Dan McQuillan

Dan has taught 20 different mathematics courses at Norwich University, often teaching Discrete Mathematics. He has more than 25 peer-reviewed publications in combinatorics. In addition, he has peer-reviewed publications in convex and discrete geometry, number theory, real functions, statistics, and mathematical pedagogy.

His major recent work is in topological graph theory, where he is working to develop new methods for calculating crossing numbers of complete graphs. His research publications cover a wide range of topics, from abstract algebra to strategies of Major League Baseball. He has collaborated on projects with many Norwich faculty, including two papers on the teaching of calculus and one on teaching proof techniques for high school students.

Some of his work involves collaboration with Norwich undergraduates, including numerous student summer research projects. This has led to four professional peer-reviewed mathematics papers for undergraduates in discrete mathematics. This work has primarily involved so-called magic labelings of graphs — an ideal topic for student involvement, as the problems are tractable after standard sophomore-level mathematics courses.

In 2002, McQuillan started Norwich University’s involvement in the William Lowell Putnam Mathematical Competition, North America’s most prestigious mathematics challenge for clever mathematics enthusiasts. He continues coaching the team today. A common theme of his research work and his teaching involves thinking very deeply about a subject, often resulting in a surprisingly simple explanation of something that was previously thought to be complicated. He is an outspoken ambassador of mathematics and has also published two mathematically based poems as filler pieces in mathematics journals.

Ph.D. Mathematics, Western University

Professor McQuillan specializes in topological graph theory, combinatorics, graph labelings, and innovative mathematical pedagogy. His work blends visual intuition with rigorous theory, structuring problems that are easy to state but complex to solve. Combinatorics underpins much of his research, while his interest in pedagogy arises from connecting seemingly unrelated mathematical concepts.

Since 2003, he has mentored Norwich University students in research, resulting in multiple publications in top journals, and collaborates internationally with scholars, including Bruce Richter and Ian Gray. He emphasizes daily practice, learning from failures, and framing new knowledge around unsolved problems, believing mathematics can enhance understanding, efficiency, and creativity.

MA 121 Calculus
MA 240 Number Theory
MA 306 Discrete Mathematics
MA 310 Linear Algebra
MA 318 Cryptograph
MA 411 Senior Seminar

Every even-regular Hamiltonian graph is vertex-magic, I. Gray, D. McQuillan and J.M. McQuillan, Discrete Mathematics, Vol. 349 no. 7 (July 2026), 13 pp.

Does the degree sequence of an (almost) regular graph determine if it possesses a strong vertex-magic total labeling?, J. Calzadillas* and D. McQuillan, Australasian Journal of Combinatorics, Vol. 90 no. 3 (2024), pp. 378-392.

Convex Drawings of the Complete Graph: Geometry meets Topology, A. Arroyo, D. McQuillan, R.B. Richter and G. Salazar. Ars Mathematica Contemporanea, Vol. 22 no. 3 (2022), 27pp. 

*NU student coauthor.