Rings and Fields · Algebra
Galois Theory — Introduction
Galois theory establishes a dictionary between subfields of a Galois extension and subgroups of its Galois group. The quintic has no formula because S₅ is not solvable.
WHAT STUDENTS WILL LEARN
✓Define the Galois group of an extension
✓Apply the fundamental theorem of Galois theory
✓Prove the general quintic is not solvable by radicals
✓Connect solvability of groups to solvability of polynomial equations
COURSE OUTLINE · CLICK A PART FOR RESOURCES