| 1 | To learn about space curves and Frenet vectors and to understand curvature, torsion, and their geometric meanings. |
| 2 | To recognize osculators, normal and rectifying planes, and pairs of curves in space. |
| 3 | Teaching the theory of surfaces and hypersurfaces. Learning the shape operator and the algebraic invariants of the shape operator. |
| 4 | Learning the Gauss transformation and the Weingarten transformation, the types of hypersurfaces, and the differentiable transformations and properties between them. |