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Do the Math

August 9, 2005

Mark Miester
Michael DeMocker

It may not have the zing of Donald Trump's "You're fired!" but Charlie Eppes' monomaniacal mantra neatly sums up the new CBS crime drama Numb3rs, a surprise hit that adds a new twist to the standard police procedural: mathematics.

tulsum05_math3Eppes, portrayed by actor David Krumholtz, is a brilliant young mathematician at a fictitious southern California university who each week assists his FBI agent brother in cracking the toughest cases through the use of mathematical formulas and equations. In the premiere episode Charlie helps to nab a serial killer by doing a statistical analysis of the killer's previous attack locations.

If that sounds farfetched, you're probably not a mathematician. The episode was based on an actual case in Louisiana in which a serial rapist was caught through geographic profiling, a statistical analysis technique pioneered by a Canadian detective.

Subsequent episodes have touched on probability theory, vector analysis, fluid dynamics, cryptography, wavelength analysis and geometric progressions. To ensure the mathematical integrity of the show, series creators receive technical advice from the math department at Caltech. That attention to detail -- the equations Eppes writes on the blackboard and uses to solve the crimes are real and workable mathematical expressions -- has given some academics hope that Numb3rs will add pop culture muscle to an old discipline that has innumerable applications for the future.

"I think there was once sort of a stereotypical mathematics culture, but that day is pretty much over," says Michelle Lacey, a statistician and assistant professor of mathematics. "For the most part, the field has become so broad that it really takes all kinds these days. There used to be a time when you could walk around campus and say, "There's the mathematician." I don't think that's so true anymore."

More people are getting into mathematics professionally. According to recent surveys by the American Mathematical Society, the number of both undergraduate majors and graduate students is on the rise.

Nationally, total undergraduate enrollment grew by 1.8 percent between 2000 and 2003. At Tulane growth has been more dramatic: The number of math majors has more than doubled since 2001. While the total of 86 majors is still small compared to other departments, it's encouraging to Terry Lawson, professor of mathematics and director of the undergraduate math major program.

"Not very many people come to college with the idea they're going to major in math," says Lawson. "Biomedical engineering is going to get a bunch of people who come in, and from day one they're majoring in biomedical engineering. They've had no exposure to biomedical engineering, yet somehow they're sold on it. It's a funny phenomenon. Math departments aren't very good salesmen."

That's starting to change. Buoyed by National Science Foundation grants aimed at improving the number of U.S. citizens entering graduate programs and careers in mathematics, the department has initiated a number of programs aimed at attracting and retaining math majors. Tulane is among the nation's leaders in the Research Experiences for Undergraduates program. Each summer, about 20 undergraduates from Tulane and other universities spend eight weeks on campus working in groups on research projects with mathematics faculty members. Recent projects have involved differential geometry, topology, applied mathematics and statistics.

Another initiative Lawson thinks may be having an impact is the senior seminar. As one of the requirements for graduation, majors work on a senior project that pairs them with a single faculty member for the entire year.

"Before, you went to a class, took notes, did your homework and then school was over and you got a summer job," Lawson says. "Now, lots of people are going to do research experiences. These things help convince them to be math majors and stick with math longer."

And when more students continue with math, the more other students choose math to begin with. "There's a tipping-point effect," says Morris Kalka, professor of math and chair of the math department. "If you're considered to be kind of weird among your peers because you're a math major, not many people will be math majors. But once there's a critical mass, it's okay to be a math major and you get more and more of them."

Why are students majoring in math?

tulsum05_math1_1"Students realize that knowing something about mathematics will help them in other areas, so we see a lot of double majors," says Lacey. "They just feel like it will help broaden their education."

"We encourage students to major in math not so much to go out and become mathematicians or actuaries but because it's great mind training," says Lisa Fauci, professor of mathematics. "Math is a great major to have if you're going to go to law school. It's the analytical thinking."

"Basically, math courses are about problem solving," says Lawson. "You're confronted with a lot of different types of problems and you learn things besides the mathematics in the course of doing that. You learn to work through things that are hard and that helps you to do other jobs more effectively."

Riley Harris (B '05), a math and finance double major, came to Tulane knowing he wanted to study finance, but as he advanced through the curriculum, he found himself enjoying the prerequisite math courses as much as the more business-oriented classes.

"I guess I like to be able to solve problems," says Harris. "Real Analysis and Complex Analysis are probably my two favorite math classes, and I don't really see any direct connection to finance."

While most students in Tulane's University College, the part-time division of the institution, tend to focus on more applied sciences, Joy Samson chose to major in math. "Every time people ask, "What's your major?" I'm kind of hesitant to tell them because when I say it's mathematics, they're like, 'Oooooooh!'" says Samson, who is scheduled to graduate in 2006.

"I'm not saying it's easy, but I always tell them if they could get past their initial fears it would make sense. As you get higher in mathematics, it becomes less about numbers and more theoretical. It's a way to develop your logical and analytical skills."

