Mathematics - Abstract Algebra - Galois theory - Explore Galois Groups

Guide the student through computing simple Galois groups. Prompts on sticky notes: (1) 'What is the splitting field of x²-2 over ℚ?' (ℚ(√2)). (2) 'What automorphisms fix ℚ? (√2 → √2 or √2 → -√2).' (3) 'So Gal(ℚ(√2)/ℚ) ≅ ℤ₂.' (4) 'Now try x⁴-2. The splitting field is ℚ(⁴√2, i). What's the degree of e