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
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 ...
Gordon students: go straight to
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
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.
- 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
- 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.
There are many things which I view as scholarship.
- Research in the mathematics of voting and choice (see
- Joint with Jinhyun Park,
in manuscripta mathematica (2018, Vol. 155, pp. 15-45) is the paper
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
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
- 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
- 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
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
Joint Mathematics Meetings are archived here
with the gracious permission of the speakers.
I co-edited a special issue of
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.
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.
Please note I am aware that my site seems oh-so 20th-century.
But I promise not to use the
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
(area: upper-level courses) for the journal
- 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
and have started doing so for
MAA Reviews too.
- I usually coordinate the
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
- I have been a member of the AMS, MAA, and
ACMS for the past 15 years or so.
Various professionally-related web profiles: