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.