In 2002, American Mathematical Society executive director John H. Ewing was asked by the Chronicle of Higher Education to address what he believed would be the next "big thing" in mathematics. His answer? Biology.

Said Ewing, "As biologists discovered the value of mathematics for decoding the genome, mathematicians in turn rediscovered that some of the most interesting parts of their subject have roots in the real world."

That's a sentiment Lacey understands. "For me, the difference between statistics and other fields is we're often motivated by real-world problems."

Biology is at the cutting edge of mathematics and nowhere is that more apparent than in the field of statistics. According to a survey by the American Mathematical Society, 289 of the 1,041 new PhDs awarded in 2003 -- 28 percent -- went to statisticians or biostatisticians, more than twice the number of any other field of mathematics.

"Scientists can access so much data and measure so many things they've never been able to measure before," says Fauci. "There has been a technological revolution in medicine and biology and with that comes enormous data collected. To make sense of it, you need a mathematician or a statistician."

Fauci is working at the cutting edge where mathematics interfaces with biology. Asso-ciate director of the Center for Computational Science at Tulane and Xavier Universities, Fauci uses mathematical modeling to help scientists in various disciplines conduct experiments that would otherwise be impossible or impractical.

"Beyond experimental laboratories, we can now use computer simulations to carry out different experiments," Fauci says. "For instance, to understand blood flow in the heart, researchers can put in different shapes of heart valves and see which would cause blood clots and which wouldn't, all done on computers."

Last semester, Fauci, who specializes in scientific computing, mathematical biology and computational fluid dynamics, co-taught a course in cardiac modeling with biomedical engineer Natalia Trayanova, an expert in cardiac defibrillation. Trayanova covered cardio-electrophysiology and related topics while Fauci went over aspects of in scientific computing. The class comprised both biomedical engineers and math grad students and the final project involved interdisciplinary teams of students.

tulsum05_math2_1According to Lacey, in the past medical researchers "kind of eyeballed the results" of their experiments, but that's no longer feasible. "When you have thousands of data points, you can't analyze things that way. It's important to have some sort of systematic way of evaluating the methodology."

Lacey attended Bryn Mawr College with the intention of majoring in English literature, but after signing up for a math course to satisfy the school's divisional requirements, she found herself growing more and more intrigued by math and more and more disillusioned with English.

"I definitely struggled quite a bit my sophomore year trying to decide which way to declare my major, but I felt like my degree would have more value to me as a person if I pursued it in math," says Lacey.

Lacey specializes in phylogeny reconstruction, which uses genetic data to reconstruct evolutionary relationships. One practical application is in the study of how HIV and other viruses mutate and spread. Lacey is also affiliated with the Tulane Cancer Center, where she helps researchers design studies and analyze data.

"It's an exciting time to go into statistics because there are really great opportunities for people to work in the medical field and really any field where huge amounts of data are being generated," adds Lacey.

Finance, public policy, the aerospace industry -- any field where compiling information is critical is a field in need of statisticians.

Jason Calmes (G '05) is a good example. A native of Loranger, La., Calmes is currently at Tulane finishing his dissertation on topology, an esoteric branch of mathematics dealing with the essential properties of shapes, but rather than enter academia, he plans to work as a statistical analayst for Lockheed Martin Space Systems at its Michoud assembly facility.

"One nice thing about a PhD in math is that you can segue into industry kind of easily and then get back into academics," says Calmes.

Statistics isn't the only hot area in math. Financial mathematics also is attracting a growing number of students combining training in business with advanced mathematics. "If you go to Goldman Sachs or any of the big brokerage houses, you'll find a lot of PhDs," says Kalka. "Mathematics is playing an increasing role in business and finance."

"Long-term capital management was one of the first instances in which very sophisticated mathematics came into finance," adds Lawson. "It led to a sort of revolution. People who go into financial mathematics programs are making large sums of money on Wall Street designing exotic financial instruments that require graduate-level mathematics and skills that most people wouldn't think related to finance directly."

Harris, the double major, recently accepted an offer to attend the University of Chicago's Master of Financial Mathematics program, one of the top five such programs in the country. "It's a new discipline that has been created at various institutions because they know the industry wants people with this kind of training," says Harris, who expects to work for an investment bank following the program.

While some students have abandoned mathematics for seemingly more applied -- and seemingly more lucrative -- fields like computer science, biomedical engineering and finance, Lawson recalls an anecdote from the career of legendary British mathematician G.H. Hardy, whenever anyone questions the value of pure mathematics.

"Hardy was a numbers theorist who gloried in the fact that no one would ever use the mathematics he was doing," Lawson says. "He was doing pure mathematics, he was doing mathematics for his own enjoyment. Well, what Hardy did forms the basis for almost all computer security, the most applied field of mathematics that exists right now. The largest number of employed mathematicians outside of universities are in the field of computer security.

"The point is," Lawson concludes, "almost all mathematics is really applicable."

Or, as Charlie Eppes might say, everything is numbers.

Mark Miester is an editor in Tulane's Office of Publications.

Tulanian

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