Reflection on Directing Undergraduate Research in Mathematics
An undergraduate mathematics research program had four projects to explore. The main one was planned for the first five weeks, and concerned so called covering systems of congruences introduced in the 30’s by P.Erdos. While studying this topic the students asked a nontrivial question that was not considered before. The question was an analog problem to the well known Theorem of Crittenden and VandenEynden. It triggered our research on this problem in the direction of a proof of this conjecture, since we all expected a positive answer. The students were successful of proving our conjecture, and they will send the manuscript for publication in (most likely) Mathematics Magazine.
The students also worked on other three projects: (i) An occurrence of any integer as first digits of a power of 2, (ii) A generalization of a certain identity for arctangents, and (iii) Exploring possible symmetries of a graph of a polynomial.
In all three projects they have obtained interesting results. They will be presented in coming Math Fest, and will be send for a possible publications in some undergraduate journals.
Keywords: Directing an Undergraduate Research Program in Mathematics
Dr. Jacek Fabrykowski
Professor, Mathematics and Statistics, Youngstown State University

Ref: L09P0266