Field Theory: We define the Galois group of a polynomial g(x) as the group of automorphisms of the splitting field K that fix the base field F pointwise. The Galois group acts faithfully on the set of roots of g(x) and is isomorphic to a subgroup of a symmetric group. We also show that this action is transitive when g(x) is irreducible over F.
Includes course on Group Theory (problems and solutions at website) and Ring Theory, and Field Theory. For Prerequisites on proofs and sets, see the Math Major Basics course.