You already know some Galois theory!

This playlist is an introduction to Galois theory as it is never taught. Indeed, Galois theory is a major mathematical paradigm used to study not only field extensions but also topology. On the other hand, most Galois theory courses are devoted to showing that the quintic cannot be solved by radicals. In this playlist, I want to show you more about how Galois theory really gets used to understand mathematics in the research of today. This first video looks at examples of Galois theory hidden in mathematics you already know. We look at real polynomials and the Mobius band from the Galois theoretic perspective.