Professor of Mathematics
Ph.D., Northwestern University
M.S., Northwestern University
B.A., Rhodes College
I am very interested in helping students to see mathematics as a lively, engaging pursuit that is intimately involved in their everyday life. A big part of this is my view that mathematics is really a liberal art that is best understood by students when they are reading, writing, and discussing it.
I work in voting theory, which is a branch of social choice theory. The basic problem is that when there are more than two candidates in an election, the outcome can be determined by the voting procedure used. That is, even if no voters change their preferences, it is possible to get different outcomes by using different procedures.
Most recently, I've been looking at some of the issues involved with electing committees. The complications arise because the voters are selecting a group of candidates, rather than a single candidate, and the voters may have complicated preferences among the candidates. This can be especially problematic if the voters have a preference for the committee to reflect some diversity criteria, such as gender or academic rank, but the voting structures do not recognize the preference.
One of the aspects that many people find surprising is that there are some very beautiful geometric models that are useful in understanding the behavior of voting systems.
I am very interested in using writing assignments in all levels of mathematics courses, especially Calculus and Linear Algebra. The MAA has published Writing Projects for Mathematics Courses: Crushed Clowns, Cars and Coffee to Go, a book that I co-authored with Annalisa Crannell, Gavin LaRose, and Elyn Rykken. It is available at the bookstore on the MAA website.
I also use pre-class reading assignments in Calculus, Intro Stats, and Linear Algebra, which has worked out really well. I have an article with Matt Boelkins of Grand Valley State about the use of these assignments at MAA Online.
I have developed a sophomore-level math course in Voting Theory that is part of the Voting Theory, Math, and Congress Connection. The broad topics we cover include measures of power in a weighted voting system, apportionment in the US House of Representatives and in proportional representation systems, and the geometric structure of multi-candidate elections. This course is a lot of fun for both the students and me.
You can also find alot of information about my courses at my website.
I have been involved with the Northeastern Section of the Mathematical Association of America in various capacities, including serving as Chair 2005-2007 and as Governor 2012-2015.
"Complexities of electing diverse committees", with Donald Saari, Social Choice and Welfare, Volume 43, Num 1 (2014), pp 55-71
"Selecting Diverse Committees with Candidates from Multiple Categories", Proceedings from AMS Special Sessions on the Mathematics of Decisions, Election, and Games (2014).
"The Politics before the Politics: Census 2010, Reapportionment, and Redistricting", with Karen Saxe, Math Horizons, Vol 18, Num 2, (2010), pp 5-9.
"Lewis Carroll, Voting, and the Taxicab Metric", College Math Journal, Vol 41, Num 4 (2010), pp 303-311.
"Selecting committees", Public Choice, Vol 126 (2006), pp 343-355.
"Some startling inconsistencies when electing committees",
Social Choice and Welfare, Vol 21, Num 3 (2003), pp 433-454.
"A comparison of Dodgson's method and the Borda count",
Economic Theory, Vol 20, Num 2 (2002), pp 357-372.
"A comparison of Dodgson's method and Kemeny's rule",
Social Choice and Welfare, Vol 18, Num 1 (2001), pp 79-89.
"A geometric approach to voting theory for mathematics majors", in Innovative Methods in Courses Beyond Calculus published in the MAA Notes series, 2005.
Crushed Clowns, Cars, and Coffee to Go . . . Writing Projects for Mathematics Courses, with A. Crannell, G. Larose, and E. Rykken, published in the Classroom Resource Materials series of the MAA, 2004.
"How we get our students to read the text before class", with M. Boelkins, FOCUS, Vol 21, Num 1 (2001), 16-17. Also available here.