Publications
Online courses
Supported by Project Welcome Novice Developer Fellowship (2001-2004) and The Johns Hopkins University Center for Educational Resources (CER): Technology Faculty Fellowship (2003-2004, 2008-2010)
We previously developed a series of interactive web modules describing the basic mathematical ideas behind Metric Pattern Theory. Developed by three undergraduate interns with strong mathematical skills, the modules were targeted at undergraduates from under-represented communities including the hearing impaired as well as non-mathematicians such as neuroscientists and clinicians.
The modules were developed using Mathwright and could be viewed offline using Internet Explorer with publicly available ActiveX controls. From 1995 to the untimely death of its developer in 2004, Mathwright was at the forefront of web-based mathematical pedagogy (White, 2002, 2004; Hare, 1997; Kalman, 1999). Paraphrasing White, the philosophy was to invite the interested reader to come into the world of mathematics and science through structured microworlds that allowed them to ask their own questions, to read at their own pace, and to experiment and play with those topics that interest them.
Now using a combination of HTML, Javascript and the new HTML5 canvas element, the workbooks have been updated and made portable across multiple platforms to supplement in-class learning with a more visceral and intuitive
understanding of complex material; for details see Steinert-Threlkeld & Ratnanather (2009).
Metric Pattern Theory forms the foundation of the emerging discipline of Computational Anatomy, which takes the view of anatomy as the orbit of images under the orbits of group actions of diffeomorphisms. Using these techniques, one can analyze shape and images of hearts, brain structures (hippocampus, planum temporale, etc.) and theoretically any anatomical shape, and compare differing images to find the "distance" between the two. This can be used to potentially diagnose or locate assorted illnesses and disorders.
The six modules cover a) group theory b) matrix groups c) group actions and orbits d) Lie Groups e) deformable templates and f) metric distances. Three additional and related modules deal with dynamic programming, curvature of surfaces and numerical methods for solving the 1D linear advection equation.
A separate and independent module on a simple model of turbulent flow in a plane channel was also developed. This particular one was developed for use on mobile devices such as ipad.
