Messenger - Vol. 4, No. 3, Page T-7 1995 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."