I am also interested in curriculum reform in undergraduate and graduate mathematics. One aspect of curriculum reform I am particularly interested in is using applications to motivate the study of mathematics. I am also interested in using graphing calculators and computer algebra systems such as Mathematica or Maple to allow students to explore mathematics through immediate, adaptable graphic visualization of mathematical concepts far more effectively than was possible through lecture or a manuscript. Calculators and computer algebra systems also make it easier for students to accurately use a combination of algebraic and computational methods in solving mathematical problems.
Current educational projects include trying to effectively use a graphing calculator in teaching the first three semesters of calculus and teaching mathematical modeling by Mathematica notebooks in a computer lab. Each of these projects is attempting to motivate the study of mathematics by applications.
The following materials are available at MathSource and are available by email to mathsource@wri.com or ftp mathsource.wri.com
0207-436: A Simplex command for Mathematica and examples of its use (July
1994)
The notebook simplex.ma contains a simplex command which produces a simplex tableau for a linear programming problem. Examples of its use to solve a standard maximization problem, find multiple optimal feasible solutions, solve linear programming problems by the Big M method, and do a sensitivity analysis are included.
0207-447: A Natural Cubic Spline coefficient command and a Clamped Cubic
Spline coefficient command for Mathematica and examples of its use
(July 1994)
The notebook nspline.ma contains a Mathematica command which produces the natural cubic spline coefficients for a set of 2D data points. Examples of its use to create and plot the natural cubic spline functions and to use these functions to estimate the derivative or integral of a function approximated by the set of data points is included. A similar notebook cspline.ma contains a Mathematica command which produces the clamped cubic spline coefficients for a set of 2D data points and an example of its use.