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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I like it!

I’m intrigued. I suspect that linear algebra would do a better job of improving algebra skills than calc. Additionally, as you hint at, calc is not a great place to be learning how to do proofs (I remember plenty of proofs in both my real and complex analysis courses, but those are very different courses than the 3-semester calc sequence that engineers take).

I suspect that the primary opposition to moving linear algebra to before calc would come from the engineering schools. Would a 1 semester delay in calc give them enough time to get all the calc-based physics in before they start all the physics-based engineering courses? There would be more consequences to the change in egineering and physics curricula than in CS or other sciences.

Hmmm…an interesting idea. However, as coderprof mentioned, engineering departments would throw riots (and possibly some departments in the sciences…from what I’ve heard from my chair, our department is routinely bitched at from the sciences for not getting every one of their majors through calculus on their first attempt–or especially at not letting them into calculus right away in their first semester).

Yes, I never made claims as to the practicality of this idea! Although I think the thing with engineering schools could be worked out. You could always ignore my suggestion that linear algebra should be a prerequisite for calculus, and then engineering students could take calculus whenever they like. Or you could have two flavors of calculus, one for engineers (no linear algebra) and one “advanced” (with LA). 🙂

Another place you’d find resistance is from the AP crowd. College calculus would look less like AP calculus, and testing out of calculus via AP exams would be harder. I like the AP Calculus course and exam, but sadly it seems that the AP curriculum determines the college curriculum these days, more so than the other way around.