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)
We have recently developed a series of interactive web modules describing the basic mathematical ideas behind Metric Pattern Theory. Developed by Dr. Ratnanather and three undergraduate interns with strong mathematical skills, the modules are targeted at undergraduates from under-represented communities including the hearing impaired as well as non-mathematicians such as neuroscientists and clinicians.
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 turbulent flows in a plane channel was also developed.
The modules were developed using Mathwright and can be viewed offline using Internet Explorer with publicly available ActiveX controls. Initially developed in 1991, Mathwright has been at the forefront of web-based mathematical pedagogy since 1995 (White, 2002, 2004; Hare, 1997; Kalman, 1999). Paraphrasing White, the philosophy is to invite the interested reader to come into the world of mathematics and science through structured microworlds that will allow them to ask their own questions, to read at their own pace, and to experiment and play with those topics that interest them. Several microworlds or workbooks can be found at the Mathwright Library.
Briefly, each module is a Mathwright microworld which is an HTML document. The document becomes a Mathwright Microworld when the author embeds a "portal" that is created independently with the Mathwright32 Author program that uses Lisp scripts. The portal in a Mathwright Microworld is a rectangular region of the web page like a Java applet. Its content is automatically downloaded -- just once -- from the author's web site when the reader comes to the page, and it is then cached on the reader's machine. But unlike most Java applets, this rectangle can hold as many "story pages" as needed. These story pages remain in the portal on the web page as the reader enters the new dimension of that page. The reader who is finished with a story page presses a button or clicks a hyperlink and is taken to another story page that is displayed in the same portal. Thus, each microworld consists of organized sequences of simulations, "quantitative/qualitative laboratory" experiments, lessons, and/or open-ended exercises tied to the conceptual themes of the targeted course. However it is no longer possible to view the books online via the portal. It is now bnecessary to view them offline on the computer.
Hare, A. "Mathwright Author and Player (Software Review)". College Math Journal, 28, 140-144, 1997 PDF
Kalman, D. "The New Mathwright Library (Software Review)" College Math Journal, 30, 398-405, 1999 PDF