| 1 | Understanding topological manifolds, differentiable manifolds, and differentiable transformations |
| 2 | Learning vector fields on manifolds, integral curves, Lie products, and differentiable forms on manifolds |
| 3 | Learning Riemannian manifolds, Riemannian connections, and L-C connections |
| 4 | Learning about Riemann curvature, sectional curvature, and Ricci curvature |
| 5 | Understanding the concepts of reduced connection on a submanifold and the Gauss equation |