Mathematics Research Papers
Knots, Virtual Knots, Pseudoknots & Knotoids
A Sequence of Degree One Vassiliev Invariants for Virtual Knots, J. Knot Theor. Ramif., Vol. 19, No. 4, 2010.
Semiquandles and Flat Virtual Knots, joint with S. Nelson. Pacific J. Math., Volume 248, No. 1, 2010.
Classical and Virtual Pseudodiagram Theory and New Bounds on Unknotting Numbers and Genus, joint with N. MacNaughton, S. Narayan, O. Pechenik, and J. Townsend. J. Knot Theor. Ramif., Vol. 20, No. 4, 2011.
Polynomial Knot and Link Invariants from the Virtual Biquandle, joint with A. Crans and S. Nelson. J. Knot Theor. Ramif., Vol. 22, No. 4, 2013.
The Theory of Pseudoknots, joint with R. Hoberg, S. Jablan, L. Johnson, E. Minten, and L. Radovic. J. Knot Theor. Ramif., Vol. 22, No. 4, 2013.
Unknotting Unknots, joint with L. Kauffman. Amer. Math. Monthly, Vol. 121, No. 5, 2014.
On the Coloring of Pseudoknots, joint with S. Jablan. J. Knot Theor. Ramif., Vol. 23, No. 12, 2014.
Minimal Diagrams of Free Knots, joint with T. Boothby and A. Leaf. J. Knot Theor. Ramif., Vol. 23, No. 6, 2014.
Isotopy and Homotopy Invariants of Classical and Virtual Pseudoknots, joint with F. Dorais, S. Jablan, and I. Johnson. Osaka J. Math., Vol. 52, No. 2, 2015.
The Signed Weighted Resolution Set is Not a Complete Pseudoknot Invariant joint with S. Jablan and I. Johnson. J. Knot Theor. Ramif., Vol. 25, No. 9, 2016.
Tangle Insertion Invariants for Pseudoknots, Singular Knots, and Rigid Vertex Spatial Graphs, joint with L. Kauffman. in Knot Theoretic Structures & Spatial Graphs, AMS, Providence, RI, 2017.
Knot Fertility and Lineage, joint with J. Cantarella, E. Magness, O. O'Keefe, K. Perez, E. Rawdon, and B. Zimmer. J. Knot Theor. Ramif., Vol. 26, No. 13, 2017.
Knots Related by Knotoids, joint with C. Adams, K. Kearney, and N. Scoville. Amer. Math. Monthly, Vol. 126, No. 6, 2019.
Virtual Mosaic Knot Theory, joint with S. Ganzell. J. Knot Theor. Ramif., Vol. 29, No. 14, 2020.
Petal Projections, Knot Colorings & Determinants, joint with R. Truax. To appear in Involve.
Games on Knots & Links
A Midsummer Knot's Dream, joint with N. MacNaughton, S. Narayan, O. Pechenik, R. Silversmith, and J. Townsend. College Math. J., Vol. 42, No. 2, 2011.
The Link Smoothing Game, joint with I. Johnson. AKCE Int. J. Graphs Comb., Vol. 9, No. 2, 2012.
Region Unknotting Game, joint with S. Brown, F. Cabrera, R. Evans, G. Gibbs, and J. Kreinbihl. Math. Mag., Vol. 90, No. 5, 2017.
The Region Smoothing Swap Game, joint with I. Johnson and J. Ostroff. Osaka J. Math., Vol. 58, No. 1, 2021.
The KnotLink Game, joint with H. Adams and S. Stoll. PUMP J. Undergrad. Research, Vol. 3, 2020.
KNOTRIS: A Game Inspired by Knot Theory, with A. Ionescu, B. Mathews, I. Ortega, and K. Tesfaye. Math Horizons, Vol. 28, No. 2, 2021.
Educational Research Papers
Reducing Math Anxiety: Findings from Incorporating Service Learning into a Quantitative Reasoning Course at Seattle University, joint with K. Lee. Numeracy, Vol. 4, No. 2, 2011.
Service Learning in a Quantitative Reasoning Course, joint with J. Anderson. Peer Review (a publication of the AAC&U), Vol. 16, No. 3, 2014.
Improving Student Success in Calculus at Seattle University, joint with J. Carter, D. Helliwell, M. Principe, and M. Sloughter. PRIMUS, Vol. 26, No. 2, 2015.
Addressing Negative Math Attitudes with Service-Learning, joint with J. M. Sloughter, J. Anderson, and E. Bahuaud. PRIMUS, Vol. 26, No. 8, 2016.
Successfully Mentoring Undergraduates in Research: A How To Guide for Mathematicians, joint with M. Dorff and L. Pudwell. PRIMUS, Vol. 27, No. 3, 2017.
Veronika Irvine: The Art and Mathematics of Making Bobbin Lace, Math. Mag., Vol. 91, No. 4, 2018.
Robert Bosch: From Dominos To Traveling Salespeople, Math. Mag., Vol. 92, No. 4, 2019.
Henry Segerman: Visualizing Topology, Math. Mag., Vol. 93, No. 4, 2020.
John Edmark: Art in Motion, Math. Mag., Vol. 94, No. 1, 2021
A Knot Game with not KNerds, with M. Cohen. Math Horizons, Vol. 20, No. 2, 2012.
Service-Learning in a Quantitative Reasoning Course, with J. Anderson. Peer Review: A Journal of the Association of American Colleges & Universities, 2014.
Visions of Mathematics, Introduction to artist's book Dreams of Pythagorus by Michael Schultheis, 2014.
The Power of Bravery, MAA FOCUS, June/July 2018.