Thread: Mathematical education

In what type of course would one learn about things like hypercomplex numbers, quaternions, octonions, sedenions, etc.? Does one typically encounter things like that as a mathematics major, or are they more specialized than that, and would only be taken up by someone specifically getting into...whatever field of math that is? I'm interested in how majoring in mathematics works, especially since I love math but am not going into it professionally... Any serious contributions are most welcome and appreciated.

Maybe complex analysis extends to those things?

You learn about these in algebra, and you touch upon some of these things in certain topics in number theory and Lie theory ("continuous sets of matrices closed under multiplication and inversion"). Aside from the quaternions, I think these are kind of viewed as mathematical peculiarities--as examples and counterexamples of various phenomena. The quaternions are nice--although they are not commutative, they are associative. The octonions (and whateer lies above) fail to be associative, and mathematicians (and nature) really like associativity.

I can talk more on the subject of the uses of the quaternions, but for now I've got to go!