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

Course Instructors (current and past)

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.

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.


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.

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.

Projects and Partners

Spring 2022

Linden Dale Farms, Lancaster County, PA, USA, produces various fresh and aged cheeses, goat milk yogurt, bottled milk, as well as pasture-raised goat meat.
Project: Optimizing the Stretchability of Goat Milk Mozzarella Cheese

Hsieh Lab, Temple University, Philadelphia, PA, USA, seeks to understand how animals respond to and manipulate naturally unstable and unpredictable environments to facilitate their daily locomotion.
Project: Understanding the Stability of Running Lizards

Spring 2018

Amber Grain Bakery, Collingswood, NJ, USA, a "back to basics" neighborhood bakery with artisan breads baked like in the Old World.
Project: Optimizing sour dough feeding schedules

Merck & Co. (MSD outside of the US and Canada), Kenilworth, NJ, USA, is one of the largest pharmaceutical companies in the world.
Project: Best injection site for intradermal medicine

Fall 2013

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

Fall 2011

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

Spring 2010

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


The unveiling of the 2011 cappuccino foam project poster at Elixr.
Members of the 2011 cockroach project team; with two cockroaches.