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Research Spending & Results

Award Detail

Awardee:MORAVIAN COLLEGE
Doing Business As Name:Moravian College
PD/PI:
  • Nathan B Shank
  • (610) 861-1300
  • shank@math.moravian.edu
Co-PD(s)/co-PI(s):
  • Eugene R Fiorini Jr
Award Date:02/13/2019
Estimated Total Award Amount: $ 321,759
Funds Obligated to Date: $ 214,506
  • FY 2020=$107,253
  • FY 2019=$107,253
Start Date:04/01/2019
End Date:03/31/2022
Transaction Type:Grant
Agency:NSF
Awarding Agency Code:4900
Funding Agency Code:4900
CFDA Number:47.049
Primary Program Source:040100 NSF RESEARCH & RELATED ACTIVIT
Award Title or Description:REU Site: Research Challenges of Computational and Experimental Mathematics
Federal Award ID Number:1852378
DUNS ID:073619405
Parent DUNS ID:073619405
Program:WORKFORCE IN THE MATHEMAT SCI
Program Officer:
  • Cesar Silva
  • (703) 292-7522
  • csilva@nsf.gov

Awardee Location

Street:1200 Main Street
City:Bethlehem
State:PA
ZIP:18018-6614
County:Bethlehem
Country:US
Awardee Cong. District:07

Primary Place of Performance

Organization Name:Moravian College
Street:1200 Main Street
City:Bethlehem
State:PA
ZIP:18018-6650
County:Bethlehem
Country:US
Cong. District:07

Abstract at Time of Award

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.

Publications Produced as a Result of this Research

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Brown, S. and Daugherty, S. and Fiorini, E. and Maldonado, B. and Manzano-Ruiz, D. and Rainville, S. and Waechter, R. and Wong, T. "Nimber Sequences of Node-Kayles Games" Journal of integer sequences, v.23, 2020, p.. Citation details  

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