Douglas Ravenel, a mathematician who has helped develop ways to boost student interest in math at the University of Rochester and who is known internationally for his expertise in an area of mathematics with applications from robotics to the shape of the universe, has been named Daniel Burton Fayerweather Professor of Mathematics.
Ravenel has enjoyed working with numbers for as long as he can remember, and as a youngster he had a flair for the subject. For his 12th birthday he went out to a bookstore and treated himself to his first calculus textbook. "In mathematics, you have complete control over what you're doing," says Ravenel, who is chair of the Department of Mathematics. "It's not like making a sculpture, where you need to worry about whether the materials will do what you want them to. In mathematics, the material you're working with is entirely conceptual. That's part of the attraction for me."
During the three years that Ravenel has headed the department, it has gained a national reputation for its innovative teaching. Four years ago its faculty members launched a new way to use the Web to customize homework assignments and give students immediate feedback. The software package, known as WeBWorK, is now used by math teachers at several other universities. Another innovation has been workshops where students work together in teams, helping each other learn the material and boosting student involvement. As a result, the department received the Goergen Award for Curricular Achievement last year, and mathematicians have won Goergen outstanding teaching awards in each of the last three years. Even more telling, the number of students taking calculus is growing even as the size of the overall student body is decreasing, and more students are majoring in the subject and taking on honors calculus.
"Dr. Ravenel is a widely respected mathematician and a very effective teacher who has been generous in his service to the University," says Thomas LeBlanc, dean of dean of the faculty of arts, science and engineering. "Under his leadership, the department's teaching and the involvement of faculty in undergraduate education have improved dramatically."
Helping students overcome their fear of math is a high priority for Ravenel. "A lot of people think of studying math like eating their vegetables: They know it's good for them, but they really don't want to do it," says Ravenel. "A good math teacher works at overcoming that aversion. Every mathematician has an inherent enthusiasm for the subject, and mathematicians like to convey that to other people. We try to be as hospitable as possible, for students who plan to major in math or for others who simply take calculus because they need it for another major."
In his research, Ravenel is an expert on algebraic topology, an abstract branch of mathematics that is a modern form of geometry, but that focuses on structure and space, not angles or distances. To algebraic topologists the world can be thought of as made from taffy, allowing them to stretch and pull objects into new and different shapes that can be defined with numbers.
"There's an old joke about this branch of mathematics," says Ravenel. "A topologist is a person who doesn't know the difference between a doughnut and a coffee cup." That's because a topologist can envision how the shape of a coffee cup made of a flexible material like putty can be changed so that it becomes a doughnut, without breaking or tearing the material.
While the ideas are abstract, the field has contributed tools to help scientists understand the characteristics of electrons and other elementary particles and provided ideas used a few years ago to prove one of mathematics' most challenging problems, Fermat's Last Theorem. It's useful for understanding knots and robotics. Physicists use algebraic topology to try to figure out the shape of the universe, helping them understand what they can observe and giving them tools to imagine what they cannot observe. Its ideas are also central to "string theory," where physicists conceive of space as having not just three dimensions but 10 or even more.
"Topology gives you way to deal with 10-dimensional objects without actually seeing and touching them. It's like flying on instruments alone-even though your senses can't actually comprehend the information, you're still able to perform the task," Ravenel says.
The University has one of the five strongest departments in the country in algebraic topology. Students from around the world seek out Rochester to continue their studies in the area, studying with Ravenel or other faculty members who specialize in the field, including Fred Cohen, Joseph Neisendorfer, Samuel Gitler, and John Harper.
Ravenel attended Oberlin College, graduating in three years and receiving a bachelor's degree with highest honors in math. He then earned his master's degree and doctorate in math from Brandeis University. He was on the faculty at Columbia University and the University of Washington before joining the University in 1988.
Currently Ravenel is chair of the Faculty Senate executive committee. He is also an editor of the New York Journal Of Mathematics and serves as a referee for several other math journals. He has been named an Alfred P. Sloan fellow and has written two books on his specialty, Complex Cobordism and Stable Homotopy Groups of Spheres and Nilpotence and Periodicity in Stable Homotopy Theory.
The Fayerweather honor is named for a wealthy New York City leather merchant who left bequests to the University and several other educational institutions when he died in 1890.