Dan McQuillan

Dan has taught eighteen mathematics courses at Norwich University, often Discrete Mathematics. He has more than twenty 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. He also has two mathematically-based poems published as filler pieces in mathematics journals.

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. An outspoken ambassador for the field of mathematics, he has collaborated on projects with many Norwich faculty outside his department, including two papers on the teaching of calculus.

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 the area of 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.

Ph.D. Mathematics, Western University 

M.Sc. Mathematics, Western University

B.A. Mathematics, Carleton University, Canada

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 306 Discrete Mathematics 
MA121 Calculus I
MA101 Mathematics

Strong vertex-magic and super edge-magic total labelings of the disjoint union of a cycle with 3-cycles, D. McQuillan and J.M. McQuillan, Discrete Mathematics, Vol. 346 No. 9 (September 2023). 

Vertex-magic trees with n central vertices and kn leaves have bounded order for each k exceeding the square root of 3, J. Calzadillas* and D. McQuillan, Bulletin of the Institute of Combinatorics and its Applications, Vol. 97 (February 2023), pp. 117-127. *Norwich Student.

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.