Basic Professional Information
I am a tenured Associate Professor of Mathematics at Gordon College, on Boston's North Shore. I teach a variety of math courses running the gamut from core courses to senior-level ones.
I received my PhD in Mathematics from the University of Chicago; my thesis, "Chow Groups of Zero-Cycles Relative to Hyperplane Arrangements", was completed under the direction of Spencer Bloch. Before that, I studied mathematics and keyboard instruments at Northwestern University and Roosevelt University.
I'm fortunate to have support from students through administration to:
- Develop several truly interesting courses which are also inspiring to our students, such as a non-major course in the mathematics of voting and choice and a serious number theory course with a broad point of view (calculus to geometry).
- Attempt needed innovations in core courses, including continued development of a truly conceptual one-semester calculus course, and a service-learning component in mainstream calculus.
- Use innovative technologies like the Sage cell server to enhance student engagement and learning.
- Guide students in research in the mathematics of Voting and Choice.
- Conduct independent studies in areas such as Representation Theory and Lie Groups with talented students heading to PhD programs.
Some work related to this has ended up published or otherwise reached a broader audience, see below.
Scholarship and Other Professional Activities
Here are some of the professional things I have been up to lately:
- Working on research in the mathematics of voting and choice (see below).
- Work on resources and code for the open source math program Sage.
- I give a lot of talks about math of voting and choice.
- Here is a version of a general overview talk, which I gave at Colby College in 2014.
- A more research-oriented, but still undergraduate, talk I have given is in these slides.
- Creating more IBL modules for my non-major calculus course (funded by the Academy of Inquiry-Based Learning).
- The tutorials I cowrote with Rob Beezer and Jason Grout for introducing college faculty to Sage are now part of the standard documentation.
- I've had service-learning work by students in several different calculus classes. I helped organize a special session in this at the 2011 Joint Mathematics Meetings. All the papers are archived on my site with the gracious permission of the speakers, and I co-edited a special issue of PRIMUS about this topic.
- This "Notebook" for courses of the Bridge or Transitions variety; an article about this appeared in PRIMUS.
- A brief article introducing the symmetries of the permutahedron to abstract algebra teachers, appeared in CMJ.
- Those interested in teaching number theory in a way that connects to lots of other courses as well as incorporating dynamic visualization and computer exploration may wish to peruse my Number Theory: In Context and Interactive text.
- If you are interested in learning how to embed one-click interactive demonstrations in a webpage for your lectures, this tutorial from a talk I gave about this could be useful.
- I'm also interested in math applied to music theory, particularly reinterpreting the geometric work of Callender-Quinn-Tymoczko in algebraic terms.
- I am an Associate Editor of the journal PRIMUS, and occasionally referee papers for other journals.
- I act as a reviewer for Math Reviews/MathSciNet as well.
Math of Voting
Here are some brief summaries of projects I've worked on.
In the mathematics of voting, extending the work of Orrison and his students to social preference functions. They interpreted much of Saari's decomposition work in a more explicitly algebraic framework, using irreducible subspaces of the profile space under the action of the symmetric group to characterize various voting rules.
My own work (in Cont. Math. 624) extends this to the case of 'scoring' social preference functions. The main result is to connect the Borda Count and Kemeny Rule as giving rise to the 'most symmetric' members of this large class of procedures. For a broader audience, here is a talk I gave about this some time ago.
For a more recent, generalist talk on some topics I think about (including voting on cyclic orderings), read these slides from a talk given at Willamette University in 2016.
Several years ago, my student Sarah Berube and I extended work of Saari and Bargagliotti in characterizing sets of profiles which arise in nonparametric statistical tests. This appeared in Mathematical Social Sciences. An earlier version is here, and here are slides from an invited talk I gave in Irvine about this.
Please note I am aware that my site is behind the times, oh-so 20th-century. It's a decision that had to be made, but someday I hope to make it more snappy.
Various professionally-related profiles: