- Foundations: Low-Dimensional Spaces
- Flatland
- Other two-dimensional worlds
- The shape of space
- Seeing More: Projections
- Coordinate transformations
- Matrix representations
- The hypercube and hypersphere
- Breaking it Down: Unfolding
- Counting parts of a polyhedron
- The Platonic and Archimedean solids
- Dual polyhedra and polytopes
- Classification of regular solids in higher dimensions
- Decomposing the hypercube
- Building it Up: Slicing
- Views of the hypercube
- Orthographic projection
- Stereographic projection
- Reducing Dimensions: Slicing
- Slices of cubes and hypercubes
- Decomposing polytopes
- The semi-regular polytopes
- Level surfaces
- Computing volumes and hypervolumes
- Applications: Complex Analysis
- Graphs of complex functions as surfaces in four-space
- Riemannian surfaces
- Applications: Configuration Spaces
- Double pendulum
- Phase spaces
- Multi-dimensional data sets
- Applications: Embeddings of Surfaces
- Surfaces in higher-dimensional manifolds
- Orientable and non-orientable spaces
- The shape of space
See the course calendar for details concerning exams and quizzes.
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