I don't think it really works, at least not for most people. Abstract algebra (i.e. actual algebra, as opposed to doing useless stuff to poor polynomials) requ

I don't think it really works, at least not for most people. Abstract algebra (i.e. actual algebra, as opposed to doing useless stuff to poor polynomials) requires one to have developed the mathematical maturity to iron out informal thinking. Good luck explaining "prime" and "irreducible" are not the same. I think a path that would work better is through problem solving, like olympiad problems. But even that definitely isn't for everyone.