Project mentor: Steve Butler

Shuffling has been used for centuries in card games, and for nearly as long magicians have been using shuffling to help perform magic. Perhaps the most famous example is the faro shuffle (or perfect shuffle) though many others exist. The goal of this REU project will be to explore some variations of shuffling doing mathematical analysis of what can be accomplished with these shuffles. This includes enumeration of patterns, identifying group structure using the shuffles as generators, as well as looking for new magic tricks based on shuffles.

Prerequisites:  Proof-based math course; exposure to linear algebra and group theory; mathematical curiosity; familiarity with programing; good communication skills and ability to work well in a group. Freshman and sophomores are encouraged to apply.
Students with advanced coursework (e.g. graduate level courses) are likely not to get as much benefit from this project; but may still apply.