[The interplay of conversation here has become rather a mess...]

At my school, LinearAlgebra is usually taken at the same time as Calculus 3. Annoyingly enough, NumericalAnalysis is usually taken at the same time as Calculus 3.  However, all three are not usually taken at the same time. This leads to a couple of questions:

First, would be better to take LinearAlgebra or NumericalAnalysis first?

Second, if I'm only going to take one of the three classes, which would be the best one to take? I ask this because after taking one of the three classes, neither of the others help me get closer to graduation, and I already am going to have over a semesters worth of credits that don't get me closer either.

''I can't tell you anything about the courses at your school, of course. However: lots of things in NumericalAnalysis assume a decent familiarity with the elements of LinearAlgebra; the reverse isn't true. So you're more likely to win by taking LinearAnalysis first.''

'''''That helps a lot. Actually. LinearAlgebra isn't listed as a pre-req where I go to school.'''''

''Maybe it isn't one. Perhaps either the NumericalAnalysis course doesn't include any of the bits LinearAlgebra would help with, or else the LinearAlgebra course doesn't cover the sort of stuff that helps with NumericalAnalysis. Both of these are certainly possible. Or perhaps it's '''helpful''' but not '''necessary'''.''

''Which one would be best to take? Whichever one you're most interested in. If you're not interested in any of them, why are you studying mathematics? Or: Whichever one you're likely to be best at. Only you know this. Or: Whichever one is most likely to be useful in your future career. That depends on what your future career is.''

'''''My professors keep telling me they think I'd find LinearAlgebra or NumericalAnalysis interesting. Of course, which they tell me seems to depend on their background. The reason that I'm studying math is because it is required for my major. Specifically, I need Calc 2, and one upper level elective, which could be filled by any of the above classes, as well as advanced statistics. I don't think I'd like stat though.'''''

''If your major is in computer science and you plan a career in programming or something of the kind, then linear algebra is probably more likely to be useful to you. Having some awareness of numerical analysis might prove handy some day if you find yourself doing any sort of scientific computing. Neither is likely to come up every day, unless you're doing the sort of work for which you need a lot more mathematics than this. I can't comment on "Calculus 3", because I have no idea what's in that.''

This is one of those YMMV (Your Mileage May Vary) things.
My undergrad is in Math with an emphasis on CS, and have been doing high tech since then. I've gotten a lot more mileage out of linear algebra than I have out of numerical analysis (or calculus). Linear algebra pops up in statistics (linear regression) operations research, and econometrics (regression again).

''I'm told that linear algebra also is useful a lot for graphics work.''

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CategoryMath