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Remainder Wheels and Group Theory

Award: George Pólya

Year of Award: 2009

Publication Information: College Mathematics Journal, vol. 39, no. 2, March 2008, pp. 129-135

Summary: The author investigates an example of abstract mathematics lurking within the elementary school algorithm for the calculation of repeating decimals. This leads to a discussion of group theory, and considers remainders, cosets of n*, and factor groups.

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About the Author: (From Prizes and Awards, MathFest 2009) Lawrence Brenton was educated at the University of Pennsylvania (B.A., 1968) and the University of Washington (Ph.D., 1974). After completing post-doctoral research work at the University of Bonn, he joined the faculty at Wayne State University, where he has served since 1975. Professor Brenton's field of research is algebraic geometry and several complex variables, with recent particular interest in singularities of projective varieties and applications to cosmology. At Wayne State, he has received excellence in teaching awards at both the college and university levels. He is an enthusiastic advocate for integrating mathematical research and mathematics education at the college level.

Author (old format): 
Lawrence Brenton
Author(s): 
Lawrence Brenton
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Publication Date: 
Wednesday, August 26, 2009
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Summary: 
The author investigates an example of abstract mathematics lurking within the elementary school algorithm for the calculation of repeating decimals. This leads to a discussion of group theory, and considers remainders, cosets of Zn, and factor groups.

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