Wolfram Computation Meets Knowledge

The Mathematica Story: A Scrapbook

Three Decades of Contributions to Invention, Discovery and Education

Donald P. Gaver, Biomedical Engineering, Tulane University

In ~1987 I saw Stephen Wolfram present his ideas of Mathematica at Northwestern University, and I was completely struck by the beauty and usefulness of his vision. I began using Mathematica upon its release, and three years later I became a faculty member at Tulane University. In my opinion one of the most beneficial aspects is the ability to quickly create simulations of complex mathematical systems and graphically observe the behavior. This provides an exceptional ability to couple intuitive understanding with mathematical rigor.

In ~1995 I developed a graduate mathematics course for biomedical engineers that I always wanted to have taken as a student. This course “Mathematical Modeling and Analysis of Biological Systems” is used to teach students how to develop analytical models of biological systems, observe the behavior, and then improve on the model based upon the observations. After three years it was then moved to the undergraduate curriculum where it remains a required course for biomedical engineering students at Tulane University.

I taught this course for 10 years as a collaborative learning course where students worked with me to develop models (AIDS transmission, biological signaling, insulin-glucose dynamics, etc). Student groups would define a project and would create Mathematica notebooks and then share these with their student colleagues. After teaching the section, they would then give homework to the rest of the students. Students would then use the Mathematica notebooks and improve upon the original models.

This interdependency between students was fascinating. Furthermore, this process was an excellent way of teaching the beauty of mathematical modeling, the need for continuous improvement, the link between simulation and observation, and the importance of intuition. This type of teaching pedagogy would be very difficult without Mathematica.

I’m thrilled with the growth of Mathematica as a research and teaching environment. I look forward to the next 25 years of growth of this exceptional one-of-a-kind resource.