The previous lecture in this series is here. The next lecture in this series is here.
We define the discriminant of a finite field extension, and 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 A2 should be det(A)2 On sheet 5 at 11:00 there are some sign errors on the bottom right: the polynomial should be b3–b-1 with discriminant -23.
This video is part of a lecture course by Richard Borcherds from 2020-21.