Dear Sir/Madame:
My name is Ghaith Hammouri and I am an undergraduate at the University of
Hartford. I am writing this email in hopes to get my attached paper published
at your respectful journal. This paper was written during the academic year of
2001/2002.
I’m currently majoring in Electrical Engineering and physics with a minor in
math. The idea of this paper originated while solving a differential equation
problem, I needed a formula to denote only every third term in a sequence, I
tried searching for such formula in my books and on the Internet with no luck.
Eventually I decided to approach the problem my self, and finally came up with
the formula. Consequently I became more interested in the topic, and soon
managed to find applications for the formula. It turned out to be very helpful
in tackling some topics relating to prime numbers.
I hope to graduate in May 2003, and hopefully will try to obtain my PhD in
Electrical Engineering. I owe a great deal of appreciation to professor
Raymond McGivney without whom I wouldn’t have been able to write this paper.
He has supervised me during the whole process, and provided a lot of
mathematical insight.
Attached you will find all required documents, thank you for your time and
effort. I look forward to hearing from you in the near future.
Sincerely yours
Ghaith Hammouri
Email: Hammouri@hartford.edu
Ghaith81@yahoo.com
----------------------
January 10, 2003
Editor
Rose-Hulman Institute of Technology Undergraduate Math Journal
Dear Sir/Madame:
Early last spring a colleague asked me to look at some independent work of one of her students, Ghaith Hammouri, whom I had never met. As I was on sabbatical I agreed to meet with Ghaith and our work together progressed throughout much of that semester.
My role was simply that of an editor. All of the mathematics is his.
Although my field is not number theory, I find the originality and interrelations of several major fields of mathematics to be impressive for a sophomore engineering major. Although the sequences he was studying are composed entirely of integers, his paper is based on the complex roots of unity, basic properties of algebraic groups, and prime number theory, subjects usually covered in upper level undergraduate classes. When I asked where he had learned this material, he explained that he simply “found” what he needed to know. Furthermore, each question that he answered raised still others and before long he had gathered six pages of results which neither my colleagues could recall seeing before.
Having taught a theoretical discrete math course to sophomores for a number of years, I know that it is a major accomplishment for an undergraduate to learn how to construct proofs of theorems. However, it takes quite a different level of ability to be able to learn mathematics on one’s own and from this study formulate a set of results. Ghaith Hammouri has done this at a higher level than any student I have known (and without having taken discrete math).
I do certify that Ghaith Hammouri did all of this work while a second semester sophomore at the University of Hartford.
Sincerely,
Dr. Raymond J. McGivney
Professor of Mathematics
Department of Mathematics
University of Hartford
200 Bloomfield Avenue
West Hartford, CT 06117
mcgivney@.hartford.edu