2001-2002  As a part of the International Baccalaureate high school program, all degree candidates are required to write an 'Extended Essay' on a topic of their choosing.  I wrote my essay in the field of Number Theory.  I developed a series of proofs to characterize exactly which natural numbers can be expressed as a sum of two perfect squares.  Much of the work in the essay was performed during the summer of 2000, which I spent at the PROMYS program at Boston University studying advanced math techniques through number theory.