The previous lecture in this series is here. The next lecture in this series is here.
We use the theory of splitting fields to classify finite fields: there is one of each prime power order (up to isomorphism).
We give a few examples of small order, and point out that there seems to be no good choice for a standard finite field of given order: this depends on the choice of an irreducible polynomial.
Finally we show how to count the number of irreducible polynomials of given degree in a finite field (using the field of order 64 as an example).
This video is part of a lecture course by Richard Borcherds from 2020-21.