Summer Conference for Secondary Teachers

Phillips Exeter Academy

Exeter, New Hampshire

June 22 – 27, 2003

http://mathconf.exeter.edu

A short course on the Polynomial Calculus will be held at the Exeter Summer Conference. The course description is given below. Information on registration is available on the Exeter web site.

The Calculus as Algebra II

On this point the conventional wisdom is simply wrong. It holds that in order to determine the area under a parabola we must first approximate that region with rectilinear figures and then determine the exact area of the region in terms of the limit of the area of these rectilinear figures. It claims this is so because the region under a parabola cannot be decomposed into a finite number of triangles, or rectangles, or any type of finite polygon. Actually the area under a parabola, or for that matter the area under the graph of any polynomial function, can be determined exactly - without approximations or limits - using nothing more than high school algebra and geometry. In fact the complete differential and integral calculus of polynomial functions can be reconstructed and taught as simply a thematic reorganization of the content of a high school Algebra II course. During this workshop we will come to understand both how and why this is so.

Session Leader: William Crombie

E-Mail: bcrombie@aol.com