Pure and Applied Mathematics:
After my Ph.D. (1992), my published work includes: some results in C*-algebras and operator theory (historically, the mathematics that emerged from quantum mechanics); collaborative work on applications of Lie groups to solution sets of differential equations; joint work on population dynamics in mathematical biology (HIV, and tumor growth); and then other joint work in mathematical biochemistry, random walks, identifying active sites of proteins, and the development of elementary computational methods for random walks and data bases.
My initial work here includes elementary implications for teaching, based on observations about types of understanding in mathematics. These results were very much thanks to help taken from Bernard Lonergan’s book Insight: A Study of Human Understanding. Other articles in mathematics pedagogy include sample lessons in calculus and differential equations. In those co-authored articles, we tried to both take advantage of, and bring out, some details of dynamics of learning. Such work is directly relevant to mathematics education, but also provides data for foundational development more generally.