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Computer Algebra Systems at UNF


Program Pages:

Below are links for pages specifically focusing on the four computer algebra systems used at UNF.

What are computer algebra systems?

In the broadest sense, they are programs designed to do mathematics.  The main duties involve:

Examples:

At UNF, we have Maple, MathCad, Matlab, Mathematica, TI-89/TI-92, Scientific Workplace, SASS, and SPSS.  The calculators (TI-89/TI-92) are a limited version of Maple or Mathematica.  Scientific Workplace is more of a mathematical word processor, but it does have some computational capabilities.  SASS and SPSS are both powerful statistics programs.  This page will focus on the first four programs, which best fit the idea of a CAS.

Applications:

Think of any task in research or teaching where mathematical computation is needed.  Think of any task in research in teaching where mathematical visualization would be useful.  In all these tasks, a computer algebra system can be used.  The following is a brief list of problems at UNF for which I have used CAS's.

  • Integrating/differentiating functions
  • Numerical/exact solutions to ODE's, PDE's
  • Solving equations/systems of equations
  • Evaluating complicated functions
  • Plotting functions, 2-D and 3-D
  • Implicit plots, data plots
  • Designing graphs for exams or publications
  • Massive expression manipulation
  • Programming
  • Computational number theory/group theory
  • Matrix operations
  • Visualizing 4-D objects/complex graphs
  • Statistics
  • Fourier transforms
  • Signal/Image processing
  • Cryptography
  • Basis reduction
  • Vector calculus
  • Financial mathematics


Programming Examples:

The following are a few programs I have used in various classes.  These are designed to show how CAS's visualization abilities can be used to make some interesting projects for the students.



Written by Daniel Dreibelbis as part of the Faculty Fellows project: Using Computer Algebra Systems in Teaching and Research
Last modified: March 2005