Learning

Differential Geometry of Surfaces

Multivariable Calculus → Gauss-Bonnet Theorem

This learning path guides graduate students from multivariable calculus and curve theory to a rigorous understanding of surface geometry, covering parameterization, fundamental forms, curvature, and geodesics. It emphasizes the conceptual dependencies and culminates in the Theorema Egregium and Gauss-Bonnet theorem.