## Ken Monks’s Undergraduate Student Research Program Information

In 1991 the University of Scranton created an Undergraduate Faculty-Student Research Program (FSRP) designed to allow undergraduates to gain research experience for transcript recognition, with no fee or credits involved. Participation in the program has been strictly voluntary for both the students and the faculty. The University also has an Honors Program in which students do independent study culminating in a senior thesis. There are also in-house competetive grants for funding undergraduates to do research over the summer.

In mathematics, I have directed several student research projects. Their work has resulted in the following student papers.

### Student Papers

- 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.

Get: [the paper in pdf format]

Ben and Keenan’s paper was published in the journal Discrete Mathematics! - Monks, Maria (my daughter),
*Endomorphisms of the shift dynamical system, discrete derivatives, and applications.*, Discrete Mathematics, Vol. 309, Issue 16 (2009), 5196-5205.

Get: [the paper in pdf format]

Maria’s paper was published in the journal Discrete Mathematics! - 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 Get: [the paper in pdf format]

Ken’s paper was published in the Procedings of the American Mathematical Society journal! - Yazinski, Jonathan,
*Pseudoperiodicity and the 3x+1 Congjugacy Function*, honor’s thesis, Spring 2003

Get: [the paper in dvi format] , [the paper in pdf format] - Riggi, Carla,
*Hutchinson Operators in***R**^{3}, honor’s thesis, Spring 2001

Get: [the paper in dvi format] , [the paper in pdf format]

Carla also wrote some 3d fractal software in Maple:Get: [the Maple Source code for Chaos3d] and [the Maple help file for Chaos3d] - Kucinski, Gina,
*Cycles for**the 3x+1 Map on the Gaussian Integers*, preprint

Get: [the paper in dvi format] , [the paper in pdf format] - Fraboni, Mike,
*Conjugacy and the 3x+1 Conjecture*, preprint

Get: [the paper in dvi format] , [the paper in pdf format]

Mike’s paper is the winner of the 1998 MAA EPADEL section Student Paper Competition.Congratulations, Mike! - Fusaro, Marc,
*A Visual Representation of Sequence Space*, Pi Mu Epsilon Journal, Pi Mu Epsilon Journal 10 (6), Spring 1997, 466-481

Get: [the paper in dvi format] , [the paper in pdf format]

Marc’s paper is the winner of the 1997 MAA EPADEL section Student Paper Competition.

Congratulations, Marc!

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.

Congratulations again to Marc!

[Note: The dvi file includes text, but no figures. If you wish to see the figures print the pdf.] - Joseph, John,
*A Chaotic Extension of the 3x+1 Function to Z*_{2}[*i*], Fibonacci Quarterly,**36.4**(Aug 1998), 309-316

Get: [the paper in dvi format] , [the paper in pdf format]You can also get a longer, more detailed version of John’s paper in pdf format.

John’s paper is the winner of the 1996 MAA EPADEL section Student Paper Competition.*Congratulations, John!* - 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

Get: [the paper in dvi format] , [the paper in pdf format]

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.Congratulations, Carolyn, Mike, and Brian!

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