Field Theory: We consider the case of simple extensions, where we adjoin a single element to a given field. The cases of transcendental and algebraic arise, depending on whether the kernel of the evaluation map is zero or not. In the algebraic case, we define the minimal polynomial, show it is irreducible, and calculate the degree of the extension.
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.