Geology
University of North Carolina, Chapel Hill
Geomathematics: A new course with Mathematica
Reproduced with permission from NeXT
Computer, Inc.
A Reference
Guide to NeXT in Higher Education, Fall 1992
ª
1992 NeXT Computer, Inc
José Rial, an associate professor of geophysics at the
University of North Carolina (UNC), Chapel Hill, has little
regard for the belief among his classically trained
colleagues-that geologists need only minimal training in
mathematics and computer modeling to excel in their field.
"In an increasingly competitive academic and industrial
market, geologists need to adapt the tools of mathematics
to their everyday work," he says. "In the next century, it
will be necessary for them to perform skillfully in a
computer-based-almost entirely quantitative-environment,
where high-
performance computer modeling and simulations of everything
from the accumulation of sediments in a basin to real-time
remote exploration of mineral resources on the Moon or Mars
will be commonplace."
To prepare UNC geology students, Rial last year developed a
new course, called Geomathematics. He uses NeXT computers
and Mathematica in conjunction with a traditional
textbook.
"NeXT is a very good machine for geologists, largely
because of its graphical interface," says Rial. "The
computers help students visualize things in three
dimensions, in nice projections from different viewpoints,
and for all the domains of the parameters they want.
Geologists appreciate that because they perceive things
graphically as much or more than other scientists. It's
difficult for them to grasp formulas solely on a
blackboard. They have pictures-not equations-in their minds
when they think."
Rial has used Mathematica Notebooks to design
several interactive tutorial modules for the Geomathematics
class. The modules aid students in graphically simulating
geological dynamic systems, such as the cooling of
intrusive magmas and the drifting and collision of tectonic
plates, as they become familiar with fundamental
mathematical concepts and learn to solve differential
equations commonly encountered in these phenomena.
The modules cover a variety of topics, including
geomechanics, systems of ordinary differential equations,
and nonlinearity of geodynamic systems. Each module focuses
on a particular subject and features examples of
computations or graphing. In the tutorial portion of the
module, students are typically asked to read about a
particular formula, evaluate it and graph it, study its
range and validity, change the controlling parameters and
graph it again, all within the same Notebook, which can
then be stored on disk.
"With Mathematica on the NeXT platform it's easy
for an educator to create graphics to convey complex ideas
or difficult concepts to the student. Through graphing or
displaying formulas, numerical data or analytic results,
students can see the object of study and experiment with
it-all in a computing environment that does not require
major proficiency in computer programming or the mastery of
complicated operating systems," says Rial.
Rial, who is a seismologist specializing in wave
propagation, chaos, and nonlinear dynamic systems, also
adds that NeXT technology "has been a salvation for my
research work," which depends heavily on graphical
representation of mathematical functions. In his primary
project, "earthquake hazard estimation," Rial uses data,
such as seismograms, to perform mathematical analyses that
help him to predict how a particular area will behave
during an earthquake.
"I've been doing some beautiful graphics with
Mathematica, evaluating functions," he says.
"Using Mathematica with NeXT computers is a dream
because of all the graphic software, and because of the
very high-quality printout."
He concludes, "I really like my NeXT machine. I originally
planned to buy a Sun SPARCstation. In fact, I was ready to
write the purchase order for the Sun when I saw the NeXT
machine. I thought I'd test the NeXT for a half hour or so
and the next thing I knew, several hours had passed-I was
hooked. It's a superior machine, without doubt. It has a
great display, and I like the fact that it's a UNIX machine
with better-than Macintosh interface features. Sun machines
don't compare to the NeXT's ease of use. When I received my
NeXT, it was up and running within 10 minutes. Some of my
colleagues spent weeks getting their Sun systems set up."
For more information, please contact:
José Rial
Associate Professor Geophysics
Department of Geology
University of North Carolina, Chapel Hill
Chapel Hill, NC 27599
(919) 966-4553
jar@antipode.geosci.unc.edu