D.A., Mathematics, Carnegie Mellon University, 2013.
Dissertation: Textbook and Course Materials for 21-127 Concepts of Mathematics.
Advisors: Dr. Jack Schaeffer, Dr. John Mackey.
M.S., Mathematics, Carnegie Mellon University, 2010.
B.A., Mathematics & Physics, Hamilton College, 2007.
I studied mathematics and physics in college, and went on to graduate school to study applied math. While there, I found a passion for teaching and learning, and my dissertation instead focused on teaching students to read and write mathematical proofs. I still love mathematics for its usefulness in the sciences, and I do enjoy teaching students about the utility of mathematical thinking in the real world. But I also think of mathematics as a gigantic puzzle to play with, and I enjoy helping students explore how the pieces of that puzzle can fit together. Indeed, some of my research and teaching focuses on practical applications (like the theory of voting) while some of it is more recreational in nature (like pursuit-evasion games and crossword puzzles). Overall, I love thinking about and doing mathematics, and I hope that passion comes across and inspires my students to learn and use mathematics in their own lives.
What I Love about Emmanuel:
The students, faculty, and staff I’ve worked with are so supportive. I appreciate the Emmanuel community’s focus on helping each other to learn and to make positive changes in the world.
For my doctoral thesis, I wrote a textbook for a course that introduces students to mathematical proofs and problem-solving, entitled Everything You Always Wanted to Know about Mathematics (but didn't even know to ask): A Guided Journey into the World of Abstract Mathematics and the Writing of Proofs. Publication details forthcoming. I use this text in our course MATH2109 Introduction to Proofs, and it has been in use at Carnegie Mellon University for their course 21-127 Concepts of Mathematics for several years.
Current research: Pursuit-evasion games on graphs, especially Lazy Cops & Robbers.
I recently conducted a summer research project with two Emmanuel students. We investigated the Lazy Cops game on particular graphs, including graphs based on the movements of Chess pieces. We obtained several new and significant results and are currently working on publications to be submitted to scholarly journals. In addition, the two students (Niko Townsend & Mikayla Werzanski) will presented some of our results at the Young Mathematicians Conference at Ohio State University in Auguat 2015. Here is a link to the abstract for their presentation which summarizes our results.
Past research: In my undergrad and graduate careers, I worked on projects in a variety of math branches:
Overall, I typically find myself interested in problems where several (perhaps seemingly unrelated) branches of mathematics collide.
I also maintain an active interest in the Basel Problem and the always-growing number of proofs of this centuries-old fact. I am compiling a list of all published proofs of this fact and have plans to write a book about them.