Before I officially started at UT Martin, I had already said yes to my first undergraduate researcher, a student who had taken differential equations and numerical analysis. A senior colleague had suggested we work together, and I said yes without thinking twice. We began meeting over Zoom that summer, before I had taught a single class here, and kept going through the year.
 

I will be honest that I was still learning how to do this. I started us on problems drawn from my own dissertation work, which I now see were scoped beyond where a first project should begin, and I struggled to chart where they would lead. We met, we read, we tried things, and that year my student presented our work as a poster at the MAA-SE meeting in 2024. The real lesson of that first year was mine: I came away certain I needed a better answer to a question I could not put down. How do you do genuine, reachable research with an undergraduate, when your own work lives in functional analysis that students cannot get to in a semester or two?
 

Over the summer of 2024 I sat with that question and read widely, and slowly an answer came into focus.
 

The problems I study in differential equations have discrete versions, the same questions asked on a grid of points instead of a smooth line, and those discrete problems are genuinely reachable. A student with Calculus 1 can work on the uniform discrete version of a problem I care about, another on the non-uniform version, and the mathematics is real, open, and publishable in undergraduate journals. That was the whole world of difference equations opening up, and it is where this program lives now.

The vision from here is simple: keep going in the same direction. I have worked with students on ordinary difference equations; the next step is partial difference equations, harder problems, the same idea, still within reach of a student who has taken Calculus I.