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Department of Mathematics
Davidson College
P.O. Box 1719
Davidson, NC 28036
rineidinger@davidson.edu
May 16, 2000
Dear Rose-Hulman Undergraduate Mathematics Journal staff,
Amy M. Smith recently submitted her paper "Basins of Roots and
Periodicity
in Newton's Method for Cubic Polynomials." I am Amy's honor's thesis
advisor and this paper was the product of our work this spring, building
on
the project undertaken with Dr. Tim Flaherty at the Summer Undergraduate
Institute at Carnegie Mellon University. Amy will receive her Bachelor's
degree this May 21, so this paper was completed as an undergraduate.
I believe that the paper is well-written and of interest to a wide range
of
readers. You may want to omit the appendix of programs and replace the
one
parenthetical reference to it with: (True Basic programs to generate the
figures are available from the author or Neidinger at
rineidinger@davidson.edu). Most of the content is well-known by those
familiar with this topic but the paper succeeds in introducing a solid
background in relevant numerical analysis and dynamical systems, as well
as
developing a thorough analysis of Newton's method dynamics for all cubic
polynomials with real coefficients. This latter task was the original
idea
of Amy's REU project with Dr. Flaherty. We were able to rigorously
formulate and prove ideas from the REU work, complete some of the
analysis
and add a bifurcation diagram approach.
I did notice one error in creating the electronic version sent to you.
The
images of Figures 10 and 11 are switched. Figure 10 should have 3 "bars"
and Figure 11 should have 2 "bars."
Thank you for considering the paper.
Sincerely,
Richard D. Neidinger
Professor of Mathematics
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