I was rejected by Princeton, Berkeley, Duke, and Wisconsin-Madison. My first acceptance came today, and all I can say is that the process is extremely arbitrary provided that you meet the minimum requirements.
People on this forum have talked about math, SOP, research experience, GPA, etc being important factors in the admissions process. But my experience tells me that even if you excel in all these areas, it's still not sufficient. (N=1, so take my words with a grain of salt.)
I took advanced math and programming classes and graduated with a minor in computer science. I worked as a