The most rewarding thing about working with students is when they change. Suppose a student can’t do a problem immediately. My job is to get them to tackle the problem and help them work their way through to being able to do it.

George Exner

In the introduction to his 1996 book, An Accompaniment to Higher Mathematics, Professor George Exner, mathematics, writes that the main pleasure in his field lies “in the process of doing: exploring, inventing and discovering” – similar to music or sports. He says he enjoys helping students with process because it allows him to witness the “aha” moments.

“The most rewarding thing about working with students is when they change,” Exner says. “Suppose a student can’t do a problem immediately. My job is to get them to tackle the problem and help them work their way through to being able to do it.”

Mathematics is like constructing a building, he adds. “Our work might be a brick that we put near the base of the wall. Eventually, someone builds a tower on top of that brick. Since we prove things, we never throw the work away – eventually, someone will build something from it. Humbly, the second brick from the bottom on the left will be a little piece of our work. It’s very much math for math’s sake.”

Exner’s current research is in Hilbert space operator theory and the invariant subspace problem, part of the larger field of functional analysis. One of his teaching interests is operations research, an area of mathematics designed for business applications. For example, students might analyze lines at retail stores and study how staffing decisions are made to avoid long checkout lines. “When Walmart has a certain number of cash registers open because they have a certain number of people to run them, someone decided that would be the right number of people.

“We study sales forecasting. We study dynamic programming, which is very useful in inventory problems, and we study linear programming, which helps with optimization,” he says. “We are trying to help businesses figure out how to make the most money they can by deciding what to produce. These are all very valuable tools for people who are going into production, logistics or supply-chain management.”

Posted Feb. 12, 2015

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