Dear Editor
My name is Kudzai Zvoma. I am currently a senior math major at
Middlebury College and have written on behalf of my colleagues Dylan
Cutler, Jesse Johnson and Ben Rosenfield to submit a research article
to the Rose-Hulman Undergraduate Mathematics Journal.
Our work, as covered in the article, involved the polynomial mediated
mapping from fields to themselves. The main body of research took place
over the 2002 spring semester and editing of our article was finally
completed over the summer. The course was a blend of undergraduate
research experience and more in depth and focused work in topics of
abstract algebra.
You will shortly be receiving a letter of reference from Dr. Priscilla
Bremser who supervised and instructed the course, which was entitled
MA400. Given that this day marks the deadline, I apologise and ask your
understanding in the delay our sponsor has had to make in allowing us
to finish and submit.
Each of the contributing authors is described briefly below and the
.tex and .pdf versions of the article are attached.
============================================
Ben Rosenfield is a senior math major at Middlebury
College and enjoys the culinary arts.
Dylan Cutler is a math major at Middlebury College. Hailing from
western Massachusetts,
he enjoys being outdoors, geology and of course math.
Kudzai Zvoma is a math major at Middlebury, who hopes to persue a
career in education.
Jesse Johnson graduated from Middlebury in 2002 and is now a graduate
student in mathematics at
The University of California at Davis.
============================================
Hopefully all the requested information is included.
My e-mail is: kzvoma@middlebury.edu incase any further correspondence
is necessary with either Dr. Bremser or myself.
Sincerely
Kudzai Zvoma
Dear Editor,
The paper "Classifying and Using Polynomials as Maps of the Field
F_{p^d}" was written by the students in my course, Research Experience
in
Mathematics, in the spring semester of 2002.
I introduced the notion
of
degree-preserving polynomials over finite fields and suggested open
questions that they could pursue. The four of them worked out a lot of
special cases using Maple, looked at the data, noticed some patterns,
suggested and refined some conjectures, and came up with the results
(Theorems 7 and 8) in the paper you see.
In my view, the article clearly reflects a level of mathematical
maturity that goes well beyond standard undergraduate work. The four
student authors came to a thorough understanding of the structure of
finite fields (material suitable for a second course in abstract
algebra), learned the definition of degree-preserving polynomials, and
(based on their observations of their
data) recognized the utility of "degree-annihilating polynomials"
(their
term) in classifying the DPP's. The paper is well-organized and
accurate. I suggested that they aim for an audience of undergraduates
who have completed one semester of abstract algebra; I think they have
accomplished this.
While the mathematics was done collaboratively, each student wrote
particular sections of the paper on his own, so there are clear shifts
in writing style. However, I think those shifts are only a small
distraction. Given the fact that they were undergraduates and the
constraints of a twelve-week semester followed by editing via email, I
am satisfied with the final product.
The four students were all undergraduates at the time that they were in
my course. Jesse Johnson graduated in May after all of the students
had written their portions of the paper; since then Kudzai Zvoma has
been the keeper of the file. Kudzai emailed a draft to the other three
this summer and Jesse noticed a couple of typographical errors. I hope
that is consistent with your requirement that the students did the work
as undergraduates.
Sincerely,
Priscilla S. Bremser
Department of Mathematics and Computer Science
Middlebury College
Middlebury, VT 05753