The University of Arizona Mathematics Department has many people, both faculty and students, who are software developers. Both research-related software and instructional software are being developed. In some cases, graduate students involved in faculty members' research are also writing software.
This is a sample of free mathematical and graphics software packages. For most of them the source code is provided, in agreement with the Open Source principle.
Prof. Goriely's research deals with the integrability and nonintegrability of ordinary differential equations (ODEs), dynamical systems theory (including elasticity and the dynamics of filaments), and symbolic computation. In connection with his research, he has co-authored two software packages.
POVDISPLAY,
a graphics package written for the computer algebra system MAPLE.
It is an interface between MAPLE and POV-ray, the Persistence of Vision ray
tracer, which is a powerful tool for creating 3D graphics.
POVDISPLAY contains routines for the representation of
surfaces, filaments with twist, and ribbons, and contains a library of all
prime knots up to eight crossings.
NODES
(Nonlinear ODE Solver), another package written for MAPLE.
It manipulates systems of nonlinear differential equations, computes
first integrals and normal forms, and provides some tools for bifurcation
analysis.
Prof. Maier has developed a general-purpose 2D vector
graphics library, called libplot, for preparing 2D data
plots. This library can be used by any C or C++ program on a Linux or
Unix platform. It can render 2D vector graphics to a popped-up
X window, and export graphics files in Postscript, PCL 5,
Illustrator, pseudo-GIF, WebCGM, SVG, and several other formats. It can draw
polygonal lines, circular and elliptic arcs, quadratic and cubic
Bézier curves, and text.
The 
GNU
plotutils package includes both libplot and
some sample command-line utilities for data plotting. The Free Software Foundation (also known as the
GNU Project) has adopted the package, and is distributing it. The plotutils
manual (PDF format) is available.
Prof. Maier has also developed libxmi,
a C library for rasterizing 2D vector graphics primitives,
such as wide polygonal lines and elliptic arcs. The libxmi
manual (PDF format) is available.
Prof. Rychlik's research is in the area of dynamical systems; in particular, their algebraic aspects. For use in his research, he has written two substantial software packages.
Iterator
is a package for viewing 2D dynamics of maps on an X Window
System display. It runs under the Linux operating system and also
some versions of Unix. It is written in C, and its source code
is available as a gzipped tar file. It should be of interest to
non-specialists.
CGBlisp
is an experimental package for calculating an object called a
Comprehensive Groebner Basis. CGBlisp is used for solving
parametric problems in algebraic geometry. An example would be an
explicit computation of the dimension of an algebraic variety, as a
function of parameters. A tarred, gzipped version of the source code,
which is written in the Common Lisp programming language, is available.
Some experience with Lisp is needed to make maximum use of the package.
Dr. King, who obtained his Ph.D. in the department and who
recently moved to the University of California, Davis, has written 
many items of
mathematical software related to his research areas of applied dynamical
systems and population biology. Several Mathematica packages are included.
Dr. Zou is now Lecturer in the University of Texas Mathematics Department. While a Ph.D. student and (later) visiting faculty member at the University of Arizona, he wrote the following software.
EZWGL (the
EZ Widget and Graphics Library) is a C function library that
provides a set of "widgets" for developing graphical user interfaces in the
X Window System programming environment. It has a high level of
support for 3D graphics, including features like a z-buffer, double
buffering, and lighting.
Prof. Lega has written VectCalc, a MATLAB Graphical
User Interface Program to help students understand contour diagrams and
functions of two and three variables. It was originally designed as a
teaching aid for Math 223 (Vector Calculus), but students in other
undergraduate classes may find it useful. VectCalc is
available to all users of the Mathematics Department's Open Access Computer
Lab (Rooms 226/228, Math Building). Click here for VectCalc information.
Prof. Lovelock has written a suite of approximately 60 educational programs that are designed for use by instructors and students in classroom, laboratory, and home environments. It includes the popular "Are You Ready for Calculus?" and other "Are You Ready?" programs. The software suite is available in executable form for computers running the MSDOS operating system (some portions are also available for MacOS). Instructions in both English and Spanish are provided. Click here for more information on Prof. Lovelock's software suite.
Prof. Rychlik has written
JOde: a Java applet for the visual
solution of pairs and triples of coupled ODEs (ordinary differential
equations). It plots direction fields and integral curves. There are
many user-specifiable options. Click here to start the
JOde applet.
Students in ordinary differential equation classes may find this applet useful.
Chris Sinclair, a former Arizona mathematics undergraduate who is now Research Scientist Associate in the University of Texas Applied Research Laboratories, has co-authored two Java applets for surface plotting. One applet allows the user to specify a function of two dimensions to be plotted. The other applet allows the user to specify a 3D parametric equation. Both applets generate a surface that appears in its own window. The surface can be rotated and otherwise manipulated.
Students in multivariate calculus classes may find these applets useful. (Martin Kraus deserves credit for writing the display code.)
Also worth a look: Chris Sinclair's Orbit Visualization research project, which he worked on at the Geometry Center at the University of Minnesota, during his final summer at UA.
Prof. Thompson is actively involved in the development of a new sequence of courses for business majors. This includes the production of an electronic version of the new course Math 128ab (Business Mathematics I and II), in collaboration with Prof. Chris Lamoureux, Head of the Finance Department. A novel feature of the new course is that it is available in its entirety as PowerPoint presentations. Click here for information on Business Mathematics.
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Updated: 5 July 2001 rsm
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