### Student Research and Awards

**Nathan Anderson-Stahl '16**: Winner of the Andrew Mutch Scholarship to attend the University of St. Andrews, Scotland**Kate Lorenzen '16**: Counting Cayley-Sodoku Tables**Amy Ankney '15**: Social Network Analysis of First Year Students**Arnold Schwemmlein '15**: Studying Nonlinear Systems of Equations Using Newton's Method and Microsoft Excel**Victoria Arthur '14**: A Survey of Statistical Clustering Techniques Using Biological Data**Lola Lesi '14**: Dieception: Die within a Die**Lucas Lingenfelter '13**: An Analysis of Gray Codes Applied to Gene Sequences**Zhongwei Hu '12**: The Zero-Forcing Number of Circulant Graphs**Abigail Lutz '12**: The Chromatic Number of the Generalized Petersen Graph

### Faculty Research and Exhibitions

#### John Bukowski

Dr. Bukowski's current research interests include the history of mathematics, particularly that of the 17th and 18th centuries. He has done research on the Dutch mathematician and scientist Christiaan Huygens. Dr. Bukowski has given math history lectures in the United States, Brazil, France, and the Netherlands. His recent publications include the following:

- "History of the Allegheny Mountain Section," prepared in celebration of the Centennial of the Mathematical Association of America, August 2014
- "Christiaan Huygens - The Premier Ornament of His Time," Eureka! 44 (April 2014), 24-26
- "Christiaan Huygens and the Problem of the Hanging Chain", College Mathematics Journal 39 (2008), 2-11.
- "Huygens, Holland, and Hanging Chains, or L'affaire de la chaine", Juniata Voices 6 (2006), 85-95.
- "The Quantitative Requirement at Juniata College," in Current Practices in Quantitative Literacy Programs, MAA Notes, Washington, DC, 2006.

#### Henry Escuadro

Dr. Escuadro’s research area is graph theory; in particular, his interests include distances in graphs, graph colorings, and graph structures. His recent publications include the following:

- "On the Total Detection Numbers of Complete Bipartite Graphs," H. Escuadro, C. Musick, and F. Fujie-Okamoto. Discrete Mathematics Vol. 313 Issue 24 (2013) 2908-2917
- "On the Hardness of Recognizing Triangular Line Graphs," P. Anand, H. Escuadro, R. Gera, S. Hartke, and D. Stolee. Discrete Mathematics Vol. 312 Issue 17 (2012) 2627-2638
- "The Total Detection Numbers of Graphs," H. Escuadro and F. Fuhie-Okamoto, Journal of Combinatorial Mathematics and Combinatorial Computing 81 (2012), 97-119
- "Geodetic Domination in Graphs," H. Escuadro, R. Gera, A. Hansberg, N. Jafari Rad, and L. Volkmann, Journal of Combinatorial Mathematics and Combinatorial Computing 77 (2011) 89-101
- "Triangular Line Graph and Word Sense Disambiguation," P. Anand, H. Escuadro, R. Gera, and C. Martell, Discrete Applied Mathematics Vol. 159 Issue 11 (2011) 1160-1165

#### Gerald Kruse

Dr. Kruse's research interests include Algorithm Experimentation, Scientific Computing, and Parallel Computing, and he is always interested in ways to teach Mathematics and Computer Science more effectively. His recent publications and presentations include the following:

- "A Useful Case-Study in Algorithmic Experimentation: Unexpected Timing Results for Heapsort," SIGCSE 2007 Poster Session, Covington, KY, March 2007.
- "How I Taught a Full Semester of Computer Graphics in Two Weeks, in Germany, and Lived to Tell About It...," SIGCSE 2006 Poster Session, Houston, TX, March 2006.
- "How Google Relies on Discrete Mathematics," Joint Mathematics Meetings, Atlanta, GA, January 2005.
- " 'Magic Numbers' Approach to Introducing Binary Number Representation in Introductory Computer Science Classes," Joint Mathematics Meetings, Phoenix, AZ, January 2004.
- "Introducting Writing in the CS Curriculum," SIGCSE 2004 Panel, Hampton, VA, March 2004.
- "Spectral Element Methods for Transitional Flows in Complex Geometries," P.F. Fischer, G. W. Kruse, and F. Loth, Journal of Scientific Computing, December 2002.

#### Kimberly Roth

Dr. Roth’s current research interests include chaos theory and the behavior of fractals. Her recent publications include the following:

- "Non-uniform Porosity for a Subset of Some Julia Sets", to appear in the refereed proceedings of Complex Dynamics: 25 Years After the First Appearance of the Mandelbrot Set, published in the Contemporary Math Series of the AMS, 2006.
- "Teaching outside my comfort zone", Cardinal Perspectives, 2004-2005.
- "Julia Sets that are Full of Holes", to appear, Mathematical Intelligencer.

#### Catherine Stenson

Dr. Stenson's research interests include the combinatorics of polytopes and hyperplane arrangements, the applications of mathematics to biology and chemistry, and modeling cooperation. Her recent publications include the following:

- "Weighted voting, threshold functions, and zonotopes," in The Mathematics of Decisions, Elections, and Games, Contemporary Mathematics, vol. 624, Amer. Math. Soc., Providence, RI, 2014, pp. 89-99
- "Let π be a function," (with Juniata student Justin Schultz '08). Mathematics Magazine 86 (2013), pp. 177-188.
- "Tiling (2xn)-boards with squares and dominoes," (with Juniata student Matt Katz '08). Journal of Integer Sequences 12 (2009), Article 09.2.2.
- "Families of tight inequalities for polytopes," Discrete and Computational Geometry 34 (2005), 507-521.
- "Relationships among flag f-vector inequalities for polytopes," Discrete and Computational Geometry 31 (2004), 257-273.
- Book: S. Stahl and C. Stenson Introduction to Topology and Geometry, 2nd edition. Wiley, Hoboken, NJ, 2013.