- My research interests. My research
interests focus on the interaction of two branches of ring
theory.
- Cohn, Schofield, and Bergman explored the techniques of
universally inverting maps between projective modules as a way of
localizing rings. The nature of the technique does not lead to
easy examination of the resulting ring. The resulting rings
however are often interesting objects in their own right. My
research looks at ways of explicitly producing these rings.
(Explicit here means that the elements have normal forms that can
be used for computations.) In particular I look at ways of
reducing the instruction "invert all full maps" to "invert a well
selected finite set of maps".
- One place that this technique shows promise is with finite
dimensional algebras. The techniques of universal localization
give promise of explicitly producing various large modules, like
the generic modules. Most of the work in this field has focused on
modules that are finite dimensional over a field that is central
to the original ring. The focus seems to be driven by the fact
that the homological methods use double duals. The universal
localization techniques do not seem to require this finite
dimensional restriction.
Academic interests - My academic
interests include:
- Calculus reform - The department is deep into the process of
implementing calculus reform. The possibilities are exciting. The
question of integrating new technologies into the curriculum gave
us the opportunity to review the larger questions of what we are
trying to do when we teach calculus. This process has us
reexamining the pedagogical methods we are using in core
mathematics cores. Hopefully, the lesson we learn will spread up
and down the mathematics curriculum.
- Abstract Algebra - I am of course interested in teaching my
specialty. This has included the undergraduate and graduate
sequences in algebra. It should lead to further advanced topics
courses as well. As I teach these courses, I am exploring ways
that various computer programs can be used to improve student
understanding in these courses. The courseware is less available
at this level, so the effort will involve more developmental work
than with calculus.
- Technology in education - As the department computer czar, I
keep looking at the question of how we can use technology to more
effectively do the teaching and research that is the fundamental
mission of the department. Since, as a mathematician, my focus is
on how to use computers to use computers to teach mathematics
rather than trying to teach computers, I find that there is a
great need to think about when computing power can be used to
illustrate concepts instead of providing a computing black box.
There will also be a need to develop materials for the teaching
assistants and new instructors so that the technology becomes a
useful tool rather than just something else to cover. It is a
challenge to find the right mix, being a professor who thinks
routine drill, board races, group projects, and computer algebra
systems all have an appropriate role in the classroom.
My nonacademic professional life. As a
Jesuit priest at a Jesuit university, I am also involved with a
number of pastoral activities including:
- Saying Mass on Wednesday nights in Reinert hall, the dorm
where I live as a campus minister.
- A regular rotation in the daily Masses at College Church
- The Sunday campus ministry and parish Masses at College
Church
- Being available to help with student retreats and
reconciliation services
- Whatever else comes up
The rest of my life. Well, that subtitle
is probably a bit strong, but even overworked junior faculty need
a few outside interests. Mine include
- swimming,
- baking (and eating) decadent chocolate desserts,
- reading science fiction, and
- listening to country western music.
