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June 91 - Mathematics Computing at the University of Arizona

Mathematics Computing at the University of Arizona

Dale Curtis


While developing educational software in a university setting, I found it difficult to discover what others were doing with object programming technologies, even at my own institution. I thought there might be other developers in a similar situation; so, I suggested to the MADA Board that we have an education column in FrameWorks, to allow developers at educational institutions who have object programming projects to find out what is happening elsewhere.

You know what happens to people who make suggestions: here I am! My hope is that those of us with similar interests will use the Academic Developers column to contact and assist each other, and find out about software targeted at the university level. I'll lead off with a synopsis of activities at my site.


The Mathematics Department at the University of Arizona is involved with the education of over 14,000 students per semester. Of these, approximately 4,000 students per semester are in our two-year calculus sequence for science and engineering students: Calculus I, II, III, Ordinary Differential Equations, and Linear Algebra. We are in the process of remodelling this program so it will use computer technology for instructional purposes. The goal is to create an environment where the student:
  • Becomes comfortable using computers to explore, calculate, review, and to promote self learning.
  • Is challenged to think independently and to tackle a variety of problems which, because they are new to the student, do not have the artificial flavor of the overworked examples in present texts.

We've identified five non-traditional ways of using computers for instructional purposes:

  • To aid the instructor during class with slide shows, a collection of screen images of functions that are difficult to draw on the board; simulations, a collection of programs that simulate mathematical concepts that are otherwise difficult to perform in class; and demonstrations, which let the instructor present lengthy, but elementary, step-by-step calculations in class without the distraction of algebraic errors or loss of continuity due to time delay.
  • To aid students. The software can deal with complex calculations and aid in the development of mathematical intuition through support for graphical displays.
  • To encourage students to treat mathematics as an experimental subject. Students can change the values of variables and coefficients, alter equations, and see the effects numerically and graphically.
  • To capture the excitement of current developments in mathematics. For example, chaos in calculus, fractals in linear algebra, and modelling AIDS in ordinary differential equations.
  • To aid instructors and students during lectures and examinations. Since October 1989, our fully computerized classroom has drastically changed the way we teach, the problems we assign, and the way we test.

We have 35 packages to support these approaches. They were developed by students, working with faculty, within the context of a 3 credit hour semester course in math software development. The students were primarily math or engineering students who knew how to program in C.

Because the students had a time limitation, and were focusing on mathematics rather than programming, the packages were initially developed under MS-DOS. But in February, the mathematics department hired a full-time staff member (me) to-among other things-set up a development lab to include both IBM compatibles and Macintoshes.


So, what is the best way to introduce students to developing on the Macintosh? We are working on that. For use by student and faculty developers, we have acquired the three Apple Developer University Self-Paced Training modules, plus AppMaker, MacApp, C++, and Think C. We have developed a prototype framework for several programs and are creating IBM-compatible display fonts so we can use the data files that drive the programs on both platforms.

Our experience in building this framework in Think C 2.0 using only Inside Macintosh Volumes I-III, without recourse to tools like MacApp, convinced us of the value of object programming! We anticipate using object programming technologies in rewriting the prototype and constructing another framework for a second set of programs, porting at least the C code that does the mathematics itself into Mac applications.

You might ask why we bother to develop on two platforms. The software we have developed is in the public domain so every student and educational institution can benefit from it, and availability on the two most popular platforms is important to widespread distribution. In the last six months, we have had requests for over 2,500 disks from universities and colleges throughout the country. The "Are You Ready" series of programs has generated requests from over 1000 academic institutions in Australia, Canada, Cyprus, England, France, Malta, New Zealand, Scotland, Wales, and the United States. Anyone interested in the software can contact me at the address appearing at the start of this column.


In future columns, I plan to report on personal experience with development tools, software or development efforts that you let me know about, and relevant meetings or training opportunities. (Anybody want to send me to MacWorld in Boston?) I definitely want to use Academic Developers to showcase projects from other academic sites, so articles by guest columnists are very welcome. Please let me know what you want to see. Don't be bashful-see you here next issue!


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