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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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I'm more with "simultaneously with" rather than "before" or "after"... –  J. M. Sep 15 '11 at 14:28
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I have to say that I don't really like these "Who is more important? Mozart or Beethoven?" type questions. Both calculus and linear algebra are tremendously important throughout both pure and applied mathematics and have been so for much longer than I have been alive. It's really not a contest.... –  Pete L. Clark Sep 15 '11 at 14:32
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...If you are asking whether in some areas in which mathematics is applied linear algebra is even more indispensable than calculus, the answer is certainly yes: I think it is absolutely impossible to do computer graphics without knowing some basic linear algebra, for instance. (And in general, linear algebra is probably more prominent in the CS fields than calculus, although both are extremely important.)... –  Pete L. Clark Sep 15 '11 at 14:34
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(You could also teach linear algebra and calculus at the same time, but with neither subjugated to the other...along with other stuff as well. This more "holistic" approach is common in Europe, for instance, and to all appearances it works at least as well as the "modular" American approach.) –  Pete L. Clark Sep 15 '11 at 14:39
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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. –  Chris Taylor Sep 15 '11 at 14:54
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