Math 8107: Mathematical Modeling for Science, Engineering, and Industry
This course is quite different from the typical mathematics course. Participating students work in groups on projects that arise in industry, engineering, or in other disciplines of science. In addition to being advised by the course instructors, in all projects an external partner is present. The problems are formulated in non-mathematical language, and the final results need to be formulated in a language accessible to the external partner. This means in particular that the mathematical and computational methods must be selected or created by the students themselves.
Students learn modeling by doing. On the way, they train a wide variety of skills, such as creative modeling, literature and internet research, group discussions, applied analysis, scientific programming, and presentation skills. Each student will be a master of his project, and in addition understands and learns about the other students' projects.
The course grading is based on the weekly presentations, the project reports, and on class participation. The are no exams. More than in traditional lectures, the success of the project research depends on the students' own creative work. We expect each student to devote at least 10 hours per week to the project work.
Why Should I Take This Course?
The active process of modeling is a crucial component of research in applied
mathematics and related fields. Yet, in traditional lectures it is rarely
taught. In this course, students receive extensive advising and mentoring
in modeling, active research, and interactions with an external partner.
Since the unique experience of this course grows with the diversity of
Projects and Partner Companies
Current projects and partner companies:
Valley Regional Planning Commission (DVRPC),
Philadelphia, PA, USA,
is the metropolitan planning organization repsonsible for
transportation and regional planning in the greater Philadelphia area.
In order to decide on the allocation of funds, DVRPC runs large simulations
of the transportation in Philadelphia and adjacent counties in PA and NJ,
enabling predidictions of the travel demand over the next decades.
A crucial component of these simulations are models for the
distribution of trips that residents and employees in the metro area take.
U.S. National Park Service.
Marble and granite monuments (from the Washington Monument down to
historic grave stones) are affected by lichens and biofilms.
Fundamental question for the preservation of the national heritage are:
Are lichens harmful to the stone? Or could they possibly help preserve the
stone by protecting it from acid rain? Could the cleaning be more harmful
to the stone than the presence of biofilms and lichens?
Past modeling projects have been conducted in collaboration with the following companies:
Philadelphia, PA, USA, is the coffee place with the best cappuccino
in the western hemisphere. For them, the creation of a perfect
cappuccino foam is an aspect of pride; and also of great interest
to be understood from a scientific perspective.
Hsieh Lab, Temple University.
Prof. Tonia Hsieh and her postdoctoral researchers and students study the
locomotion of lizards, cockroaches, and other animals. The creation and
study of mathematical models is of crucial importance for the understanding
of the underlying dynamics of locomotion.
Warminster, PA, USA, is a company that designs and manufactures electrochemical
instruments, in particular impedance-scanning quartz crystal microbalance
is one of the leading weather services in Europe, with subsidiaries in
Germany, Switzerland, Canada and the USA. One of their products is weather
forecast for television. Meteomedia produces weather reports for the German
state TV broadcaster ARD and numerous other TV and radio stations in Germany.
|The unveiling of the cappuccino foam project poster at Elixr.|
|Members of the cockroach project team; with two cockroaches.|