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!
2. Video: Flatland: the Movie
3. Video: Flatland: the Film
3. Reducing Dimensions: Unfolding
1. The hypercube
2. Counting parts of a polyhedron
3. The Platonic solids and their analogues
4. Dual polyhedra (optional)
5. The Archimedean solids (optional)
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 (optional)
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

See the course calendar for details concerning exams and quizzes.

 Math 53 (Fall 2010) web pages Created: 24 Aug 2010 Last modified: Aug 25, 2010 7:43:02 AM Comments to: `dpvc@union.edu`