[Wyman]

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I could care less about the formal definition of a determinant, or how to use that to prove that switching two rows in a determinant switches its sign.


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Lately, I have been considering adding a math major (along with econ). If anybody has advice on whether this would be a good fit for me or not based on what I wrote above, please let me know.

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I was just going to say no, based on your feelings about the determinant proof. But upon further thought, I think you should:

Take a real analysis class and an algebra class. Then decide if you want to be a math major. If you decide not, take a stats class and a combinatorics class. Then redecide. By this point, you're already a math major though. Hey, you learned a whole bunch of (interesting? applicable?) stuff, and you still did your econ major.

There is so much math that has nothing* to do with calculus and linear algebra that you really can't know how much you like "math". You can appreciate beautiful proofs in different areas, but usually you find some area of math that really appeals to you (even if you hate other areas), and you go with it.

If you enjoy calculus, why not take more? Maybe a few years down the road, after a serious algebra course, perhaps, you'll think back on this proof that switching rows of the matrix negates the determinant and think "wow, that's kinda nice." Or, maybe not.

*Obviously, I don't mean "nothing", but I mean that upon a cursory glance, the courses seem to have nothing to do with each other.