Bill Pletsch* (USA), bpletsch@email.tvi.cc.nm.us 

A Discrete Look at Elementary Functions

The collection of algebraic combinations of polynomials, exponential, and
trigonometric functions and their inverses compose the class of elementary
functions.  The behavior of the elementary functions has been studied
extensively for centuries.  Nonetheless, these functions as seen from the point
of view of the discrete, reveal some surprises and some new insights.  We will
revisit these old friends from the discrete approach of the data set.

One major insight will be that data sets representing an elementary function
often have a unique signature by which they can be classified.  For example, it
is not well known that the negative harmonic mean of consecutive elements of
the harmonic sequence 1, 1/2, 1/3, ... yields a constant, or that the negative
harmonic mean can be used to generate the sequence recursively.  It is so, and
the result can be extended to a whole class of rational functions.

The possibilities for discovery by students are enormous.  A major theme of
this workshop will be the adaptability of the material to the classroom.  The
insights gained can aid both instructors and students alike in achieving a
deeper understanding of these functions.