Math 1100 Mathematics in Decision Making
Math in Decision Making is intended for a general college audience, and satisfies a Liberal Arts Core requirement for graduation. (That’s a thing.) In my version of the course, we study some basic knot theory and Cantor’s remarkable discovery about infinity before moving on to the required probability and statistics unit. I keep a web page for the course with lots of details.
Math 3600 Euclidean Geometry
This course is an introduction (or a re-introduction) to axiomatic mathematical work. We shall study planar geometry, but the focus is on developing a mathematics professional’s skill set. A lot more can be found on the course web page.
Math 3630/5630 Differential Geometry
We take up the classical material on curves and surfaces in space. The main idea is to use Calculus to measure how objects bend, so we end up looking at lots of second derivatives. This is an advanced topics course. The undergraduate and graduate versions of this course share a web page.
Mathematics is best learned by doing it yourself. With this in mind, I use Inquiry Based Learning or a modified Moore method in many of my courses. Most of the focus in class is on each individual student (sometimes small groups) making sense of the mathematics on his or her own terms, and sharing that progress with the class for critique.
I am an active member of the Academy of Inquiry Based Learning, and currently help organize the annual Legacy of RL Moore meeting.
In order to facilitate better communication with my students about their progress, I am experimenting in some courses with the ideas behind Standards Based Assessment and Reporting. The big idea is to focus on the key learning goals for the course and orient our work directly at them. This sounds simple (and it is), but it has some major consequences for how things are done. At this point, I am only working on this in one course (Euclidean Geometry).
The ready availability of computers for doing mathematical work enables mathematicians (at all stages of development) to work in new ways. I am a big fan of the free and open software movement, and my favorite mathematical software tools are
I have taught a wide variety of courses. I think this is the complete list.
At University of Northern Iowa: | |
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(Advanced) Euclidean Geometry, Geometric Transformations, (Introduction to) Modern Geometries, Mathematical Problem Solving, Differential Geometry, Differential Calculus, Integral Calculus, Introduction to Statistical Methods, The Real Number System, Dynamical Systems: Chaos Theory and Fractals, Topics in non-Euclidean Geometry, Combinatorics, Mathematics in Decision Making, Linear Algebra | |
At Williams College: | |
Linear algebra, Discrete Mathematics, Geometric ODEs | |
At Rice University: | |
Differential Calculus, Integral Calculus, Multivariable Calculus, Ordinary Differential Equations, Introduction to Lie Groups and Lie algebras, Introduction to Partial Differential Equations |
In October 2013, I was honored with the Teaching Award by the Iowa Section of the Mathematical Association of America.