Solving Polynomial Equations: Basics and Applications

This lecture covers the basics of solving polynomial equations, focusing on equations of degree 2. It introduces the methods of solving equations historically developed by mathematicians like Del Ferro, Tartaglia, Cardano, Bombelli, and Ferrari. The lecture also discusses the properties of matrices over a field, including invertibility and determinants. Additionally, it explores the concept of imaginary numbers and their historical origins. The lecture concludes with the study of subrings and fields within matrix algebras, emphasizing the properties of commutativity and invertibility.