Dummit And Foote Solutions Chapter 14 (iOS)

For problems asking for subfields, physically draw the subgroup lattice of the Galois group and "flip" it to get the field lattice. It prevents mental errors. Discriminants are Your Friend:

Many "solutions" found online skip the verification of the 5-cycle. A complete Dummit And Foote Solutions Chapter 14 answer must include the mod $p$ reduction argument or a resolvent calculation. Dummit And Foote Solutions Chapter 14