BiographyDr. Neil spent his undergraduate years at Lake Forest College, where his love for mathematics was born. After receiving his Ph.D. from The University of Iowa, specializing in knot theory, he spent three years as an Assistant Professor at William Jewell College. In 2010, he arrived at North Central College, where he is now an Associate Professor in the Department of Mathematics & Actuarial Science. He is passionate about not just teaching mathematics; he is passionate about engaging the individual to help each and every student find the path for them. Whether it is through informal conversations, mentoring of student groups, research collaboration or some other avenue, he consistently reiterates his life mantra to his students: in all that you do, settle for nothing less than your absolute best.
His research interests lie mainly in the fields of geometric knot theory and discrete and computational geometry, though he also has peer-reviewed work in sustainable service learning and relationships between knot theory and musical rhythm. The primary goal of his research is to collaborate with students. Thus, finding projects accessible by undergraduates is always his top priority and has resulted in multiple co-authored peer-reviewed articles.
Beyond the classroom, Neil is North Central College's Faculty Athletic Representative (FAR) to the NCAA and serves as advisor the NCC Cycling & Multisport Club. He chairs the Faculty Elections Committee as well as the informal faculty Fermentation Committee, has served as a Director-at-Large for the Illinois Section of the Mathematical Association of America, and has served as a Coleman Foundation Faculty for his weaving of entrepreneurial approaches into his general education courses.
Dr. Neil has been very active in the M3 math modeling competition, serving as a grader for their national competition and having written multiple problems for their monthly dialogues. He was the primary author of the 2016 national competition question, partnering with the National Park Service to write, "From Sea to Shining Sea: Looking ahead with the National Park Service."
Beyond North Central, Dr. Neil spends much of his time devoted to his passions of running (not fast but far), ultra-distance mountain bike racing and bikepacking. He is also the founder of DTS (Dream, Train, Succeed) Coaching and works with athletes of all levels to achieve their running goals. And last, but certainly not least, Dr. Nicholson, along with his amazing wife Elizabeth and fantastic son Zeke, spends ample time addressing the needs of Gordon and Gus, his two cats.
Areas of Research / Professional Expertise
Geometric knot theory, discrete and computational geometry, graph theory, algorithmic game theory
Running, cycling, mountain biking, U.S. national parks, bikepacking, coaching
Published: May 02, 2019 by Minnesota Journal of Undergraduate Mathematics
Authors: Jack Billings, Neil Nicholson
Using previous work on lattice point visibility as the foundation for our approach, the topic of weak visibility preserving functions is explored. Two particular types of functions are investigated, with one always being weak visibility preserving and the other never so.
Published: Aug 01, 2016 by Polymath: An Interdisciplinary Arts & Sciences Journal
Authors: Jonathan Kirk, Neil Nicholson
Visualizing Euclidean rhythms using tangle theory (a field of knot theory) is explored.
Published: May 02, 2016 by Involve: A Journal of Mathematics
Authors: Neil R. Nicholson, Rebecca Rachan
Necessary and sufficient conditions for a lattice point to be weakly visible are determined.
Published: Nov 01, 2013 by In Service-Learning in Higher Education: Connecting the Global to the Local: University of Indianapolis Press
Authors: Mary Embry, Neil R. Nicholson, Deborah Scarfino
An exploration of the impact of short-term versus long-term service-learning projects
Published: Mar 01, 2013 by Journal of Knot Theory and its Ramifications
Authors: Donglun Liu, Steven Mackey, Neil R. Nicholson, Tyler Schroeder, Kyle Thomas,
The average bridge number over all resolutions of a knot shadow is completely determined and is shown to be one half the number of precrossings.
Published: Oct 01, 2011 by Journal of Knot Theory and its Ramifications
Authors: Neil R. Nicholson
An investigation of low-edge number piecewise-linear virtual knots.
Published: Mar 01, 2010 by Involve: A Journal of Mathematics
Authors: Neil R. Nicholson and Christopher Sharp
A minimum distance for a point must be from a rectangular array in order to weakly view the entire array is determined.
Published: Aug 01, 2008 by Journal of Knot Theory and its Ramifications
Authors: Neil R. Nicholson
An investigation of the "nonalternatingness" of knots and the impact of such on the Jones polynomial.