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Katherine Cordwell, 17, of Albuquerque, submitted a mathematics project to the Intel Science Talent Search concerning noncommutative algebra and representation theory, which have potential applications in quantum physics. A noncommutative structure is one for which the multiplication of two objects (A times B) does not necessarily equal the reverse (B times A). Representation theory involves replacing certain objects in mathematics (such as the algebra of polynomials) with other simpler algebraic objects that share similar characteristics. Katherine's research considered a series of algebraic objects, with each object having an infinite number of components. Katherine's goal was to characterize the structures of a defined set of quotients. She used computer software to recognize a pattern in these small examples and then proved that these patterns always arise. Katherine has studied the piano since the age of six and loves to read. A student at Manzano High School, she has remained active in the Saturday math seminar since middle school. The daughter of William and Rosemary Cordwell, Katherine has wanted to become a math professor since fifth grade and hopes to share her love of mathematics with future students.
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