Elliptic Curves: Singular Points and Group Law

This lecture delves into the concept of singular points on elliptic curves, explaining how to compute partial derivatives and identify singularities. The instructor demonstrates the importance of the point at infinity in projective space and introduces the group law for adding points on the curve. The lecture explores the definition of the group law, the identity element, and the ambiguity in defining the sum of a point with itself. The proof of associativity in the group law is presented through the intersection of cubic curves. The discussion concludes with a detailed explanation of how to define the sum of a point with itself on an elliptic curve.