[Om3] target K14 for reading content-math spec any realistic?

[Stan Devitt]

Dear all,

This discussion on the level of detail to include in the mathematical
definitions raises some very important points centering on usability.  

1.  The exercise here should be primarily of choosing a "usable" default
definition. 

The MathML3 work has greatly improved the mechanism and precision with
which definitions and overrides can be specified, but most of the time
it should not be necessary to use the mechanism.

The default definitions remain usable right up to the point where the
differences between the defaults and your useage interfere with or
become the focus of the mathematical  point you are trying to present.
For example, in most  K-14 mathematical discussions around trigonometric
functions, the exact choice of branch cuts, etc. doesn't matter.

If you were asked what a specific function is, you would most likely
refer the person to a "standard reference".  Those are the definitions
people expect, and the ones that should be used.  That way you only need
to reference an alternative definition when you are working on the
fringe cases.


2.  Whereever possible the default mathematical functions should be
close to those used by common computational systems such as matlab,
mathematica, maple, and others.

For "ordinary computational uses" (whatever that means) it should not be
necessary to override the default defintion.  The author should only
need to override the default definition when it is important to the
mathematical discussion.  (for example, a document that discusses the
differences in how the three systems above handle a specific function.)

Note that is is analogous to how the systems are used in practice.  The
boundary cases are sometimes important, but most of the time have no
bearing on the discussion.  Their definitions are also derived from
standard references.  

Again, by refering to a standard definition, the only time you need to
refer to a "different" definition is when the mathematical discourse /
computation strays into the areas where the system in use differs from
such a standard reference.

3.  A final point.  The technical details of a specific function do not
really change whether it is being used by a new student, or an advanced
mathematician - only the amount / type of detail that the user is aware
of or focussed on.  

----

This suggests to me that it is perfectly okay to define functions (for
example) by reference to definitions from Abromovitz and Stegun, but
provide a K-14 accessible summary.

In both cases, this approach minimizes the number of times an author
needs to point out their readers that the function they are using is
different.


Stan Devitt