Recent Developments in Computer Algebra Technology and Their Impact on Mathematical Research and Teaching
Douglas Meade meade@math.sc.edu
Mathematics University of South Carolina U.S.A.
Abstract
Computer algebra systems have come a long way from its infancy
almost forty years ago with the MACSYMA project at MIT. This first
generation of computer algebra systems, characterized by one dimensional
input and output and ASCII plots, emphasized the implementation
of symbolic algorithms. Graphical user interfaces did not appear
for twenty years – Mathematica 1.0 in 1988. The user interfaces
that characterize the second generation brought significant improvements
in the presentation of mathematical output and graphical presentation.
Earlier this year, nearly another twenty years later, Maple 10 is
likely to be the viewed as the beginning of a new generation of
computer algebra. The most revolutionary develops of this generation
are
(i) the twodimensional entry of mathematics that eliminates the
need for the typing of commands and the associated syntax problems
and
(ii) the ability to break free from the traditional linear structure
imposed by scripts, worksheets, and notebooks.
While it is too early to assess the full impact of the new features,
it is safe to say that computer algebra has entered a new paradigm.
In this talk I will briefly summarize some of the significant steps
in the early development of computer algebra systems. The majority
of the talk will be devoted to explicit examples that illustrate
the new paradigm. In addition to new uses of the traditional “worksheet”,
the examples will show how computer algebra systems can be used
to develop enhanced standalone webbased applets for the presentation
of research results and to provide webbased supplemental support
for student learning (drill and assessment). The mathematical topics
will involve calculus, linear algebra, differential equations, and
number theory.
