Reflection on Directing Undergraduate Research in Mathematics

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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 Vanden-Eynden. 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.

Stream: Technology in Learning; Maths, Science and Technology Learning

Paper: A paper has not yet been submitted.

Dr. Jacek Fabrykowski is a Professor of Mathematics at Youngstown State University in Ohio. His research interest focuses on number theory and problem solving techniques. He published over 20 research papers and is involved in American Invitational Mathematical Examination subcommittee. Hi is proposer of competition problems for a number of mathematical competitions.