REU Site: Research Challenges of Identifying Integer Sequences Using the OEIS

Muhlenberg College, Allentown PA

Investigators

Abstract

This award provides support for REU Site: Research Challenges of Identifying Integer Sequences Using the OEIS, at Muhlenberg College. Projects make an effective use the On-line Encyclopedia of Integer Sequences (OEIS) as a resource tool, and provide glimpses into future. The research impact of the OEIS across disciplines continues to grow. Applications of the to the life sciences, physical sciences, and earth sciences abound. The OEIS has also impacted research in scientific and engineering fields beyond the mathematical sciences. There are currently more than 3,000 papers and books in many areas of mathematics, computer science, and many other branches of science that reference and/or acknowledge the OEIS. The large number of citations and links to OEIS attests to its impact on advancing many areas of active research and its appeal to a broad multidisciplinary community. The intellectual focus of this research concentrates on the important role sequences play in mathematics, as well as their contributions to other fields. The program will contribute to the OEIS knowledge base through projects that are influenced by recent developments and tackle challenges of mathematical and scientific discovery inspired by integer sequences. These challenges include experimentation by developing computational algorithms and meta-algorithms through the use of computers. The methodologies applied to these challenges have come to be loosely defined as "rigorous experimental mathematics" and have proven effective in developing conjectures in areas that include number theory, algorithmic and enumerative combinatorics, combinatorial number theory, and many other mathematical fields. Our program aims to prepare students to become the next generation of mathematical scientists efficient in researching sequences and their applications through the OEIS database, the most successful of whom will have the capacity to look to the OEIS for inspiration. We will nurture this capacity by highlighting the contributions to the mathematical sciences of the On-Line Encyclopedia of Integer Sequences. A particular emphasis of our program will be to discuss the important role the OEIS has played in developing conjectures in areas that include number theory, algorithmic and enumerative combinatorics, combinatorial number theory, and many other mathematical and scientific fields, as well as the tools necessary for identifying such conjectures.