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A slightly nasty side comment: it is a common idea, outside mathematical and computer science cultures, that exact math is superfluous, and a hindrance to true understanding. Having math and CompSci, I reject this for the reason: understanding requires full logic down to a mechanical level – irrespective of the background of the pupil. Exact math is the sole way to succeed (but it's not a complete prerequisit, of course). Said: Rursus   "