Pi Mu Epsilon - Mathematical Association of America

Thursday Pi Mu Epsilon Session #2 August 2, 2012
PME Session #2
Room: Meeting Room P
2:00P.M. – 3:55P.M.
2:00–2:15
Using Differential Algebra to Solve Differential Equations
Daniel White
Fordham University
Most approaches to solving systems of differential equations rely on numerical techniques from
advanced calculus. We are using techniques from differential algebra to solve systems polynomial
equations that arise from systems of ordinary systems of differential equations symbolically by
using the Dixon Resultant.
2:20–2:35
Bifurcation and Non-convergence in Hansen-Patrick’s Root Finding Method
Preston Hardy
St. John’s University
Hansen-Patrick’s root finding method is a family dependent on a single parameter alpha. It is
known there are polynomials for which these methods do not converge to a root, but instead converge
to an attracting period n-cycle. We explore what happens to these cycles when the Hansen-
Patrick parameter alpha varies.
2:40–2:55
Neither Rain, Nor Sleet, Nor Snow. What About the Internet
HanQin (Caesar) Cai
St. Norbert College
The internet is having a profound impact on the United States Postal Service. The volume of “snail
mail” sent in this country decreased by 42.36% from 2008-2009. In 2010, I participated in a group
competition studying this effect and this talk will revisit and update our results.
3:00–3:15
A Scale, Some Coins, A Problem
Sarah Stiemke
St. Norbert College
This is a variation of the classic counterfeit coin problem. Given a collection of n coins of weights
1, 2, or 3 grams and a balance scale, we prove the minimum number of weighings needed to determine
the weight of each coin is n.
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