Algebra 2: Field extensions and Galois Theory

Just as there is a formula for solving a quadratic equation, there are similar formulae for solving the general cubic and quartic. Galois theory provides a solution to the corresponding problem for quintics --- there is no such formula in this case! Galois theory also enables us to prove (despite regular claims to the contrary) that there is no ruler and compass construction for trisecting an angle. Topics to be covered include: - Galois Theory - fields - Field extensions - Normal extensions - Separable extensions - Revision of group theory, abelian and soluble groups - Galois' Theorem - Solubility of equations by radicals - Finite fields - Cyclotomic fields Note: Graduate students attend joint classes with undergraduates but will be assessed separately.