"I want my students to recognize and appreciate the beauty and usefulness of mathematics, develop a logical, patient approach to solving problems and write and speak clearly about rigorous ideas."

Jeffrey Langford's favorite graduate school lecturer didn't actually lecture. Instead, he would come to class seemingly unprepared, write a theorem on the board and work the problem in audible stream of consciousness.

"If anyone asked a question during his work on the board, he would raise a hand to silence them," says the professor of mathematics. "It wasn't every student's cup of tea, but I found it incredibly interesting. His style really helped me develop my critical thinking. Math is about logic and problem solving, as opposed to just learning how to use formulas," he says.

When Langford first began teaching, he simply wanted to give clear lectures and assignments to help students with key concepts and computational proficiency. "But as my teaching developed, I realized that my students could walk away with so much more," he says. "I now teach every course with three additional goals in mind: I want my students to recognize and appreciate the beauty and usefulness of mathematics, develop a logical, patient approach to solving problems and write and speak clearly about rigorous ideas. They need to understand math on their own and explain to me how they solved a problem." Langford tells his students that being able to present their work in front of him or a group is incredibly useful for any future job.

Langford's scholarship focuses on partial differential equations (PDEs), which he says arise naturally when modeling various physical phenomena. "PDEs are important to physicists, engineers and mathematicians alike," he says. "While I am mostly interested in PDEs from a theoretical point of view, it is often useful to have some physical intuition about a problem in order to guess what the solution might look like." Rearranging a room's heat source with the hope of creating a more energy-efficient system is one example of a problem where the results are about comparing the solutions of two PDEs, he says.

Langford also works on eigenvalue problems: He looks for "inputs" into a system where the "output" is a multiple of the input. Eigenvalues are related to tones, such as the tones of a drum. "The eigenvalue problems that interest me are about trying to minimize these tones, he says."

The Midwestern native was drawn to Bucknell because it allows him to both teach and pursue his research. "I want to guide students and help them learn," he says, "yet I want to keep my research career going strong. Here, I can achieve both of my goals."

*Posted October 10, 2013*

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