Student and Faculty Collaboration

The 700-level senior seminar, a capstone experience for every mathematics major, involves working closely with a faculty member. In addition to this required component of the major, many students engage in research with faculty as an independent study project (MATH 500) or working in the summer. Students have the opportunity to give presentations on their work in our weekly seminars or at regional conferences such as the annual Hudson River Undergraduate Math Conference.

John Schmitt, Seunghwan Oh ’25, and Xianzhi Wang ’23

Seunghwan Oh (’25) and Xianzhi Wang (’23) recently co-authored a manuscript with Professor John Schmitt which addresses a 48-year-old conjecture of Martin Gardner. They use the polynomial method to show that any placement of queens on a chessboard that is maximal with respect to the property of no-3-in-a-line must have size at least n+1 in the case that n>1 is congruent to 1 modulo 4. Their paper will be published by the European Journal of Combinatorics in March 2025 and is available at https://arxiv.org/abs/2401.03119.  (Pictured left-to-right: Seunghwan and Xianzhi at a celebratory moment.)

Graph Theory

Bryan Currie ’22 and Professor John R. Schmitt collaborated with Professor Jill Faudree (U. Alaska Fairbanks) in writing a revised and greatly expanded survey paper in the field of graph theory. The 98-page paper was published in October 2021 by the Electronic Journal of Combinatorics and is titled A Survey of Minimum Saturated Graphs. As of January 2025, the paper has garnered close to 100 citations on GoogleScholar. Currie was supported by the College’s Undergraduate Collaborative Research Fund during the summer of 2020. Seamus Turco ’21.5 and Chris Hauptfeld ’21 assisted in preparing the bibliography and gathering resources. Bryan is now a Ph.D. student at New Jersey Institute of Technology studying applied mathematics.

2020 Summer Research Assistants

In the summer of 2019 Chris Hauptfeld ’21 joined a long-term project in graph theory. This summer Bryan Currie ’22 and Seamus Turco ’21.5 continue that project. The aim is to revise and update a survey paper on saturated graphs of minimum size coauthored by Professor Schmitt, his most cited paper.

Alex Lyford, Thomas Rahr ’20, and Tina Chen ’18 Article Published

Alex Lyford, along with research assistants Thomas Rahr ’20 and Tina Chen ’18 published an article titled Using Camels to Teach Probability and Expected Value in the journal Teaching Statistics. This article was the culmination of a project where Alex, Tom, and Tina developed 1) a classroom activity designed to teach students how to reason about probability in the context of the board game Camel Up and 2) an app designed to help students better understand probability through the use of simulation. In Camel Up, players place bets on various camel races, and the player with the most money at the end of the game wins! Players with a developed knowledge of probability and expected value typically outperform those without such knowledge, and this activity is designed to teach that knowledge in a way that can be transferred to other situations such as making decisions about jobs or insurance. Alex loves using this activity in MATH 116 - Introduction to Statistical Science.

John Schmitt and Tommaso Monaco ’20

During the 2019 summer, Prof. Schmitt worked with Tommaso Monaco ’20 on a problem arising in combinatorial design theory. A conjecture posed by Marco Buratti (U. Perugia, Italy) states that for the cyclic group of order p and any multi-set of p–1 elements coming from the first (p–1)/2 elements of the group, there exists a Hamiltonian path in the complete graph on the cyclic group of order p where the edge lengths of the path are the elements of the given multiset.

Tommaso and Prof. Schmitt showed how one can use the polynomial method to formulate a solution to this problem. They shared this progress with their collaborators whom they met for the first time during the ninth Slovenian International Conference on Graph Theory, held in Bled, Slovenia, in June 2019. Together they are writing a manuscript containing a collection of results with Simone Costa (U. Brescia, Italy), Matt Ollis (Marlboro College, Vermont), Anita Pasotti (U. Brescia, Italy), and Marco Pellegrini (U. Cattolica del Sacro Cuore, Italy).

Steve Abbott and Jingyi Wu ’17

A Bohr Mollerup Theorem for Interpolating the Triangular Numbers recently appeared in the Journal of Complex Analysis. This project grew out of Wu’s interest in learning more about the gamma function as part of an independent study project she initiated in her junior year. Wu is starting a PhD program in Logic and Philosophy of Science at University of California, Irvine. Read the article.