REU Site: Research Challenges of Computational and Experimental Mathematics

Moravian University, Bethlehem PA

Investigators

Abstract

This award provides support for the REU Site "Research Challenges of Computational and Experimental Mathematics" at Moravian College. As a collaboration between Moravian College, Muhlenberg College, and Cedar Crest College, this program will concentrate on research projects associated with experimental mathematics and its role in stimulating new research. Experimental mathematics uses computer-assisted techniques to investigate mathematical patterns and properties. Experimental mathematics is impacting research in scientific and engineering fields beyond the mathematical sciences, giving it the potential to increase partnerships between academia, industry, and government. As society's reliance on data and data driven results has increased, so has the need for a workforce capable of analyzing and interpreting that data. This program will equip those students with the necessary tools to understand (as well as close) the gaps between conjecture, a statistically significant result, and a formal proof. The investigator and his colleagues will nurture this capacity by highlighting the important role computers have played in developing conjectures in areas that include number theory, algorithmic and enumerative combinatorics, combinatorial number theory, graph theory, game theory, and many other mathematical fields, as well as tools necessary for identifying such conjectures. Projections of more powerful computational devices present the future mathematician with interesting challenges, including experimentation by developing computational algorithms and meta-algorithms through the use of computers. The intellectual focus of this research concentrates on the increasing importance of integrating computer technology into pure mathematics methodology, as well as its contribution to other fields, such as algorithmic applications in computer science, biology, and medicine. Mentors are drawn from the Lehigh Valley Association of Independent Colleges (LVAIC) and neighboring institutions. Research projects include experimental mathematics topics such as the Ghandhan problem, Beatty Pair of sequences, perfect powers that appear uniquely in the Catalan triangle, and problems emanating from generalizing existing sequences in the Online Encyclopedia of Integer Sequences. The mentors have experience accessing, researching, and contributing to open problems in experimental mathematics. The program goals are to publicize the growing importance of experimental mathematics among a cadre of students and early-career researchers to help establish it as a tool in their research arsenal; encourage participants to continue their education into graduate school and pursue careers in research; and contribute toward the training of the twenty-first century workforce. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.