Research

Mathematics faculty at Kutztown are engaged in research, and seek to include undergraduate students in our work. Students are active contributors, and many go on to present at local, regional, and national conferences.

Student research presentations...

at a Mathematical Association of America conference

Student research presentations...

at the PASSHE STEM Conference

Faculty and student research presentations...

at the Modeling and Optimization: Theory and Applications (MOPTA) Conference

Faculty research presentation...

at a Mathematical Association of America conference

Student research presentation...

at the Moravian Student Mathematics Conference

Student research presentation...

at the Moravian Student Mathematics Conference

Faculty research presentation...

at the Joint Mathematics Meetings national conference

Faculty research presentation...

at the Joint Mathematics Meetings national conference

Student research presentations...

at the PASSHE STEM Conference

Student research presentation...

at MathFest, a national conference

Faculty and student research presentations...

at the Modeling and Optimization: Theory and Applications (MOPTA) Conference

Faculty research presentation...

at the Joint Mathematics Meetings national conference

Student research presentations...

at the PASSHE STEM Conference

Faculty research presentation...

at the Annual International Conference of the German Operations Research Society in Hamburg, Germany

Faculty and student research presentations...

at the Modeling and Optimization: Theory and Applications (MOPTA) Conference

Student research presentation...

at a Mathematical Association of America conference

Student research presentation...

at a Mathematical Association of America conference

Faculty research presentation...

at the Joint Mathematics Meetings national conference

Student presenters with faculty mentors at a conference
Student presenters with faculty mentors at a conference
Faculty and students presenting at a conference
Faculty presenting at a conference
Student presenting at a conference
Student presenting at a conference
Faculty member presenting at a conference
Faculty member presenting at a conference
Students and faculty mentors at a conference
Students presenting their poster at a conference
Faculty and Students at a conference
Faculty member presenting at a conference
Students at a conference
Faculty member in front of conference banner
Faculty and Students at a conference
Student conference presentation
Student conference presentation
Faculty conference presentation
Examples of research projects

  • Combinatorics and Algebra: Algebraically Defined Graphs

Combinatorial graphs are essentially networks: they contain nodes (called vertices) and edges.  These graphs are called algebraically defined if edges are created according to whether given algebraic conditions are satisfied.  Certain important properties of these graphs may be discovered by studying when special equations (or systems of special equations) have solutions.   Questions related to this project have applications to incidence geometry.  Dr. Kronenthal is interested in this topic, and has collaborated with undergraduate students to study related questions.

  • Graph Coloring Games

Coloring the vertices or edges of combinatorial graphs to satisfy certain conditions is a popular research area.  Dr. Wong worked with Diego Manzano-Ruiz, an undergraduate student, on a coloring problem in the context of a two-player game.

The name "Cable-Trench" comes from the fact that a physical application of the CTP is the problem of minimizing the cost to create a campus network in which each building on a campus is connected to a central server with its own dedicated cable. There is one cost to dig trenches between buildings and a separate cost to purchase and lay the cables. In their 2002 paper, Dr. Vasko and his co-authors proved that there is no known efficient algorithm that finds the optimal solution to CTPs.  The CTP has been applied to numerous real-world applications, such as medical research, cancer detection, and identifying blood clots.  Dr. Landquist, Dr. Lu, and numerous Kutztown students have worked on this and closely related projects.

  • Jaeger's conjecture

Let A be an invertible n-by-n matrix over a prime field of size at least 5. Do there always exist two vectors x and y of length n such that all entries of x and y are nonzero, and y=Ax?

Dr. Wong is very interested in this open conjecture. Partial progress has been made, and he is looking for collaborators to further his findings.  

Metaheuristics are solution strategies (as opposed to specific algorithms) that can be used to generate very good solutions (perhaps optimal) to problems in reasonable computing time.  These problems are so difficult that finding an exact solution could require days, weeks, months or even years.  Metaheuristics that can generate high quality solutions using little or moderate computer resources are very desirable because of their wide industrial and business applications.  Dr. Lu and Dr. Vasko are especially interested in this area of study.

  • A probabilistic take-away game

Alice and Bob are playing a very simple game. Each of them starts with a pile of n chips, and they take turns to lose p chips or q chips randomly and independently with equal probability. The first player who removes all chips from their pile is the winner. We are interested in finding the winning probability for Bob. This project is an extension of the research paper that Dr. Wong and Ms. Jiao Xu coauthored. Ms. Xu graduated from Kutztown University in Spring 2017.