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Course Outline:

  1. Introduction to Dimensions
    1. Counting dimensions
    2. Coordinates
    3. What is the fourth dimension anyway?

  2. A First View: Flatland
    1. 2 dimensions, 3 dimensions, and higher!

  3. Reducing Dimensions: Unfolding
    1. The hypercube
    2. Counting parts of a polyhedron
    3. The Platonic solids and their analogues
    4. Dual polyhedra
    5. The Archimedean solids

  4. Reducing Dimensions: Shadows
    1. Views of the hypercube
    2. Orthographic projection
    3. Stereographic projection

  5. Reducing Dimensions: Slicing
    1. Slicing a cube
    2. Slicing a hypercube
    3. Level sets, critical points
    4. Video: The Hypercube: slices and projections

  6. Connections: The Hypercube and the Hypersphere
    1. Decomposition of the hypercube
    2. Video: The Hypersphere: Projections and foliations

  7. Student Project Presentations

See the course calendar for details concerning exams and quizzes.



[HOME] Math 53 (Winter 2005) web pages
Created: 01 Jan 2005
Last modified: 01 Jan 2005 00:00:00
Comments to: dpvc@union.edu
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