The more I teach linear algebra, the more I think that perhaps it — and not calculus — ought to be the standard introductory math course for those majoring in “technical” fields (science, math, CS, economics, etc.). Let those students take a calculus-free version of linear algebra (which would be easy to whip up) in their first year and bring in applications from statistics (e.g. least-square problems), numerical analysis, linear difference equations, and so forth. Linear algebra also provides a nicely accessible avenue into theory and the concept of proof. Save calculus for the second year, require linear algebra as a prerequisite, and then soup calculus up some since the students enrolling in it would have a year of college linear algebra under their belts.
Here’s a book that purports to do some of this, and it’s free. Check it out.
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