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.


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.


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.



  • 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
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