Computer program gives honors students a new way of 'seeing' mathematics

He asked students to develop equations and computer-generated graphs that modeled a complex double revolution staircase designed by Italian artist Leonardo da Vinci in 1519.

"Computers have fantastic properties, including symbolic calculation and graphing," he noted. "Using computers can allow us to go far beyond the capacities of a traditional blackboard in teaching a subject like calculus. They allow the solving of very complex equations."

By visually representing the equations as three-dimensional images, computers also allow students to see their calculation errors and successes, Neumann said. In addition, some computer programs offer the potential to animate images.

Beginning this semester, Neumann has been able to implement a leading computer algebra program, "Mathematica," in classes that deal primarily with vector calculus. The computer software and hardware were provided jointly by the College of Engineering, the College of Arts and Sciences, the University Honors Program, and the Department of Mathematics and Statistics.

"Thanks to the contributions made by these units, we were able to add an exciting component to instruction in the class," he said. "This is a beginning. We hope that we'll be able to expand our use of computers to complement our traditional classroom methods."

Neumann has designed projects in which students can use the software to solve problems he's named "Deceiving Mountains," "Graphing Donuts," and "Creating Monkey Saddles," among others. All illustrate complex mathematical principles.

Extra-credit laboratories familiarized students with the capabilities of the software and allowed them to learn the programming language. "For many, this was the first introduction to this technology."

David Gray, a junior electrical engineering major from Corinth, says that using the Mathematica program has given him a new view of calculus. "I enjoy a graphic approach to calculus. It lets you see what's going on with various functions. It's been challenging and rewarding."

Craig McNight, a junior electrical engineering major from Lucedale, said the program has helped him develop new insights about the subject. "When I can see the image on the computer screen, I understand the process much better," he said. "It's something I wouldn't be able to do on my own."

The program has been so successful that Neumann plans to continue using it in his calculus classes. "Because of computer capabilities, the study of mathematics is changing," he said. "In the long run, we'd like to change even more."

Neumann has taught at Mississippi State since 1989. He has been a visiting professor at the California Institute of Technology and the University of California at Los Angeles. He holds bachelor's, master's, and doctor of science degrees from the University of Saarbrucken.