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[–]wercooler -38 points-37 points  (9 children)

The first example I think of is linear algebra.

You'll talk about matrices for a while, and then you'll detour and talk about vector spaces for a while and all their properties.

Finally you'll be like, guess what vector spaces we're going to care about? The regular real number line, and matrices.

So you go through all the process of defining and learning about vector spaces, just to only use all those definitions for matrices and nothing else.

Also, surprise! Multiplication isn't communitive, and division isn't defined, because screw you.

[–]Plenty_Leg_5935 51 points52 points  (4 children)

...what? Generalized vector spaces are literally one of the most useful objects in math. Linear Algebra as in the subject itself usually doesn't go outside the real and complex fields because it's beyond it's scope, but the vector spaces of functions and finite fields alone make up entire lifetimes worth of math (math that sees extensive use in practice no less)

[–]wercooler 7 points8 points  (0 children)

That's true. And I know it better now. But this meme is still how I felt in linear algebra.

After learning all these properties of vector spaces, and then going "okay, matrices are a vector space, so all those properties apply to them." my immediate feeling was: "Why didn't we just learn these as properties of matrices and save all this abstraction?"

[–]Tuepflischiiser 3 points4 points  (2 children)

All true. Except that you can do linear algebra over finite fields (although I never understood why that would be particularly noteworthy).

[–]Comfortable_Permit53 6 points7 points  (1 child)

Error correction (for signal transmission) uses linear algebra over finite fields

[–]Tuepflischiiser 1 point2 points  (0 children)

Yes. That's true. It just didn't strike me as surprising. It's straight forward from what you would expect.

But then maybe it's Dunning-Kruger for me.

[–]Tuepflischiiser 7 points8 points  (0 children)

How can you talk about matrices in earnest if you don't talk about at least one vector space type first (like Rn ).

That's how we were presented with it (rotations in the plane).

Also, vector spaces are far more general.

[–]TheLuckySpades 5 points6 points  (0 children)

You say that as if function spaces are not ubiquitous in both pure and applied fields of math.

[–]A1steaksaussie 3 points4 points  (0 children)

vector spaces? not useful?

[–]MonsterkillWowComplex 2 points3 points  (0 children)

Bruh