Developing Mathematical Ideas
Less than 1000 people in the world can do a "perfect shuffle" of a deck of cards, and doing so has surprising consequences. This course explores connections among seemingly different areas: permutation groups, number theory, and expansions for rational numbers in various bases, all starting from the analysis of perfect card shuffles. The course brings coherence to several ideas that run throughout school mathematics: rational number arithmetic, different representations for rational numbers, geometric transformations, and combinatorics.
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