| Date | Topic |
| 1 | 1/22 | Overview of the material, parametrizations |
| 1/24 | Graphs and level sets |
| 2 | 1/27 | The Implicit Functions Theorem |
| 1/29 | Tangent vectors |
| 1/31 | Tangent spaces and regular surfaces |
| 3 | 2/03 | Diffeomorphisms, reparametrization of curves |
| 2/05 | Reparametrization of surfaces |
| 2/07 | Curves as graphs |
| 4 | 2/10 | The Local Inverse Theorem |
| 2/12 | Surfaces as graphs, wrap-up of Chapter 2 |
| 2/14 | Arc length |
| 5 | 2/17 | Shortest curves and unit speed reparametrization |
| 2/19 | Quadratic forms |
| 2/21 | Snow day |
| 6 | 2/24 | The First Fundamental Form |
| 2/26 | Introduction to areas and plane integrals |
| 2/28 | Midterm 1 |
| 7 | 3/02 | Double integrals |
| 3/04 | Surface areas |
| 3/06 | Curvature of plane curves |
| 8 | | Spring Break |
| 9 | 3/16 | No class |
| 3/18 | No class |
| 3/20 | Online meeting |
| 10 | 3/23 | Curvature of unit speed curves, the tangent angle - online |
| 3/25 | Curvature of space curves, torsion - online |
| 3/27 | The Frenet frame, Frenet formulas - online |
| 11 | 3/30 | The Darboux Frame, normal and geodesic curvatures - online |
| 4/01 | Properties of the normal curvature - online |
| 4/03 | The shape operator - online |
| 12 | 4/06 | The Second Fundamental Form - online |
| 4/08 | Principal curvatures - online |
| 4/10 | Classification of points on surfaces - online |
| 13 | 4/13 | Review - online |
| 4/15 | Midterm 2 |
| 4/17 | Gaussian curvature - online |
| 14 | 4/20 | No class |
| 4/22 | Christoffel symbols, intrinsic geometry - online |
| 4/24 | Proof of Gauss' Theorema Egregium - online |
| 15 | 4/27 | Isometries and gaussian curvature - online |
| 4/29 | Examples and wrap-up - online |
| 5/01 | Review - online |
| ★ | 5/04 | Final Examination |