Galois theory: Discriminants

This lecture is part of an online graduate course on Galois theory.
We define the discriminant of a finite field extension, ans show that it is essentially the same as the discriminant of a minimal polynomial of a generator. We then give some applications to algebraic number fields.
Corrections: On the first sheet A^2 should be det(A)^2
On sheet 5 at 11:00 there are some sign errors on the bottom right: the polynomial should be b^3-b-1 with discriminant -23

[@anthonymurphy5689]

Example at 11:00 looks wrong? Discriminant of second poly is also -31, not 23. Fields are isomorphic via b=-a.

[@mmereb]

I guess he wanted b^3-b+1 or something like that

[@anthonymurphy5689]

@@mmereb yep. Great series of lectures overall though.

[@mmereb]

@@anthonymurphy5689 definitely

[@m322_yt]

thank you, these uploads are coming at the perfect time.

[@constantijndekker8343]

At minute 2, I think the lecturer meant to write “det(A)^2” instead of A^2.

[@m322_yt]

yes, I was puzzled there as well