65th Annual STS (2005-2006)
Finalists
Kimberly Megan Scott

MASSACHUSETTS
Kimberly Megan Scott, 17, of Wellesley, combined algebra and logic for her Intel Science Talent Search project in mathematics to analyze Ehrenfeucht-Fraisse‚ games, named after the two logicians on whose work these games are based. E-F games measure the similarity of two mathematical structures. She showed how many plays of the games are required before differences are certain to be discovered, in the concrete instances of fields and vector spaces. For algebraically closed fields of equal characteristic, she found an exact bound on the length of the game; this bound is given in terms of the transcendence degrees of the fields. In the more complicated vector space setting, she provided lower and upper bounds in terms of vector space dimension and minimal number of generators for the base field. At Wellesley High School, Kim is captain of the Science Olympiad team and earned perfect SAT scores in verbal and math. Her hobbies include drawing, reading and playing trombone and flute. The daughter of Dr. Steven and Laurie Scott, her German fluency has earned her acceptance in the German Honor Society. She hopes to study mathematics at Caltech or MIT.