My goal is for my students to see that mathematics is much more than rote computation. It is a precise art form that can be highly beneficial in most any career path they choose.
Professor Kelly Bickel, mathematics, originally viewed her discipline as a tool to quantify ideas in other fields. As an undergraduate she was particularly interested in economic policy and began studying mathematics in order to better understand economic models.
But after taking several advanced mathematics courses, Bickel was hooked and couldn't imagine pursing research in any other field. "Mathematics is so intrinsically beautiful," she says. "In philosophy, you learn about Plato's 'ideal chair' – a chair that is so perfect it dispels any ambiguity associated to the word chair. All of mathematics is like that. Every object is precisely defined and there is no ambiguity. This allows one to prove absolute truths."
Bickel points out the many concrete applications of the abstract mathematical world. In her scholarship, which focuses on the overlap between harmonic analysis, operator theory and several complex variables, she studies properties of functions that accept several inputs and give a single output. Such functions appear everywhere. For example, an air-conditioning system measures air temperature at several points throughout a house and releases air of another temperature.
A dual engineering and mathematics conference showed Bickel how the connections go even deeper. "I was surprised to learn that many questions in my area have close ties to open problems in control engineering," she says. "Learning that certain abstract problems about function theory have applications to another discipline added a new dimension to my research."
Bickel encourages her students to experience the creative and useful sides of mathematics. They discuss and answer conceptual questions and brainstorm solutions to difficult problems in group activities. "Writing an elegant explanation or solving an interesting problem is exhilarating. Such activities have a strong creative component, akin to painting a picture or writing a clever essay," she says.
Bickel also emphasizes practical applications whenever possible. For example, when teaching Boolean logic, she asks students to design simple digital circuits using those ideas. "My goal is for my students to see that mathematics is much more than rote computation. It is a precise art form that can be highly beneficial in most any career path they choose."
Posted Sept. 29, 2014