Mathematics

Dr. Ton Boerkoel received his Ph.D. at the University of Texas in Austin in 1994. Although his primary area of interest is number theory, he enjoys working in many other fields such as combinatorics, geometry, abstract algebra, complex analysis, and cryptography.

Dr. Boerkoel has been teaching at DigiPen since 2006, and prior to coming to Washington, he taught at universities in Iowa, Texas and Kansas. He has been teaching mathematics for three decades, mostly in the U.S., and taught the gamut of subjects from remedial math to undergraduate and graduate classes, including trigonometry, calculus I-III, college geometry, linear algebra, abstract algebra, matrix theory, discrete math, number theory, real analysis, complex analysis, combinatorics, and problems solving, as well as online courses.

Dr. Boerkoel has given many presentations and talks on a wide range of mathematical topics, not just in the U.S., but in Holland, Chile, and India as well. He loves teaching at DigiPen and enjoys its student population and their mix of interests in computers, games, and art.

Dr. Matt Klassen earned his Ph.D. in mathematics from the University of Arizona in 1993, specializing in number theory and algebraic geometry. Since joining DigiPen in 1999, his interests moved to mathematics relating to computer graphics and geometric modeling with particular emphasis on splines. He went on to develop special courses on quaternions with application to computer graphics and animation, and spline curves through the perspective of linear algebra. Some of this course work led to a paper: “Generalized Vandermonde Determinants and Splines,” presented at a conference in honor of Peter Borwein, May 2008, at Simon Fraser University.

Klassen also developed an interest in combinatorial game theory and has been teaching a course in the subject which is attended by undergraduate and graduate students in computer science. At least one graduate student chose to do a masters thesis in this area under the supervision of professor Klassen, entitled “Solving the 4x3x3 Three Dimensional Domineering Game.”

Relating more to his original studies in geometry and number theory, Klassen explored non-associative structures on curves, which led to a paper presentation: “Non-Associative Loops on Fermat Curves of Odd Degree,” Summer Workshop on Computational Number Theory, IRMACS Center, Simon Fraser University, September 2009.

In 2011, Dr. Klassen laid the groundwork for two new programs at DigiPen, requested by President Claude Comair: the BA in Music and Sound Design, and the BS in Computer Science in Digital Audio (originally BS in Engineering and Sound Design). He has taught courses in Mathematics of Music (for the BA program), and in Digital Signal Processing (for the BS program). In spring semester 2018, Klassen will teach a special topics course on “Computation and Modeling of Head-Related Transfer Functions,” which will explore methods of spatial sound processing with applications for virtual and augmented reality. This course precedes an international conference in August 2018 called “Audio for Virtual and Augmented Reality,” hosted by DigiPen. The conference is chaired by Klassen, and jointly organized by DigiPen and Dr. Edgar Choueiri at Princeton University 3D3A Lab.

“DigiPen provides a dynamic context for teaching and learning mathematics,” Klassen says. “Students are highly motivated and generally appreciate the power of mathematics, which shows up in their project work in signal processing, graphics and game development.”

Dr. Alexander Young has an honors MS in Mathematics from Brown University (2007) and a Ph.D. in Mathematics from the University of California, San Diego (2012). In classroom and private coaching settings, he has over 17 years of combined teaching and tutoring experience.

Dr. Young’s published work is in non-commutative algebra. He has crafted online textbooks and written WeBWork code for several of his classes, implementing tools such as interactive graphical illustration and randomized practice resources. In addition to his written work, he contributed the mini-game Chess Invaders to the 2016 game Frog Fractions 2.

Dr. Young enjoys the level of personal interaction between professors and students that is possible at a place like DigiPen. He views his goal in teaching math as handing down an invaluable tool — and source of inspiration — that can last a lifetime.

Selected Publications

• K. Chan, A. Young, and J. J. Zheng (in press), “Noncommutative cyclic isolated singularities,” Transactions of the American Mathematical Society.
• K. Chan, A. Young, and J. J. Zheng, “Discriminants and Automorphism Groups of Veronese Subrings of Skew Polynomial Rings,” Mathematische Zeitschrift, 288 (2016) No. 3-4, pp 1395-1420.
• K. Chan, A. Young, and J. J. Zheng, “Discriminant Formulas and Applications,” Algebra & Number Theory, 10 (2016) No. 3, pp 557-596.
• Agata Smoktunowicz and Alexander Young, “Jacobson Radical Algebras with Quadratic Growth,” Glasgow Mathematical Journal, 55 (2013) issue A, pp 135-147.
• Jason Bell and Alexander Young, “On the Kurosh problem for algebras over a general field,” Journal of Algebra, 342 (2011) issue 1, pp 265-281.
• T. H. Lenagan, A. Smoktunowicz, and A. Young, “Nil Algebras with Restricted Growth,” Proceedings of the Edinburgh Mathematical Society, 55 (2012) issue 2, pp 461-475.