Most abstract algebra texts begin with groups, then proceed to rings and fields. While groups are the logically simplest of the structures, the motivation for studying groups can be somewhat lost on students approaching abstract algebra for the first time. To engage and motivate them, starting with something students know and abstracting from there
Numbers, Polynomials, And Factoring. Rings, Domains, and Fields. Rings. Unique Factorization. Ring Homomorphisms and Ideals. Group Homomorphisms and Permutations. Constructability Problems. Vector Spaces and Field Extensions. Galois Theory.