Alan Shuchat

My current research activity is in discrete mathematics, focusing on questions that combine graph theory and operations research. An example of this is applying methods of linear programming and network flow theory to ranking the elements of a set when comparisons can be made between some, but not necessarily all, of the elements. With Professors Randy Shull and Ann Trenk, I have studied several important classes of partial orders from the standpoint of rankings like these. An earlier area of my research was functional analysis, which uses techniques of analysis to study infinite-dimensional vector spaces and their linear transformations. I wrote my dissertation in this field and published several articles on measure and integration theory in topological vector spaces.

I teach a range of courses at all levels of the mathematics curriculum. I especially like to teach courses that combine theory and applications and ones that draw on concepts and examples from different fields. I often ask students to use computers to visualize mathematical concepts and simplify calculations. Some of my favorite courses to teach are Linear Algebra, Probability and Statistics, Operations Research, and Real Analysis. I have directed several independent and honors projects in areas related to these courses. Some recent projects have been on Markov chains and queueing theory, operations research, and population modeling using linear algebra.

Some of my other interests are in the application of mathematics in archaeology and ecology, and in the history of mathematics. I have translated a collection of biographies of mathematicians and physicists from Russian into English. To help students and others use mathematics software in their work, Professor Fred Shultz and I created an easy-to-use interface for the computer algebra system Mathematica. We published The Joy of Mathematica software and book, enabling students to use Mathematica without learning its syntax and subtleties, and enabling faculty to include computing in a course without taking time from mathematics.

My outside interests include music, languages, and genealogy. I enjoy playing Baroque music (recorder and harpsichord) and klezmer (melodica), and I'm learning to play jazz piano. My wife and I love to learn new languages and to use them while traveling.

Math Department Faculty