Student Use as a Tool

Teaching and Research

Award-winning mathematical expositor Stan Wagon can't imagine life before Mathematica. He uses it in many of his undergraduate courses and in his research and has written many books around it.

He also teaches summer workshops on Mathematica and was assistant editor of the journal Mathematica in Education and Research. Why is he so driven?

The Age of Discovery

Students go further, he says. "I get great pleasure seeing how students who learn Mathematica in my mathematics courses go on to use it in their other science or economics work. They can clearly do more with mathematical modeling and visualizations in these other fields than they could do with other software. In mathematics our students are able to carry out quite sophisticated modeling projects and symbolic investigations."

"I think it is critical that we take our incoming, computer-literate students and show them the vast power that is available with good software. They are at an age where they can appreciate the things that Mathematica is doing. If they have an academic interest in computing, then Mathematica provides ample opportunity to explore questions such as 'How does the program do that?' This naturally leads to valuable discussions of important topics in algorithms and numerical analysis."

Revolutionized Research

When asked which Mathematica features are critical to use in his courses, Wagon replied, "I couldn't be without the sophisticated number theory capabilities or the powerful and programmable graphics. And of course, platform independence means we can easily send notebooks with typeset mathematics to colleagues around the world, simply removing one headache that many of my colleagues have with other software. The adaptive precision capabilities have allowed me to explore and understand subtle numerical computations in ways I couldn't imagine with anything else." By emphasizing the breadth of the Mathematica program and its value throughout much of the college curriculum beyond mathematics, Wagon has convinced other faculty at Macalester College to use Mathematica.

In his research, Professor Wagon credits Mathematica with allowing mathematicians to take a theoretically feasible computational idea and with very little development time turn it into a running program. This means that investigations can be carried out in diverse fields very efficiently. The sophisticated research projects in which Wagon has used Mathematica include:

• The theory of graph coloring (leading to a proof of a 20-year-old conjecture about coloring Penrose tiles)
• Primality patterns in the Gaussian primes (where Wagon and others have completely automated the generation of functions that estimate the number of primes in certain patterns)
• An investigation of different prime-testing algorithms
• Using differential equations to make better images of complicated surfaces
• Generating animations to understand the topology of the Costa minimal surface

In fact, says Wagon, "I cannot imagine investigating a mathematical problem without having Mathematica on my desk. It has totally revolutionized the way I think about, do, and communicate mathematics."

Wagon has won the prestigious Lester R. Ford Award for expository writing from the Mathematical Association of America. He is founding editor of the magazine UltraRunning, has served on the editorial boards of the American Mathematical Monthly and Mathematica in Education and Research, and was assistant editor for Mathematica in Education and Research.

Contact Information
Stan Wagon
Macalester College
web: http://stanwagon.com
Send email to Stan Wagon