Introducing undergraduate students to mathematics through research is a core component of who I am as an educator. From my first full time position as a Visiting Assistant Professor at Iona in 2012, through the present day, I have used undergraduate research as a way to provide students a space to learn mathematics outside of the usual curriculum, and experience what research is first hand. The usual pattern includes informally working on a volunteer basis with whichever students are interested for about a year, before turning the work into some classroom credit to write up their work, and then hopefully a presentation at a conference. Formally, my dedication to undergraduate research have led to roles such as Honors Thesis Advisor (Iona 2015), Assistant Director of the Honors Program (Iona 2014-2015), Member of Undergraduate Research Advisory Committee (SJC 2017-present), and now the Director of Undergraduate Research (SJC 2020-present). In addition, I now routinely teach the Math Seminar course at SJC which is a one-semester capstone type course where we try to experience a more streamlined approach to undergraduate research. I am also pleased to be a member of the 2020-2021 cohort of the PIC Math Program which will bring my undergraduate research experience into the realm of more applied problems coming from industry.
By my last estimate, I have worked with over 40 students on projects following an undergraduate research type approach. More often than I’d like, a lack of resources prevents students from prioritizing and completing their projects. Below are some select instances of my students who produced exemplary work, for the sake of showing the types of projects we have worked on:
- S. Greendige and N. Gallagher. “Computing Čech Cohomology of and a Genus-n Surface”. Presented at Nebraska Conference for Undergraduate Women in Mathematics (2015).
- A. Knowles and B. Moore. “Computations of the (Weak) Global Dimension of a Ring.” Co-advised with R. Schwarz. Presented at the Nebraska Conference for Undergraduate Women in Mathematics (2019).
- J. Andre and D. Rossano. “Using Squares to Compute the Čech Cohomology of a Data Set“. Presented joint at BMCC’s C-STEP Data Analytics Workshop (2018) and then by D. Rossano at MAA MathFest (2019).
- H. Cole. Projects ranging from “Free Resolutions Defined by Free Modules” presented at SJC Undergraduate Research Symposium (2019) to “Minkowski’s Theorem” and “Introduction to the Geometry of the p-adics” which were never presented due to COVID-19.
- N. Forman, A. Isiofia, and A. Sutton. “Quantum Gates” and “Universal Property of the Tensor Product”. Presented at the SJC Undergraduate Research Symposium (2021).
- N. De Lanerolle, K. Delaney, and S. Silvestri. “Simplicial Sets and their Applications”. Presented at the SJC Undergraduate Research Symposium (2021).