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Math 8107: Mathematical Modeling for Science, Engineering, and Industry


Course Instructors

Course Description

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.

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Course Goals

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.

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Grading

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.

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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 student backgrounds, students from pure mathematics, as well as other fields of science and engineering are highly encouraged to contact the instructors about this course.

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Projects and Partner Companies

Current projects and partner companies:

Delaware 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.
Project: Destination choice models in travel demand forecasting

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?
Project: Effect of lichens and biofilms on marble and granite monuments

Past modeling projects have been conducted in collaboration with the following companies:

Elixr Coffee, 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.
Project: Stability of cappuccino foams

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.
Project: Modeling inverted cockroach locomotion

Gamry Instruments, Warminster, PA, USA, is a company that designs and manufactures electrochemical instruments, in particular impedance-scanning quartz crystal microbalance systems.
Project: Efficient impedance measurements at low frequency

Meteomedia AG 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.
Project: The automatic detection of weather fronts from forecast data

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Photos

The unveiling of the cappuccino foam project poster at Elixr.
 
Members of the cockroach project team; with two cockroaches.

Modeling Course - Fall 2013

The course is currently running.
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Modeling Course - Fall 2011

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Modeling Course - Spring 2010

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Links

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