Publications

Books

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.

Preprint | Publication

Semiquandles and Flat Virtual Knots, joint with S. Nelson. Pacific J. Math., Volume 248, No. 1, 2010.

Preprint | Publication

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.

Preprint | Publication

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.

Preprint | Publication

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.

Preprint | Publication

Unknotting Unknots, joint with L. Kauffman. Amer. Math. Monthly, Vol. 121, No. 5, 2014.

Publication

On the Coloring of Pseudoknots, joint with S. Jablan. J. Knot Theor. Ramif., Vol. 23, No. 12, 2014.

Preprint | Publication

Minimal Diagrams of Free Knots, joint with T. Boothby and A. Leaf. J. Knot Theor. Ramif., Vol. 23, No. 6, 2014. 

Preprint | Publication

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.

Preprint | Publication

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.

Preprint | Publication

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.

Preprint | Publication

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.

Preprint | Publication

Knots Related by Knotoids, joint with C. Adams, K. Kearney, and N. Scoville. Amer. Math. Monthly, Vol. 126, No. 6, 2019.

Publication

Virtual Mosaic Knot Theory, joint with S. Ganzell. J. Knot Theor. Ramif., Vol. 29, No. 14, 2020.

Preprint | Publication

Petal Projections, Knot Colorings & Determinants, joint with R. Truax. To appear in Involve.

Preprint | Publication

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.

Preprint | Publication

The Link Smoothing Game, joint with I. Johnson. AKCE Int. J. Graphs Comb., Vol. 9, No. 2, 2012.

Preprint | Publication

Region Unknotting Game, joint with S. Brown, F. Cabrera, R. Evans, G. Gibbs, and J. Kreinbihl. Math. Mag., Vol. 90, No. 5, 2017.

Publication

The Region Smoothing Swap Game, joint with I. Johnson and J. Ostroff. Osaka J. Math., Vol. 58, No. 1, 2021.

Preprint | Publication

The KnotLink Game, joint with H. Adams and S. Stoll. PUMP J. Undergrad. Research, Vol. 3, 2020.

Publication

KNOTRIS: A Game Inspired by Knot Theory, with A. Ionescu, B. Mathews, I. Ortega, and K. Tesfaye. Math Horizons, Vol. 28, No. 2, 2021.

Publication | Play KNOTRIS!

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.

Publication

Service Learning in a Quantitative Reasoning Course, joint with J. Anderson. Peer Review (a publication of the AAC&U), Vol. 16, No. 3, 2014.

Publication

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.

Publication

Addressing Negative Math Attitudes with Service-Learning, joint with J. M. Sloughter, J. Anderson, and E. Bahuaud. PRIMUS, Vol. 26, No. 8, 2016.

Publication

Successfully Mentoring Undergraduates in Research: A How To Guide for Mathematicians, joint with M. Dorff and L. Pudwell. PRIMUS, Vol. 27, No. 3, 2017.

Publication

Artist Interviews

Veronika Irvine: The Art and Mathematics of Making Bobbin Lace, Math. Mag., Vol. 91, No. 4, 2018.

Publication | Veronika's Artist Page

Robert Bosch: From Dominos To Traveling Salespeople, Math. Mag., Vol. 92, No. 4, 2019.

Publication | Robert's Artist Page

Henry Segerman: Visualizing Topology, Math. Mag., Vol. 93, No. 4, 2020.

Publication | Henry's Webpage

John Edmark: Art in Motion, Math. Mag., Vol. 94, No. 1, 2021

Publication | John's Artist Page

Articles

A Knot Game with not KNerds, with M. Cohen. Math Horizons, Vol. 20, No. 2, 2012.

Publication

Service-Learning in a Quantitative Reasoning Course, with J. Anderson. Peer Review: A Journal of the Association of American Colleges & Universities, 2014.

Publication

Visions of Mathematics, Introduction to artist's book Dreams of Pythagorus by Michael Schultheis, 2014.

Publication

The Power of Bravery, MAA FOCUS, June/July 2018.

Publication