It can be said that not only our students benefit from the internship and industrial collaborations, our industry partners also attest to the value they have gotten in their interaction with the Center. Indeed, many of the companies we have worked continue to take our students for internships year after year.
The impact of the center can be measured also by the broadening of the mathematical experience our students are exposed to. Beyond the internships the Center and the IMA jointly sponsors the Industrial Problems Seminar. In this series, a speaker from industry makes a presentation about his or her research and explains how mathematics are used to answer important questions that arise. Many of these issues are in product development, while others arise in the service sector. Nearly all our speakers spend time discussing with students in an informal setting about job opportunities and careers in industry.
Research in the department has also been enriched by the Center's contacts with industry. The accompanying article by Bob Gulliver, Fadil Santosa, and Jing Wang, gives an account of a research project that was started during an internship, and eventually lead to the filing of a patent.
report on the Center, which goes deeper
into the activities and accomplishments
of the Center, and includes candid
testimonials from our former students
and industry contacts, is available
upon request. Please send email to
to ask for a copy.
Nevertheless, the result of this initial conversation was to set up an internship for Jing Wang, then third year graduate student in Mathematics, for the following summer. At the end of summer of 2000, Jing came back and told Fadil about the project he worked on, and his interests in further developing his research experience into a thesis topic. After many hours of discussion, it was clear that the problem was basically that of surface design, and involves a lot of geometry. It was also clear that we needed to recruit a geometer, so they convinced Bob Gulliver to be coadvisor to Jing.
The design of progressive ophthalmic lenses, which are worn by many adults over 40 years old, call for creation of an optical element whose power vary smoothly over different portions of the lens. More negative correction is usually needed in the far distance-viewing zone, and less is required in the near distance-viewing zone. Geometric optics is an accurate theory for describing the light bending phenomena. But upon further simplification, the problem can be reduced to that of prescribing mean curvature, which is proportional to power. While there are many ways to achieve the desired power distribution, for the purpose of minimizing aberration, it is desirable to have small principal curvature difference. In a nutshell, we want to create a surface over the xy-plane such that
While this idea is not new, what is new in our approach is the idea to linearize the problem around a base surface and look for a perturbation. The resulting problem is a fourth order elliptic partial differential equation. We also devised an accurate and efficient numerical method to solve the problem. Jing defended his thesis in August 2001, and is now a postdoc at the IMA. The work we did resulted in two papers published in international applied mathematics journals.
we showed our results to our contacts
in the lens industry, we were encouraged
to market the method. We then got
in touch with Jim Hildebrand at the
University of Minnesota’s Patents
and Technology Management Office about
our method. Jim hired a lawyer and
we started working with him in writing
a patent application. This in itself
was a very interesting and educational
process for us.