# Faculty Research

## Faculty Research

**Patrick Bennett's **research is in probabilistic and extremal combinatorics. I specialize in the design and analysis of randomized combinatorial algorithms. Usually, the goal is to prove the existence of some object with interesting properties (e.g. extremal properties) by arguing that it is the likely output of a random algorithm. Of course, the challenge is to design an algorithm that performs well subject to the constraint that this algorithm must be possible to analyze rigorously. Perhaps surprisingly, my research often involves differential equations.

**Andrzej Dudek's** broad research area is combinatorics, with emphasis on extremal combinatorics and random graphs. Extremal combinatorics studies how large or how small a collection of finite objects (e.g. numbers, graphs, sets) can be if it has to satisfy certain restrictions. A random graph is a graph that is generated by some random process. The theory of random graphs lies at the intersection between graph theory and probability theory. Dudek is an author of over 80 research articles published in the mainstream journals. Dudek's research has been supported by National Security Agency and Simons Foundation.

**Laura R. Van Zoest** is a professor of mathematics, specializing in mathematics education, in the Department of Mathematics at Western Michigan University. She specializes in secondary mathematics teacher education and is interested in how people become effective mathematics teachers, teacher educators, and researchers, and ways university programs can accelerate that development. Lines of research have included investigating the effect of reform curriculum materials on teacher development, the use of practice-based materials in university methods courses, and the cultivation of productive norms in teacher education. Her work on how teachers can productively use student thinking (BuildingonMOSTS.org) has been continuously supported by the National Science Foundation for over a decade.

Van Zoest has served as the principal investigator for research and professional development projects funded at over five million dollars and published in research and practitioner journals, including the Journal for Research in Mathematics Education, Journal of Mathematics Teacher Education, Teacher and Teacher Education, Cognition & Instruction, Mathematics Teacher Educator and Mathematics Teacher Learning & Teaching. She was editor of Teachers Engaged in Research: Inquiry into Mathematics Practice, 9–12, guest co-editor of the ZDM: The International Journal on Mathematics Education focus issue Theoretical frameworks in research on and with mathematics teachers, and co-editor of Research Trends in Mathematics Education. She co-chaired the 2012 PME-NA conference hosted by WMU, served as chair of the steering committee of PME-NA, chaired the Editorial Panel for Mathematics Teacher Educator and serves on the International Advisory Board for Research in Mathematics Education.

**Dr. Ping Zhang's** research is in graph theory, primarily in classical and structural graph theory as well as its applications. Among the many topics in graph theory on which she has worked are the following: colorings, labelings, domination, distance, decompositions, connectivity, Hamiltonicity, graph embeddings, Ramsey theory. She is also interested in problems in other areas of discrete mathematics as well as number theory and algebraic and topological combinatorics. She particularly enjoys working on research topics that are appropriate for and likely to be of interest to students, both undergraduates and graduate students.