:

Research Science Institute (RSI)       http://www.cee.org/programs/rsi