Student Research

Over the years I have mentored several undergraduate and high school student research projects in mathematics. Below are the papers that were written by my students, many of which have been published.

Student Publications

• Kraft, Benjamin & Monks, Keenan (my son), On Conjugacies of the 3x+1 Map Induced by Continuous Endomorphisms of the Shift Dynamical System, Discrete Mathematics, Vol. 310 (2010), 1875-1883.
• Monks, Maria (my daughter), Endomorphisms of the shift dynamical system, discrete derivatives, and applications., Discrete Mathematics, Vol. 309, Issue 16 (2009), 5196-5205.
• Monks, Ken M. (my son),  The Sufficiency of Arithmetic Progressions for the 3x+1 Conjecture, Proc. Amer. Math. Soc., 134 (10), October (2006), 2861-2872
• Fusaro, Marc, A Visual Representation of Sequence Space, Pi Mu Epsilon Journal, Pi Mu Epsilon Journal 10 (6), Spring 1997, 466-481 Marc’s paper is the winner of the 1997 MAA EPADEL section Student Paper Competition. Marc’s paper was also awarded a 1997 Richard V. Andree award after the officers and councilors of Pi Mu Epsilon judged it to be one of the best three papers to have appeared in the Pi Mu Epsilon Journal during 1997.
• Joseph, John, A Chaotic Extension of the 3x+1 Function to $\mathbb{Z}_{(2)}$, Fibonacci Quarterly, 36.4 (Aug 1998), 309-316 John’s paper was the winner of the 1996 MAA EPADEL section Student Paper Competition.
• Farruggia, C., Lawrence, M., Waterhouse, B., The Elimination of a Family of Periodic Parity Vectors in the 3x+1 Problem, Pi Mu Epsilon Journal, 10 (4), Spring (1996), 275-280 Their paper was awarded a 1996 Richard V. Andree award after the officers and councilors of Pi Mu Epsilon judged it to be one of the best four papers to have appeared in the Pi Mu Epsilon Journal during 1996.

Student Projects

• Schneider, Eric, On the Workday Number for Finite Multigraphs in a Variation of Cops and Robbers, high school research project, Summer 2013
• Yazinski, Jonathan, Pseudoperiodicity and the 3x+1 Congjugacy Function, honor’s thesis, Spring 2003
• Riggi, Carla, Hutchinson Operators in $\mathbb{R}^3$, honor’s thesis, Spring 2001 Carla also wrote some 3D fractal software in Maple and the Maple help file for her software.
• Kucinski, Gina, Cycles for the 3x+1 Map on the Gaussian Integers, FSRP project, Spring 2000
• Fraboni, Mike, Conjugacy and the 3x+1 Conjecture, FSRP project. Mike’s paper was the winner of the 1998 MAA EPADEL section Student Paper Competition.

If you are a student at the University of Scranton and might be interested in doing such a project, please contact Dr. Monks for further information.