Some comments on "attitude" and "culture". One of the greatest influences on me have been the books on data graphics by Edward Tufte. It is one reason I believe in writing literate notebooks with textual explanations and multiple and carefully designed presentations. Tufte writes: " Those who discover an explanation are often those who construct its representation." Mathematica gives you plenty of tools for constructing representations and exploring their behavior.

And why textual explanation? Because if you can't give a simple clear explanation it should leave you a bit skeptical as to your level of understanding. The same goes for documentation of a routine. If it's difficult to document maybe it should be redesigned or scrapped for some other routine. Textual explanation and documentation are not onerous chores, they are part of the learning or creative process.

I tend to eschew the terms "code" and "programming" in favor of terms such as "writing definitions, axioms, rules and specifications". After all, we're trying to do math and science. WRI can hire the programmers. It's a matter of attitude and culture.

Lots of people in academia write papers and even books as part of the process of better learning the material. Do you think they always knew it all before they started? So even if it's self-study, writing literate notebooks is good practice. And they might very well be good enough to interest other people. The same applies to having students write literate notebooks, even if they are relatively short. When they're finished they actually have something to show off. Science and technology are no good if they can't be communicated.

Also, if students can design new and clear presentations along with explanations, they are not only learning but they are adding value because these do not always exist together now.

And thanks to Luther for starting this discussion.

I basically use Mathematica for all my work unless otherwise forced asunder. I write all my documents in it and have done since around version 3 (when the typesetting became publication class).

"Just playing with Mathematica is a good strategy for staying young"

I tried that Craig and it doesn't work! Running very very fast might work in a relative sense.

More accurately, playing with Mathematica is a good strategy for maximizing the use of your time.

I first used Macsyma over a 300 baud modem over the Arpanet from Caltech to MIT back in the mid 70s. And I found a bug. They had the general solution to the cubic entered incorrectly.

Bill, Bravo. Very well articulated. Thanks.

Sadly, careful error propagation, null hypotheses, standard error and sample sizes, p values, etc are disappearing from the canonical topics of a physical science education, and many papers appear in press with no discussion of error and uncertainty.

The typical excuse for omission is "curriculum pressure". I think we are just not teaching effectively.

We have walked the same dusty trail. I had forgotten about Macsyma.

I do some of the things you suggest, but in a less ordered fashion. I have several worksheets that I have input various solutions and approaches to problems, and I just keep using the same worksheets. My memory is good enough that I remember that they are in the worksheets and I open one and start scrolling. I call it my cluttered desktop approach.

I second your admiration for Wolfram. And I will look up the reference you suggested. Thanks.

Luther, why don't you write me at djmpark@comcast.net and tell me what your project is.