REU Site: Research Challenges of Computational Methods in Discrete Mathematics

Moravian University, Bethlehem PA

Investigators

Abstract

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). The REU site “Research Challenges of Computational Methods in Discrete Mathematics” is a collaboration between Moravian University, Cedar Crest College, and Kutztown University that will bring ten students to Moravian College for nine weeks each summer to concentrate on research projects associated with discrete computational mathematics and its role in stimulating new research. The program goals are to publicize the growing importance of computational methods in discrete 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 particularly among women, minorities, and first-generation students. The intellectual focus of this research concentrates on the increasing importance of integrating computer technology into discrete computational methodology, as well as its contribution to other fields, such as algorithmic applications in computer science, biology, physics, data security, and medicine. Mentors are drawn from institutions within the Lehigh Valley region in Pennsylvania, and an emphasis will be placed on recruiting diverse groups of students. The planned activities outside of the student research projects will also serve the students well, including professional development workshops and field trips to local companies that could increase participants’ exposure to career possibilities. Participants will also interact with local middle and high school students through the Lehigh Valley Summerbridge program, as well as with students in nearby REUs through a regional conference at the end of the summer program to share their research. Modern computer technology makes it possible to explore mathematical concepts with computational speed and precision not available to previous generations of mathematicians. Computer simulation in particular plays a central role in the application of computer systems for research in discrete mathematics, harnessing computer power to promote the use of new paradigms in mathematical discovery. Examples include applications such as error checking in cryptography and mathematical games of strategy on connected graphs, both of which benefit from the insight produced by computer-generated examples. This program will equip students with the necessary tools to understand (as well as close) the gaps between conjecture, a statistically significant result, and a formal proof. Research projects include discrete mathematics topics such as arithmetic structures and their critical groups, wide and Latin non-repeating consecutive partitions, computing strategies for graphical Nim, network reliability parameters, 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 computational methods and discrete mathematics. 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.