Mathematics and its study are not simply about numbers and esoteric theory, but also about the ability to reason logically and build increasingly complex arguments on a solid knowledge base.

Emily Dryden says most of her students, many of whom are engineers, enjoy mathematics, but they come into the classroom not fully understanding the scope of the discipline or the types of questions that mathematicians try to answer in their research.

"No, we don't just solve really hard calculus problems," says Dryden. To broaden her students' view, over the course of the semester she injects glimpses of her own research and other examples of "real" mathematics into her classes.

Dryden's research primarily focuses on spectral geometry, in which she asks questions such as, "If two drums vibrate at the same frequencies when struck, are they necessarily the same shape?"

This physical question can be studied within a rigorous mathematical framework, says Dryden, and the answers can in turn inform our understanding of the physical world. "For instance," she says, "techniques in this area can be applied to helping determine properties of fault lines from the seismic data generated by earthquakes."

A French and mathematics double major in college, Dryden believes strongly in the value of a liberal arts education and in teaching mathematics within the liberal arts context. "Mathematics and its study are not simply about numbers and esoteric theory, but also about the ability to reason logically and build increasingly complex arguments on a solid knowledge base — which is a skill useful in any discipline," she says. "I'm a strong proponent of different habits of mind and am particularly pleased when I find out that my students can see how the skills I've taught have been useful in other classes."

Posted October 2012

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