Item — HN Reader

> Numerical calculations are powerful, but they're also subject to a whole host of issues related to finite-precision arithmetic; it's quite possible to set up a numerical calculation that returns nonsense if you don't have a solid intuition for what's going on.

Very true, but I think that is another argument for students doing this right away - it's a great opportunity to teach students about the issues with numerical methodologies.

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The computation is not the physics.

Students need a firm grounding in the analytical and empirical foundations of physics in order to comprehend the issues with numerical methodologies for investigating complicated physical systems properly, though. I've done plenty of work investigating unstable, nonlinear systems for which no closed-form analytical solution exists (they abound, of course, for any non-trivial problem). I'm not sure that having my undergraduate and basic graduate education "mixed up" with issues around numerical solutions would have made the work any easier to understand or deal with. It might have made it harder.

There is no reason they cannot be taught together, though, and perhaps it might be a better approach for some students. I believe that every undergraduate physics curriculum ought to have a senior level course in computational physics.

I agree with you that learning the physics is distinct from learning the numerical aspects. However, I think there is value in learning computational techniques early on (and possibly in parallel with the physics). If my experience is representative (and it might not be), the majority of undergrad physics majors do not wind up pursuing a physics research career, and the numerical skills might not be of more use than the analytic skills. Of course, it's certainly true that these numerical skills can be obtained in a separate class. I'm not sure it's clear-cut whether having them together is better or worse than having them separate. I think one could make a reasonable case either way.