A Language for Mathematical Visualization

Speaker: John Peterson

When & Where: 12:30pm, Wednesday, Oct 16, 2002, Room 400 AKW


We have applied techniques delevoped for Domain Specific Langauages (DSL) to an important new field: secondary education. In this talk I will present a language that allows students to visualize mathematical concepts in subjects ranging from basic algebra to calculus.

We have adapted an existing DSL called Pan for use in the classroom. Pan is a language of functional images: pictures are represented by a mapping from points in the coordinate plane onto colors. Using the basic tools of functional programming, users can describe complex images clearly and succinctly. Pan allows basic mathematical concepts to be visualized in new and creative ways. These visualizations are interactive: students can adjust the parameters which define the image with a GUI attached to it. Using this language, computers can be tightly integrated into the core high-school math curriculum and provide new learning opportunities that mix the rigor of mathematics with artistic creativity. The simplicity of this language and its direct relationship with the underlying mathematics makes it a tool that all students can use - not just advanced or computer-literate ones.