All numbers refer to exercises (and not "computer exercises") in Gallian. §22: 8, 16, 22, 24, 28, 36.
In addition:
Problem 1: Let a be a complex root of the polynomial x^{6} + x^{3} + 1. Find all homeomorphisms σ: Q(a) → C over Q. (HINT: the polynomial is a factor of x^{9}-1.)
Problem 2: We say that a ?eld extension E/F is quadratic if [E: F] = 2. Prove that every quadratic extension of F is normal.