> I fear you're making the calculation the end in itself (we have computers for that!) Well, I have to disagree. Of course it's rather silly to make the calcu

> I fear you're making the calculation the end in itself (we have computers for that!) Well, I have to disagree. Of course it's rather silly to make the calculation the goal in itself, but one needs to have a decent "feeling" of what would happen in a given domain. In math (up to college freshmen) or physics, that involves a lot of number-crunching. Until you get familiar with it. It's same as CS students implementing quicksort, merge sort, heapsort, etc., even though when they graduate they will all use libraries. You can't really grok quicksort by reading the textbook and say "Hmm, I see."