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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
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