Conceptual material:  review of key theorems.

• Jordan Curve Theorem; implications for mapping. 
Page 1.  Page 2. Page 3.
• Four Color Theorem and one-point compactification (stereographic projection); implications for mapping--there is no perfect map. 
Blank, outline map.  Animated map.  Page 1.  Page 2. Page 3.  Page 4.Page 5. Page 6.  Page 7. Six color map
• How many colors does it take to color a map?
• On a sphere; another use of the one-point compactification...
• In a plane
• On other surfaces
• Map-coloring in GIS software--adjacency patterns.
• Map projection as a transformation:  Thompson's fish
• Links to various projections. 
• Geosystems Handouts on Map Projections
• Classification--move the center of projection; alter the plane of capture (roll it up into a cylinder, torus, Möbius strip, or Klein bottle--developable surface).  
• Cylindrical and conical projections.
• Mercator
• Terrae Antipodum--antipodal points mapped--on Möbius strip and unrolled.