To Whom It May Concern:
My name is Jason R. Lewis, and on behalf of myself and my co-author,
Robert W. Ellis, I would like to submit our paper, Investigations into the
Kaprekar Process, to Rose-Hulman Undergraduate Mathematics Journal for
publication. The research for this paper was conducted from January 2001
to August 2001 and we finished writing the paper in January 2002. During
this time frame Mr. Ellis and I were undergraduate students majoring in
mathematics at East Tennessee State University.
I am a senior mathematics major at East Tennessee State University (ETSU),
and I will be graduating in May 2002. Robert Ellis graduated in December
2001 from ETSU with his Bachelor of Science degree in Mathematics, and he
has started his first semester in the graduate program here at ETSU.
After graduating with my B.S. in May, I will be pursuing a Masters of
Science degree in Mathematics at ETSU. We began our research into the
Kaprekar Process as a research assignment for a junior/senior seminar
class taught by our department chair, Dr. Anant Godbole. After completing
one preliminary paper on this subject, we became very interested in this
problem and wished to explore it further. For our last research
assignment in this class we conducted further research into the Kaprekar
Process when applied to four- and five-digit numbers. We presented these
findings at the Sixth North Carolina Mini Conference on Graph Theory,
Combinatorics, and Computing at Appalachian State University in Boone,
North Carolina in April 2001. When we finished our assignments for this
class we found that we still had a great deal of unanswered questions, so
we asked our professor if we could conduct an independent study into this
problem over the summer and then write a paper in the fall about our
findings. He agreed to our proposal and after working the entire summer
and part of the fall on our research and spending the remainder of the
fall on writing our paper, we finally completed our independent study in
early January.
Dr. Anant Godbole, chairman of the Department of Mathematics at East
Tennessee State University, was our adviser on this paper, and he will be
acting as our reference for this paper. He may be reached either by email
at godbolea@etsu.edu or by telephone at (423) 439-5359
_____________
Jason R. Lewis
President,
East Tennessee Student Chapter of
The Mathematical Association of America
http://www.etsu.edu/math/maa/maa.htm
President,
Tennessee Beta Chapter of
Kappa Mu Epsilon Mathematics Honor Society
Jasonlewis_tn@yahoo.com
--------------Dear Editors:
This is to certify that the paper written jointly by Jason Lewis and
Robert Ellis, titled "Investigations into the Kaprekar Process", was
conducted independently under my supervision. The research began as
part of a class project in MATH 3090, Junior Seminar, and was
completed as part of an independent study project. The authors are
both currently seniors at ETSU, and the research was conducted in its
entirety while Lewis and Ellis were undergraduates.
I believe that the content of the paper is substantial. There are
several aspects that are new; these include the statistical analyses
and the generation of the complete tree for the 4-digit Kaprekar
process. The paper is certainly not at the level of research
conducted, say, by students in the Rose-Hulman REU program. This is
only to be expected since the REU group consists of the best students
nationwide. However, the Lewis-Ellis paper does represent among the
best work done by students at ETSU in recent years and is certainly
worthy of publication in the Rose Undergraduate Mathematics Journal.
My name and address appear below, as a signature to this email.
Sincerely,
Anant Godbole
Anant Godbole
Professor and Chair, Department of Mathematics,
Director, REU Program on Discrete Random Structures
East Tennessee State University,
Box 70663, Johnson City, TN 37614
423-439-5359; godbolea@etsu.edu; FAX: 423-439-8361
http://www.etsu.edu/math/godbole/anant.htm
REU webpage: http://www.etsu.edu/math/godbole/nsf.htm
-Dear Prof Lautzenheiser:
An addendum to my letter of support. The statement "both students
are currently seniors" is not accurate. Roby Ellis graduated in
December 2001. However the independent study project was completed
in Fall 2001, when Roby and Jason *were* both seniors.
Anant