Education Spotlight-Mellon College of Science - Carnegie Mellon University

Formula for Success: Mathematics Course Delves into Real-World Problems

Mathematicians don't necessarily toil away at theoretical proofs in quiet isolation, as any student taking "Projects in Applied Mathematics" will tell you. Initiated six years ago, the Projects course has no lectures, exams or homework. Rather, students working in teams solve challenging everyday problems from mapping the best city garbage routes to optimizing financial portfolio returns.

The format provides students from mathematics, business administration, engineering, and computer science a unique opportunity to work on a real problem cooperatively and offers a glimpse of life after Carnegie Mellon, according to Reha Tütüncü, associate professor of mathematical sciences and the course developer.

"The sheer quantity and intellectual depth of mathematics course material takes up most lectures and leaves little room for application-oriented modeling exercises. Even where we include a fair amount of modeling, we often need to settle for simplistic examples," Tütüncü said. "In the Projects course, everything is real.

We have an actual customer interested in a timely and satisfactory solution of an actual problem. We use real data and have real deadlines."

Analyzing Real-World Problems

For Jing Li, the class provided the first opportunity to analyze a real-world problem and present results to a client.

"I liked this class a lot. Problems in the real world are usually sophisticated and not well defined. It's also a good experience working in a team with random people," said Li, a computational finance major who recently graduated.

Some projects require that students learn new mathematical skills. Finding the right model, solution method or tools for a given situation is critical, according to Tütüncü.

Class participants gain other skills as well. "I learned how to work with time and ability constraints," said Danyale Monteleone, a 2000 graduate.

Students have successfully completed projects contributed by companies such as Federated Investors, the nation's ninth largest mutual fund company; FORE Systems (a network equipment design and manufacturing company renamed Marconi); HJ Heinz; and Bank of America. Other clients have included UPMC Health System and the City of Pittsburgh's Bureau of Environmental Ser- vices and Department of Public Works.

Increasingly, class problems have come from the financial sector. These often require students to determine how best to manage monetary losses within an institution's planning horizon. Other projects seek to ensure that investment firms have the right monetary resources available at the right time. The bottom line in all cases is risk reduction, says Tütüncü.

Thinking Outside the Box to Find Solutions

Since the first class, Tütüncü has worked with Mark Koenig, a former graduate student (MSCF '95) and current Director of Quantitative Analysis at National City's Investment Management Company. Each year, Koenig proposes projects that align with his company's current work, but which National City isn't pursuing due to project risk or time constraints.

"A course team is like having a small research unit for a few months out of the year," said Koenig. And because they aren't part of an inner circle of "finance quants," Koenig believes that the students think outside the box.

One student team helped National City create a scheme for classifying stocks as members of the growth or value style by applying neural network and logistic regression solutions to the problem. For another project, students used a machine learning tool to identify stocks with a high probability of significantly underperforming the market. Both these efforts led to several in-house applications, according to Koenig.

"We get a lot of value out of participating," said Koenig. "For a recent project, the code the students wrote was in excellent shape, and we may end up using it practically verbatim."

Many students find that the course has played a major role in launching their post-graduate careers. Li says the course helped her get accepted to several graduate programs. Other computational finance students have gained practical experience to help them land positions at Goldman Sachs, Deutsche Banke and Salomon Smith Barney.

"Our role is to frame the problem and provide the necessary data. Then we just get to sit back, answer questions, and see what the students come up with," said Koenig. "It's a lot of fun."