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Rebecca Andersen ’06 (Acton, Mass.) and Jonathan Rowe ’06 (Reading, Pa.) are children of the technological age.
They are part of a generation that grew up using the Internet, has placed countless calls on cellular phones, and depends on e-mail to correspond with friends in far off places.
But unlike many people who take for granted that their connections will be made, calls placed, and messages received, Andersen and Rowe are spending their summer learning — and explaining via a logical mathematical expression — just how those links are made when certain parts of the system go down.
They are working as EXCEL Scholars with Lorenzo Traldi, Metzgar Professor and head of mathematics, on his research solving reliability problems.
In Lafayette’s distinctive EXCEL Scholars program, students conduct research with faculty while earning a stipend. The program has helped to make Lafayette a national leader in undergraduate research. Many of the more than 160 students who participate each year share their work through articles in academic journals and/or conference presentations.
“What you have in a reliability problem is a system with a lot of pieces, like a phone system,” Traldi says. “There are certain things that need to be working, a combination of things, in order for us to be talking. For example, in between various phones there are various things that don’t all have to be working; there could be re-routing issues, traffic issues, the hardware fails. So the particular logical statements that I’m interested in are statements that describe when a certain system is going to work.”
Figuring out exactly what that statement says is the hard part. That’s where the students come in.
They wrote a computer program that outputs specific instances of when the system will function based on its working and non-working components.
“From that, you’re able to count how often the entire network will work and the percentage of time the network is working,” said Rowe, a computer science major and mathematics minor.
These sorts of statements already exist, says Traldi, explaining that the project is an outgrowth of previous research done with a student.
“He had an idea for a more efficient way to go through steps that would get to a formula that’s more accountable,” says Andersen, a mathematics major.
That is, the professor believes there’s an easier way to rationally predict network reliability.
Having finished writing the program, which involves a very specific, multi-step mathematical process called an algorithm, the students are entering as many different problem-laden systems as possible.
As networks pervade so many aspects of life, from phones to the Internet to sewers, this research could have sweeping implications on the future design of these systems.
Throughout the summer, the students are being challenged by the work, says Traldi.
“I don’t really expect the students to get to the point where it’s easy for them,” he says, adding that Andersen and Rowe will document their work as contributors to a paper submitted to a scholarly journal.
Although the work is complicated, it’s the more inconsequential aspects, rather than the nature of the research, that have been the most challenging.
“Sometimes it can be tricky to remember parts of the algorithm and how it works,” Rowe says. “And to be able to turn that into a computer program you really have to have a complete understanding of how the algorithm works.”
“I kind of like that, knowing exactly what to do,” adds Andersen. “Anytime you’re writing a computer program, you work on it for a while and finally something works the way you want–then it’s done and you can see results.”
Especially as an undergraduate, simply being exposed to professional mathematicians is an experience in itself, says Rowe, who attended an area math conference earlier this summer and had to stretch his mental ability farther than ever to understand the difficult topics discussed there.
More specifically, working with Traldi is giving him an opportunity to apply his areas of study to an arena he otherwise would not pursue.
“I think it’s a particularly nice experience because it’s using both my major and my minor,” says Rowe, a member of the track team and Fellowship of Christian Athletes. “It’s given me an experience to see what college research is like because I really had no idea about the setting of college research, what the expectations were, what the work was like–it’s nice exposure to that.”
Andersen said her biggest hurdle is finding a happy medium between working as part of a team and independently, which allows her room to think with more focus.
Regardless of the challenges, working with Traldi has been rewarding, she says.
She is also happy to make an out-of-class connection with one of her mentors.
“He’s intelligent, but he also makes his intelligence accessible to his students,” Andersen says. “And he’s really laid back, just easy to talk to.”
She is on the executive boards of CHILL (Creating a Healthy, Interesting, Livable Lafayette) and Lafayette Environmental Awareness and Protection and is a member of Association of Lafayette Feminists.
As a national leader in undergraduate research, Lafayette sends one of the largest contingents to the National Conference on Undergraduate Research each year. Forty-two students were accepted to present their work at the last annual conference in April.