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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"...2011-09-15
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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....2011-09-15
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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.)...2011-09-15
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    ...But your curricular question also strikes me as a little strange. You are describing the way things were taught in your father's day; okay. But for some time now linear algebra **has** been taught independently of calculus. Most commonly it's taught after calculus but before real analysis, and is used by many math departments (including mine) as a "gateway" course to more rigorous / theoretical / proof-oriented mathematics. Yes, you certainly could teach linear algebra prior to calculus, as it does not depend on calculus. Are you advocating this? To what purpose?2011-09-15
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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.)2011-09-15
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    I think things did not change in the eyes of pure mathematics. It is the engineers forcing applied math community towards Linear algebra. A few examples are : solving systems of differential equations, discretizing PDEs or FEM methods for large scale structures etc. Moreover it has this peculiar property that often you convert a tough problem for calculus into an algebraic one as Laplace transform does to ODEs. I would say it is pure pragmatism.2011-09-15
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    In practical work, I'd say both subjects supply the tools of the trade, and that solutions to problems can and usually do take things from both subjects. For that, I'd say both are important and incomparable, much like saying both apples and oranges are delicious.2011-09-15
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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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