Basic Professional Information
I am 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'm very involved with a number of other mathematical endeavors, including open-source software. I also have done enough editing and refereeing now to claim some expertise in that.
Most of my formal research now is in the mathematics of voting and choice, with other scholarship more closely related to university-level teaching. 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. I also studied mathematics and keyboard instruments at Northwestern University and Roosevelt University.
Finally, I do a fair amount of speaking and workshops about several topics. Contact me if you think your colleagues or students would like to hear an entertaining and informative introduction to ...
- The Mathematics of Voting and Choice (general or aiming at research)
- Using SageMath (for teaching or research)
- Incorporating service-learning into the mathematics curriculum
- Authoring open texts with PreTeXt
Teaching
Gordon students: go straight to Canvas!
In Gordon College's department of Math and CS, I'm fortunate to have support from students through administration to innovate in several ways.
- I've developed new and truly interesting courses, including 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).
- I've had leeway to implement inquiry-based materials in a truly conceptual one-semester calculus course as well as our proof transition course, and I've implemented service-learning component in mainstream calculus. My upper-level Real Analysis courses is run using a form of the "Moore method".
- I routinely use technologies like the Sage cell server to enhance student engagement and learning.
It has also been very gratifying to guide talented students beyond our usual curriculum, including:
- Research in the mathematics of voting and choice (and guiding other students' continued research from off-campus REUs)
- Independent studies in representation theory, topology, and Lie theory
- A brief GRE subject test prep course
- Translating Euler's paper E695 from Latin to English
- Guiding student research in the connection between algebra, combinatorics, and music theory, and separate research in the algebraic geometry of early English-American mathematician Charlotte Angas Scott.
Some work related to this has ended up published or otherwise reached a broader audience, see below.
Research and Other Scholarly Activities
Mathematics of Voting
Here are summaries of voting-related projects I've worked on.
- Along with Kathryn Nyman, Erin McNicholas, and Michael Orrison, I have been working on general theory of voting on various partially ordered sets, with support provided by the SQuaREs program at the American Institute of Mathematics.
- Along with several students, I have been exploring the nature of voting on a non-poset, the set of cyclic orders on a given set. This poster, aimed at a very general audience, by my students Abraham Holleran and Josephine Noonan shows some of the interesting ideas that can come up.
- Michael Orrison and I published a survey (Arxiv) of literature using representations of the symmetric group in voting theory and (cooperative) game theory in Cont. Math., Volume 685.
- One can extend the notion of scoring rules to 'scoring' social preference
functions (whose output is one or more full rankings). In
The Borda Count, the Kemeny Rule, and the Permutahedron (Cont. Math., Volume 624)
I use this framework and the representation-theoretic techniques of
Orrison et al. to connect the Borda Count and Kemeny Rule as giving rise to
the 'most symmetric' members of this large class of procedures.
- If you didn't understand that, you should enjoy a talk for broad audiences I gave about this.
- I am interested in voting over more general combinatorial objects as well. Please see this generalist talk on this and related matters, given at Willamette University in 2016.
- Several students and I have been working on exploring a notion of 'broad support' in voting with several subgroups; a preprint should be available soon.
- 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.
- Preprint version
- Slides from a talk in Irvine, CA.
General scholarship
There are many things which I view as scholarship.
- Research in the mathematics of voting and choice (see above).
- Joint with Jinhyun Park, in manuscripta mathematica (2018, Vol. 155, pp. 15-45) is the paper Zero-cycles with modulus associated to hyperplane arrangements on affine spaces, based on a portion of my thesis.
- Traditional publications related to teaching in various journals.
- My Gordon colleague Mike Veatch and I wrote a paper for CMJ about using approximation to approach Heron's triangle area formula.
- Read a brief article in CMJ introducing the symmetries of the permutahedron to abstract algebra teachers.
- An article about a "Notebook" for courses of the Bridge or Transitions variety appeared in PRIMUS.
- An article about the role of infinitesimals in math history and what we should and shouldn't get from that, in the Proceedings of the Conference of the ACMS.
- A survey article exploring the role of mathematics in the early work of Marin Mersenne, in the Proceedings of the Conference of the ACMS.
- Work on resources and code, mostly for the open source math program
SageMath.
- The MAA's NSF-funded PREP program funded three years' of the Sage: Using Open-Source Mathematics Software with Undergraduates workshops I ran with several colleagues, which received consistently stellar reviews.
- The tutorials I cowrote with Rob Beezer and Jason Grout for introducing college faculty to Sage are part of the standard documentation.
- Some development discussion and a few contributions to the PreTeXt project for enabling better authoring of open texts came out of SageMath connections as well.
- See below for links to profiles relating to my development, review, and user assistance for SageMath.
- Introduction and promotion of various active learning topics.
- Thanks to the Academy of Inquiry-Based Learning for funding helping create more inquiry-based modules for our non-major calculus course.
- Advocating for an implementing service-learning is important and timely; see my Service-Learning and Mathematics page. All the papers from a special session I co-organized at the 2011 Joint Mathematics Meetings are archived here with the gracious permission of the speakers. I co-edited a special issue of PRIMUS about this topic. You can see a brief version of my thoughts on this from an invited panel on the related topic of social justice.
- My Number Theory: In Context and Interactive text for undergraduate number theory exemplifies dynamic visualization and computer exploration while also attempting to show the true unity of mathematics. (Now in a new Janural 2021 edition!) This contributed paper from the number theory teaching session at the 2018 Joint Meetings is a good intro to my philosophy.
- 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.
- My paper Open Source Software and Christian Thought appeared in Perspectives on Science and Christian Faith.
- I also have done a fair amount of extended book reviews of subjects at the interface of science/math and faith, including reviews for the now-defunct Books and Culture, the Journal of Humanistic Mathematics, and the Journal of the ACMS.
Other Stuff
Please note I am aware that my site seems oh-so 20th-century.
But I promise not to use the <blink> tag.
Anyway, occasionally simplicity is a virtue.
If you've never heard of AIMS, the African Institute for Mathematical Sciences, you should find out about it and the Next Einstein Initiative! I've been fortunate enough to teach Experimental Mathematics with Sage twice at the South Africa site.
I serve in various professional capacities, largely involving editing and review.
- I was until recently an Associate Editor (area: upper-level courses) for the journal PRIMUS.
- I referee papers for other journals as well, mostly the MAA journals or discipline-specific ones in social choice such as Mathematical Social Sciences and Social Choice and Welfare.
- I act as a reviewer on a regular basis for Math Reviews/MathSciNet and have started doing so for MAA Reviews too.
- I usually coordinate the Math Forum seminar and advise the Gordon Math Club.
- With Kathi Crow, I have coordinated organizing the North Shore Undergraduate Mathematics Conference for some years.
- I've been on various committees at the college, including several multi-year stints as chair of the Kenneth L. Pike Honors Program committee.
- I have been a member of the AMS, MAA, and ACMS for the past 15 years or so.
Various professionally-related web profiles:
- LinkedIn (but you really want the Gordon College Mathematics group, which is more interesting)
- MathSciNet author information
- Sage Trac query
- Github profile
- Ask Sage profile
-
- Google Scholar Profile
