My scholarly interests lie in two main areas: first in the intersections of commutative algebra, algebraic geometry, and graph theory; and second in scholarly teaching, including the use of mastery assessments, inquiry-based learning, and the interaction between mathematics, play, and the Christian faith.

### Mathematics

My dissertation research was in the exploration of the so-called containment problem. In its most general form, one may ask, given a homogeneous ideal *I*, for which *m* and *r* is the symbolic power *I^(m)* contained in the ordinary power *I^r*? In addition to exploring this question in my dissertation in the context of algebraic geometry, I explored a related question in the context of edge ideals *I(G)*. In that case, certain invariants of *I* are shown to be related to invariants of the underlying (simple) graph *G*.

### Scholarly teaching

I am also very interested in the use of research-based methods for teaching and assessment. As I describe elsewhere, I am a proponent of active learning (thought of broadly) in all my courses, and I am also interested in the use of low-stakes, mastery-based assessments tied to clear standards for the purposes of encouraging mastery of fundamental skills and the development of a growth mindset in mathematics.

I compiled some WeBWorK-based preview activities for an elementary linear algebra course.

### Play

A new project (and one that I am keen to explore on this site) is an investigation of the interplay between mathematics, play, and the Christian faith. My teaching style is inquiry-oriented, and emphasizes problem solving; many of these problems can be thought of as puzzles, and thus hopefully introduce students to the playful side of mathematics. I aim to read and write on the literature linking these three areas.

## Publications

- Delivering Pre-Class Activities via WeBWorK to Impact Student Learning, Submitted July 2019 (with V. Zonnefeld)
- Comparing Powers of Edge Ideals,
*J. Algebra and its Applications*, 2019, https://doi.org/10.1142/S0219498819501846 (with T. Kamp and J. Vander Woude) - Mastery-based testing in undergraduate mathematics, PRIMUS, 29:5, 441-460, 2019, https://doi.org/10.1080/10511970.2018.1488317 (with J.B. Collins, A. Harsy, J. Hart, K. Haymaker, A. Hoofnagle, J. Stewart Kelly, A. Mohr, J. OShaughnessy)
- Start a Math Teacher Circle: Connect K-12 Teachers with Engaging, Approachable, and Meaningful Mathematical Problems,
**The 21st Proceedings of the Association of Christians in the Mathematical Sciences**. (with T. Clark, A. Harsy, D. Klanderman, M. Maxwell, S. Robbert) - The Waldschmidt constant for squarefree monomial ideals,
**J. Algbr Comb**, 2016, http://dx.doi.org/10.1007/s10801-016-0693-7 (with C. Bocci, S. Cooper, E. Guardo, B. Harbourne, U. Nagel, A. Seceleanu, A. Van Tuyl, and T. Vu) - On the Fattening of Lines in $\mathbf{P}^3$, Journal of Pure and Applied Algebra, 219(4):1055--1061, 2015, http://dx.doi.org/10.1016/j.jpaa.2014.05.033
- Containment problem for points on a reducible conic in $\mathbf{P}^2$, Journal of Algebra, 394(0):120--138, 2013, http://dx.doi.org/10.1016/j.jalgebra.2013.06.032 (with A. Denkert)

## Talks/Presentations

**Delivering Pre-Class Activities Online to Impact Student Learning**, MAA Contributed Poster Session; MathFest 2019; Cincinnati, OH, August 2019**Promoting Inquiry via Recreational Problems in a Liberal Arts Math Course**, MAA Themed Contributed Paper Session on Inquiry-Based Learning; MathFest 2018; Denver, CO, August 2018**A first experience in a flipped Calculus II course**, MAA Themed Contributed Paper Session on Flipped Classes: Implementation and Evaluation; Joint Mathematics Meetings; San Diego, CA, January 2018**Cut Your Cake (And Eat It, Too!)**, MAA Themed Contributed Paper Session on ``My Favorite Math Circle Problem''; MathFest 2017; Chicago, IL, July 2017**An Overview of Specifications Grading**, 21st ACMS Biennial Conference; Charleston Southern University, Charleston, SC, May 2017**My Favorite Math Circle Problem: Cut Your Cake (And Eat It, Too!)**, 21st ACMS Biennial Conference; Charleston Southern University, Charleston, SC, May 2017**Specifications Grading in a First Course in Abstract Algebra**,

MAA Themed Contributed Paper Session on ``Teaching Abstract Algebra: Topics and Techniques''; Joint Mathematics Meetings 2017; Atlanta, GA, January 2017**Improving proof-writing with reading guides**,

MAA Themed Contributed Paper Session on Encouraging Early Career Teaching Innovation; MathFest 2016; Columbus, OH, August 2016**Implementing Specifications Grading in a Linear Algebra course**,

MAA Session on Assessing Student Learning: Alternative Approaches; Joint Mathematics Meetings 2016; Seattle, WA, January 2016**The importance of $\alpha$**,

MAA Invited Paper Session on Concrete Computations in Algebra and Algebraic Geometry; MathFest 2015; Washington, D.C., August 2015**Symbolic Powers of Ideals: Problems and Progress**(15 minutes),

20th ACMS Biennial Conference, Redeemer University College, Ancaster, Ontario, Canada, May 2015**Symbolic Powers of Ideals: Problems and Progress**(50 minutes),

Mathematics Seminar; University of South Dakota, March 2015**On the Fattening of Lines in $\mathbf{P}^3$**,

Oberwolfach Mini-Workshop 1508a, Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems; Mathematisches Forschungsinstitut Oberwolfach; Oberwolfach, Germany, February 2015**On an Application of Bezout's Theorem**,

Colloquium; Calvin College, February 2014**Ideals of almost collinear points in $\mathbb{P}^2$**,

Special session on Interactions Between Algebraic Geometry and Commutative Algebra; Summer 2012 Meetings of the Canadian Mathematical Society; Regina, Saskatchewan, June 2012**Containment problem for ideals of points on a reducible conic**,

Special session in Algebraic Geometry and Graded Commutative Algebra; Fall 2011 AMS Central sectional meeting; Lincoln, NE, October 2011**Results on the containment problem of ideals of fat points**,

Algebraic Geometry Seminar; University of Nebraska-Lincoln, April 2010**What is Algebraic Geometry?**(50 minutes),

Geometry and Physics on Graphs REU; Canisius College; Buffalo, NY, July 2009**A Fifteen-Minute Survey of Nonunique Factorization**,

IMMERSE at the University of Nebraska-Lincoln, July 2008