Writing Mathlets III: A Call to Math Professionals - Coming in Future Articles (Maybe)
I have several ideas in mind for future articles in this series. Here are a few ideas, in no particular order, and with no guarantee that any of these ideas will actually result in a complete article.
I have written two applets to present visual aspects of common techniques of integration, Substitution and Integration by Parts. Both use similar techniques for generating the graphs, involving combining functions with derivatives to build parameterizations. This isn't surprising, since both techniques can be viewed as changes of variables. What surprised me in writing the applets was that Integration by Parts didn't require all of the information usually used in a typical integration in order to generate the graph, but the construction is still remarkably similar to that in the Substitution applet.
An applet for computing derivatives (symbolically, not numerically) led me to consider some questions about techniques for parsing expressions and about permutations and transformations of the resulting parse trees. This is an interesting problem in the intersection of combinatorics and linguistics.
Some discussions with a colleague who writes applets for probability and statistics (see Kyle Seigrist's article, "The Probability/Statistics Object Library," JOMA vol. 4, 2004) have led me to consider the numerical techniques used in common mathematical method libraries to generate "pseudorandom" number sequences. I hope to present some visual applets to show that system developers who design the library calls must be careful about how the pseudorandom number sequence generating technique is constructed, and that applet developers may need to be wary of some pitfalls associated with pseudorandom number sequences.