- Some Linear Algebra Review
- Vectors and Vector Operations
- Linear Independence
- Basis Vectors
- Linear Maps

- Curves in the Plane and Space
- Definitions
- Arc length
- Reparametrization
- Curvature and Torsion
- Tangent, Normal, Binormal vectors
- Osculating Pane and Circle
- Involute and Evolute

- Quick Introduction to Topology
- Open and Closed sets
- Continuity
- Connectivity
- Homomorphism, Diffeomorphism

- Surfaces in Space
- Regular Surfaces
- Curves on Surfaces
- Surfaces of Revolution
- Inverse Function Theorem
- Tangent Planes
- First and Second Fundamental Forms
- Curvatures (Principal, Mean, etc)
- Gauss Map
- Geodesics
- Orientability
*Theorema Egregium*
- Gauss-Bonnet Theorem

Please the see policy on problem
sets for more about these.
See the course calendar for the timing of exams
and quizzes. The final exam will be scheduled by the registrar; see the
official exam
schedule when it is available.