59th Annual STS (1999–2000)
Finalists
Alexander Benjamin Schwartz

PENNSYLVANIA
Alexander Benjamin Schwartz, 17, of Bryn Mawr, submitted a mathematics project to the Intel Science Talent Search. Sasha worked in abstract algebra, specifically on structures known as finite abelian groups. Groups arise throughout mathematics and nature as special rearrangements of objects, such as symmetries of a molecule. Groups may contain smaller such objects, called subgroups, and their translates, called cosets. Finite abelian groups can be assigned a measure of complexity, called dimension. Sasha proves that a finite abelian group of dimension 3 or more can be partitioned into cosets of distinct subgroups. He also discusses a family of dimension 2 groups for which the analogous result fails, and he shows that in dimension 1 such partitions are impossible. First in his class of 225 at Radnor High School, Sasha is active in the juggling, math and engineering clubs. His list of honors includes top honors in national and international mathematics and chemistry contests. In his spare time, he enjoys juggling, chess, computer programming and Kenpo karate. The son Mordecai Schwartz and Kathy Fisher, Sasha plans to major in math and physics at Harvard.