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In the days when my father taught civil engineering (some decades ago), mathematical applications seemed to be mainly "scientific." (This was the "space age.) Hence the most important branch of mathematics seemed to be calculus. By constrast, linear algebra seemed to be related to "advanced engineering mathematics" (e.g. Kreyszig), to be learned after calculus, and even differential equations, had been addressed first.

In recent decades, advances in "information technology" have perhaps had the greatest impact on the storage and manipulation of large amounts of data, specifically in "strings," "Matrices," and other "arrays." This, of course, represents applications of linear algebra.

Historically, linear algebra has been taught as an "adjunct" to calculus, with the introduction of vectors at the beginning of Calculus 3 (multivariate) and the introduction of matrices at the end. Does linear algebra now have sufficient importance of its own so that it should be taught INDEPENDENTLY of (and possibly prior to) calculus?

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    To give one more data point to Pete's comments, I did all of my studying in the UK, where I learned calculus and linear algebra concurrently (alongside abstract algebra and number theory) and don't seem to have suffered for it, equally many of my friends from the US studied them sequentially and they don't seem to be any better or worse off than me - I'm not convinced that it makes a difference.2011-09-15

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