The previous lecture in this series is here. The next lecture in this series is here.
We review some basic results about field extensions and algebraic numbers.
We define the degree of a field extension and show that a number is algebraic over a field if and only if it is contained in a finite extension. We use this to show that the sum and product of algebraic numbers is algebraic, and that a root of a polynomial with algebraic coefficients is algebraic.
This video is part of a lecture course by Richard Borcherds from 2020-21.