From the Princeton Weekly Bulletin, May 26, 1997
Daubechies brings Math Alive!
Course designed for non-majors -- even with "math phobia" -- relates subject to "applications everyone knows"
By Carol Carlson
Here's an experiment to try at home -- if you dare: Take your favorite music CD. Using a pair of sharp scissors, scratch a neat straight line down the radius of the CD. Play the CD and listen carefully.
When students in Ingrid Daubechies's Math Alive! class watched this experiment last February, they hushed as she took up her scissors, then audibly protested at the sound of the scratch. But what really fixed their attention was listening for evidence of the scratch. To their surprise, the CD played perfectly, without the slightest bump, jump or click. Daubechies, professor of mathematics and applied and computational mathematics, just smiled at their reaction, knowing that by scratching the CD, she had also piqued their curiosity.
Math Alive! is a new course that Daubechies created specifically for students who are not majoring in math or science and want to avoid traditional math courses. "It's even for students who might have some math phobia," she says, because it just requires high school math, not calculus, and it investigates mathematical concepts and practical applications, rather than emphasizing computation.
Too much math, too little point
Daubechies says she first conceived of the class several years ago but
was prompted to develop it by a new requirement for a quantitative reasoning course, just put into effect for students in the Class of 2000. She teaches the course with Philip Holmes, professor of mechanical and aerospace engineering, who directs the applied and computational math program."So many people I meet have had to take far too much math for their taste without ever understanding the point of it all," says Daubechies. "That's why I created this course: to try to show the importance of math by relating it to the kinds of applications that everyone knows, just the way you teach people to appreciate history without necessarily making historians out of them."
Comments about the course, which was first offered in the 1996 spring semester, show that students think it is meeting its goals.
Among the most appealing features of Math Alive!, according to Julie Smucker '00, who took the course last fall, were the enthusiasm of the professors, their willingness to spend extra time with students who needed help, and their efforts to become acquainted with each student. The final lecturer, a guest speaker from NASA who discussed how he used mathematical concepts in his job, was one of the course highlights, Smucker felt. "It was probably one of the most informative and exciting lectures I have heard on a math subject," she said.
Michael Sherry, also a freshman, said he took the class because "It's much more satisfying to see real life applications of math than to simply manipulate formulas." Even several hours of homework in a computer lab each week were rewarding, said Sherry, "because doing an interactive computer program on voting systems or statistical bias beats doing a problem set any day."
Birth, growth, death and chaos
The course is divided into two-week modules, giving students a broad tour through the world of mathematics applications. Among the modules are cryptography; error-correcting codes; data compression; medical testing; strategies for playing "Let's Make a Deal"; birth, growth, death and chaos; fairness in politics, including voting systems; and celestial chaos, which reviews why Newton invented calculus.
And why does the CD play despite the nasty scratch? The credit goes to its error-correcting codes, the same type that enable computer specialists to reconstruct beautiful clear images from the messages sent by the Voyager spacecraft even after they have been bombarded by data-destroying interference.
"The code that creates the CD's sound, like the code that carries the Voyager's images, has a built-in mathematical redundancy," explains Daubechies, "so that even if a whole lot of encoded information is destroyed, you still have enough to reconstruct it the way it should have been."
Daubchies, who recently earned the American Mathematical Society's Ruth Lyttle Satter Prize for her "deep and beautiful analysis of wavelets and their applications," joined the Princeton faculty in 1994, the math department's first tenured woman. Previously with the Mathematics Research Center at AT&T Bell Labs, she was named a MacArthur Fellow in 1992. She earned her undergraduate and graduate degrees at the Free University Brussels.