Abstract algebra,polynomial rings I recently took my first abstract algebra class and I'm loving it, so here I am asking for some help studying
The professor mentioned how in polynomial rings, if $x$ is the ordered sequence $(0,1,0,0,...)$, then $x^2$ is $(0,0,1,0,...)$ etc. Although I get why that is, I can find no book mentioning it. Can you recommend any book or resource online with a really detailed, theoretical approach to rings, that requires no background in abstract algebra?
Thanks in advance

You will definitely find the claim that $k[x]$ is a $k$-vector space, and basic linear algebra is the only thing needed to understand this situation.
There is a particularly natural basis for $k[x]$: $\{1, x, x^2, x^3,\ldots\}$. Using this basis, you have the obvious isomorphism $k[x]\cong \bigoplus_{i=0}^\infty k$. 
The coordinates with respect to this ordered basis are precisely the sequences you mention.
