Number Theory and Algebra Working Group
Friday, July 13
"Regressing to the Binomial Expansion Theorem"
Today, our working group session began with Victoria presenting the procedures for finding regressions using the TI-89. After Victorias presentation, John brought forth the idea of perhaps creating a "Scavenger Hunt" as introduction to the Graphing Calculator (be it a TI-83 or a TI-89). The group seemed to like this idea so we decided to dedicate the last 10 minutes of our session to generate the hunt.
We then continued investigating Pascals triangle. Ryota showed us the relationship of Pascals triangle and combinatorics (nCr"n choose r"). He then led the discussion to Binomial Expansion. Ryota concluded with a short (15 minute) proof, which he shortened into a 2-minute proof QED! J
The last 10 minutes was spent brainstorming items for the scavenger hunt.
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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.