Applied Probability Summary

Monday - Friday, July 16 - 20, 2007

The final week of our working group say us turning our attention full time to our two projects: one on simple Markov Chains using a game students can play and the other was an introduction to shuffling cards aimed at a high school audience. For only three days of solid work, the projects went through a great deal of collaborative review, as we tried to make certain we were not doing too much but also giving some small glimpse of the Undergraduate Faculty Program's content (much of it inaccessible to the high school student). Be sure to check out our abstracts, and if you have the password, our projects!

For our presentation, we also wanted to share with the rest of the SSTP some of the ideas we ran across in the UFP. So, we modeled a shuffling mechanism that will not only rearrange cards effectively it also gives you a way to say that you've done enough shuffling (as we found in the UFP, it's not always clear when you should stop). Our method required that each "card" flip a coin, and moving all those with a head to the top of the pile, maintaining their order as they move. Then, we repeat until each card has a different series of heads and tails recorded from the first flip. Along with a gracious volunteer (thanks, Judi), Avery led us through the shuffle showing we had a "random" arrangements of our 8 cards within 5 flips.

Copious thanks to Darryl for not only keeping us on task but also focused mathematically. He's been a great help to all of us.

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.