Field Theory: We define cyclotomic polynomial as the minimal polynomials of roots of unity over the rationals. We show that the roots of the N-the cyclotomic polynomial are precisely the primitive N-th roots of unity, that the coefficients are integers, and that the degree is phi(N), where phi is the Euler totient function. We also note another formula for cyclotomic polynomials using Mobius inversion.
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.