Wouldn't it be better to give the students Mathematica or similar software? It could do the work [...] This is really a tough one. My opinion is no - the swea

Wouldn't it be better to give the students Mathematica or similar software? It could do the work [...] This is really a tough one. My opinion is no - the sweat is the learning. Skipping the problems would just lead to knowing a lot about math, without actually knowing any math. On the other hand, it's tempting - and in the Real World (tm), people do just plug their giant, buck-nasty equations into Mathematica and avoid doing all the book-keeping. I guess the question is: should pilots all just train on auto-pilot, while having only a conceptual understanding of what piloting is about? Or should they learn to pilot manually first, and then use the auto-pilot judiciously? There are legitimate points going both ways - but I vote for the 2nd.