Student Undergraduate Research Projects in Linear Algebra Using a Computer
Algebra System

Rosemary Carroll Farley
Manhattan College
Manhattan College Parkway
Riverdale, NY 10471
rosemary.farley@manhattan.edu

This presentation will demonstrate how the computer algebra system Maple is
used to motivate students to undertake undergraduate research problems in
linear algebra.  First, a simple four step method used to create interesting
graphs and animations is explained to the students.  The students are then
encouraged to use the computer algebra system Maple as a tool to experiment and
to use that experimentation to create mathematical hypotheses which they
ultimately prove or reject.

This presentation will first explain the four step method mentioned above and
then provide specific examples of research projects that developed as a result
of this method.  These projects all involve creating visualizations to clarify
linear algebra material.  Among these are projects creating visualizations of 
the iterates of a point under the action of a 2 x 2 matrix with complex
eigenvalues, creating visualizations of invariant planes under linear 
transformations, creating visualizations of the condition number of an ill-
conditioned matrix, and creating visualizations of a least squares solution to
an ill-posed problem.  The value of such projects in terms of linear algebra 
learned will be discussed.


Keywords:  Use of CAS, technological tools, linear algebra, animation,
eigenvalues, least squares solution, condition number of a matrix.