My background is in computer science, specifically software engineering, and not really math heavy. I know the basics of calculus (the Thomas book) linear Algebra (Strang), and some Discrete Math, Graph Theory, Complexity and Algorithms and that's about it.
I was recently working on proving that the 8-slide puzzle states are divided in to 2 disjoint sets (AI exercise). I had no clue that permutation groups were such a large field of study on their own (I can't even understand the terminology in wikipedia articles, orbits? Cayley tables?), or that their study was Abstract Algebra stuff.
My question is, what is the learning path, book-wise or just topic wise (and I'll find the books later) for someone like me, to understand the basics of Group Theory (taking into account that I don't even know what it really is) and permutation groups more specifically?
P.S. I'm not asking because I want to solve my exercise (this was simple) it just seems a fascinating topic.