Messenger - Vol. 4, No. 3, Page T-7
On Technology
Mathematics for the real world

     A swimming pool is 20 feet long, 15 feet wide, 8 feet deep and
positioned on flat terrain. If you want to empty the pool in eight
hours using only gravity, what size drain do you need? This riddle is
an example of an "inverse" mathematical problem that calls for a real-
world solution. Such problems can be painfully difficult to solve with
pencil and paper. Yet, University students routinely tackle such brain
teasers-thanks to new computer technologies.
     Scientists and engineers are constantly faced with inverse
problems as part of their work. An environmental engineer, for
example, might know that 200 gallons of gasoline had escaped from an
underground storage tank. To determine the size of the hole in the
tank, the engineer must know how to solve inverse problems.
     In the past, unfortunately, students had few opportunities to
study inverse problems because they require many time-consuming,
tedious calculations, explains John Bergman, associate professor of
mathematics. But, today's students are free to apply mathematical
principles to real-world problems while computer programs handle the
routine number crunching.
     "Historically, we have presented students with math problems by
saying, 'Here are all the values, the opening sizes and the flow
rates. Compute what will happen,'" Bergman says. "Now, we can ask
students to find values that achieve a particular result. We're not
limited to the more simplistic question, 'If you have this and this,
what do you get?'"
     In a recent class, senior John Geremia of Nesconset, N.Y., was
asked to analyze a problem involving an electric power plant located
on a nearby river. Specifically, Geremia needed to know how much water
should be directed to each of three turbines to achieve maximum power
generation. Without use of sophisticated workstations, the problem
might have been nearly impossible to solve in a timely manner.
     "Calculus classes in the past have focused on solving a numeric
problem, which usually turned out to be a lot of arithmetic, very
tedious and time-consuming," Geremia says. "Now that we have computer
programs to get the tedious stuff out of the way, we can focus on
conceptual ideas and actually apply the mathematics that we're
learning. So, we can create real-life simulations of problems."
     The Department of Mathematical Sciences maintains two computer
classrooms equipped with sophisticated workstations. Calculus,
differential equations and linear algebra are routinely taught in an
interactive format, with students working at computers instead of
transcribing notes from a chalkboard. Since the workstations offer
graphics capabilities, students also can create and manipulate images
representing mathematical problems.
     Students pursuing a non-science-related degree work with hand-
held graphing calculators. "These devices display a visual
representation of functions," Bergman says. "The technology frees
students from the drudgery of rote computations and calculations and
lets students and faculty worry about more realistic problems."