Mathematics
University of Missouri, ColumbiaNeXTSTEP brings calculus to life with Mathematica
Reproduced with permission from NeXT
Computer, Inc.
A Reference
Guide to NeXT in Higher Education, Fall 1992
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1992 NeXT Computer, Inc
These days, Professor Elias Saab's Calculus II class at the
University of Missouri, Columbia, seems more like a think
tank for experienced mathematicians than a lower-division
college course. During a recent class, 25 students learned
about Fourier Analysis, used series expansion techniques to
solve differential equations, and solved a system of 24
simultaneous equations-problems typically reserved for
their upper-division classmates.
When Saab pops into the computer lab, most evenings he
finds a group of his Calc II students hovered around NeXT
computers interpreting the results of their homework
problems. "Students are actually discussing calculus theory
with one another," says Saab. "Thanks to the computer,
undergraduate students are talking to one another about
mathematics, and they have a greater understanding of what
calculus is all about."
To concentrate more heavily on calculus theory and less on
technique, Saab decided last year to teach Calculus II as a
NeXT computer-based course. Saab replaced his traditional
textbook with Calculus&Mathematica, an
innovative curriculum developed at the University of
Illinois. Students now solve all homework problems and
submit all assignments to Saab via e-mail, something he
never thought he'd be doing.
Saab says he opted to teach on NeXT machines for several
reasons: "The biggest plus is that the NeXT machine comes
equipped with Mathematica at no extra cost. The
speed of the machine is also an important factor. Other
platforms, running at the speed of NeXT, would have been
much more expensive and would have lacked a good user
interface for students. NeXT is an easy machine to learn
because of its user interface; students grasp it quickly."
Saab adds that because NeXT machines can easily compute
solutions for a variety of calculus problems, his students
can dedicate more time to learning about calculus concepts
than students enrolled in traditional mathematics courses.
"It is no longer necessary for me to go into lengthy detail
about the technique of integration because the computer can
compute such problems faster and more accurately than
students can by hand. Instead, we have time to emphasize
the theory."
Saab also spends a good deal of class time focusing on
practical-albeit complicated-applications of calculus
theory. "There is a lot more opportunity for students to
solve interesting problems that pertain to real-life
situations. I wanted to get away from textbook examples,
most of which are dead examples. Examples on the computer
are alive. One can change them over and over to develop an
infinite number or examples. Students now solve problems
with 100 unknowns. They can't do that using the tables in a
textbook, but they can do it with a NeXT machine running
Mathematica."
Saab says the computer-based course is initially "more
work" for the students, but that their effort is paying
off. To test current students' knowledge against former
students, Saab gave one pencil-and-paper test during the
semester. In past semesters, students earned an average
score of 65 percent on the test while this class averaged
80 percent.
The winter of 1992, Nakhle Asmar, an assistant professor of
mathematics at Missouri, also tried Mathematica
and NeXT machines in his Applied Analysis course. Although
his students still solved problems with pencil and paper,
he held several computer-lab sessions during which he
solved partial differential equations, for example, using
Mathematica on a NeXT machine.
"I was skeptical at first about using computers to teach
the class," Asmar says. "That's why I didn't have the
students use Mathematica to solve equations. But
in the end, I was amazed at what Mathematica could
do in terms of graphing and how quickly equations could be
solved. Consequently, I've decided to incorporate NeXT
computers and Mathematica into the class next
fall."
For more information, please contact:
Elias Saab
Chair and Professor Mathematics
University of Missouri
Columbia, MO 65211
(314) 882-0635
elias@esaab.cs.missouri.edu