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Course Outline:

  1. Foundations: Low-Dimensional Spaces
    1. Flatland
    2. Other two-dimensional worlds
    3. The shape of space

  2. Seeing More: Projections
    1. Coordinate transformations
    2. Matrix representations
    3. The hypercube and hypersphere

  3. Breaking it Down: Unfolding
    1. Counting parts of a polyhedron
    2. The Platonic and Archimedean solids
    3. Dual polyhedra and polytopes
    4. Classification of regular solids in higher dimensions
    5. Decomposing the hypercube

  4. Building it Up: Slicing
    1. Views of the hypercube
    2. Orthographic projection
    3. Stereographic projection

  5. Reducing Dimensions: Slicing
    1. Slices of cubes and hypercubes
    2. Decomposing polytopes
    3. The semi-regular polytopes
    4. Level surfaces
    5. Computing volumes and hypervolumes

  6. Applications: Complex Analysis
    1. Graphs of complex functions as surfaces in four-space
    2. Riemannian surfaces

  7. Applications: Configuration Spaces
    1. Double pendulum
    2. Phase spaces
    3. Multi-dimensional data sets

  8. Applications: Embeddings of Surfaces
    1. Surfaces in higher-dimensional manifolds
    2. Orientable and non-orientable spaces
    3. The shape of space

See the course calendar for details concerning exams and quizzes.



[HOME] Math 153 (Spring 2005) web pages
Created: 24 Mar 2005
Last modified: Mar 24, 2005 11:12:56 AM
Comments to: dpvc@union.edu
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