| Chapter | Topics |
| do Carmo 6 | Gauss-Bonnet Theorem. |
| Lee 14 | Integration on Manifolds, Stokes's Theorem, Integration on Riemannian Manifolds. |
| Lee 1 | Manifolds with Boundary. |
| Lee 13 | Orientations of Vector Spaces, Orientations of Manifolds, Boundary Orientations. |
| Lee 19 | Distributions, Involutivity, Frobenius Theorem. |
| Lee 8 | Embedded submanifolds, Level Sets, Immersed Submanifolds, Restricting Maps to Submanifolds, Lie Subgroups. |
| Lee 7 | Maps of Costant Rank, Inverse Function Theorem, Constant Rank Maps Between Manifolds. |
| MIDTERM 2 | |
| do Carmo 5 | Riemannian Geometry of Surfaces. |
| Lee 12 | Geometry of Volume Measurement, Algebra of Alternating Tensors, Wedge Produce, Differential Forms on Manifolds, Exterior Derivatives. |
| Lee 11 | Riemannian metrics. |
| Lee 6 | Covectors, Tangent Covectors on Manifolds, Cotangent Bundle, Differential of a Function, Pullbacks, Line Integrals. |
| MIDTERM 1 | |
| Lee 5 | Vector Bundles, Local and Global Sections, Bundle Maps. |
| Lee 4 | Tangent Bundle, Vector Fields on Manifolds, Lie Brackets, Lie Algebra of a Lie Group. |
| Lee 3 | Tangent Vectors, Pushforwards, Computations in Coordinates, Tangent Vectors to Curves. |
| Lee 2 | Smooth Functions and Smooth Maps, Lie Groups, Partitions of Unity. |
| Lee 1 | Topological manifolds, Smooth Structures, Examples of Smooth Manifolds. |
Scholastic dishonesty: Copying work done by others, either in-class or out of class, is an act of scholastic dishonesty and will be prosecuted to the full extent allowed by University policy. Collaboration on assignments, either in-class or out-of-class, is forbidden unless permission to do so is granted by your instructor. For more information on university policies regarding scholastic dishonesty, see University Student Rules.
Academic Integrity Statement: An Aggie does not lie, cheat or steal or tolerate those who do. Honor Council Rules and Procedures.
Copyright policy: All printed materials disseminated in class or on the web are protected by Copyright laws. One xerox copy (or download from the web) is allowed for personal use. Multiple copies or sale of any of these materials is strictly prohibited.
Americans with Disabilities Act (ADA) Policy Statement: The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact the Department of Student Life, Disability Services Office, in Room B118 of Cain Hall or call 845-1637.