Week 1.

• Introductions; project interests.
• Website and syllabus
• Biosketches:  include background project interests.
• Latitude and Longitude
• chalkboard explanation
• link to brief explanatory material
• GIS maps

• Lab--set up website, discuss project interests.

• Coloring of maps;
• How many colors does it take, at most, to color a map in the plane?
• Animated map of the US:  animated maps can merge space and time--Blank, outline map.
• Four Color Theorem:  assumes adjacency along a line segment. Page 1.  Page 2. Page 3.
• Choropleth maps; Color; Grayscale;  Four Color Theorem  (choosing numbers of colors)
• Given that no more than four colors are ever needed to color a map in the plane, why should a GIS have so many choices for color?
• Choropleth maps with many ranges need a variety of colors
• Ranges need to make sense so that changes in data intensity are reflected in changes in color intensity
• Grayscale and color, this parallelism about data and color intensity is critical
• Four colors are sufficient to color any map in the plane; one never needs more than four.  Thus, when choosing coloring schemes, bear this fact in mind and have a rationale for color selection based on the underlying known theorem about coloring.  One such good rationale is offered above, involving choropleth maps.

Open research questions:  coloring issues with different forms of polygon adjacency; coloring on different surfaces (some solved earlier--extra reading:  Page 4.  Page 5. Page 6.Page 7. Six color map).  We may return to these later when we discuss map transformations of various sorts.
• Lab:  websites and projects

Week 3.
No Lecture.

• Scale
• Animated Maps--samples
• Animaps.
• Animaps, II.
• Animaps III:  Color Straws, Color Voxels, and Color Ramps.
• Animaps, IV:  Of Time and Place
• Animaps, Again
• Animap Sequences
• Animated Map Timeline, Syria
• The Lights Are On, All Over the World
• Beach Closures in Oakland County, Michigan:  Using GIS as an Investigative Tool
• The Possibility of Extending the Streetcar Line in Kagoshima City, Japan
• Interactive Maps--samples
• Mapplet:
• Animaps, IV:  Of Time and Place
• I-maps
• The Relationship between Bicycle Accidents and Lanes of Travel at Downtown Ann Arbor Intersections
• Bus Stops and Bus Users in the City of Detroit

• Map projection:  Stereographic projection.

The One-point Compactification Theorem (blackboard demonstration):
shows that the skin of a spherical globe cannot be perfectly flattened into the plane; it fails to do so by at least one point. Thus, there can be no perfect map in the plane.
• Four Colors are sufficient for any map on a sphere, as well.  An application of the one-point compactification theorem.
• 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; try a cone).
• Cylindrical and conical projections--choose a projection suited to need.
• Mercator--conformal--well-suited as a navigation chart.  Equal area projection better-suited to showing map of the world.

• Syria MIS, see pop-up menu on main page
• Bromley NIS, see pop-up menu on main page

• Material on a geometric model of Central Place Theory (Christaller/Lösch).
• Classical central place theory--basic triangular lattice.
• K=3 hierarchy, marketing principle
• calculation of distance between competing next nearest neighbors
• superimposed layers of hierarchy
• K=4 hierarchy, transportation principle
• calculation of distance between competing next nearest neighbors
• superimposed layers of hierarchy
• K=7 hierarchy, administrative principle
• calculation of distance between competing next nearest neighbors
• superimposed layers of hierarchy
• Fractal central place theory.
• K=3 hierarchy
• K=4 hierarchy; animated version
• K=7 hierarchy; animated version
• Illustration of exact fit of the two approaches, showing that the fractally-generated tiles fit together precisely to form the classical central place landscapes.
• K=3 hierarchy
• K=4 hierarchy
• K=7 hierarchy
• Interactivity
• eBook--show on CD
• I-maps
• The Relationship between Bicycle Accidents and Lanes of Travel at Downtown Ann Arbor Intersections
• Bus Stops and Bus Users in the City of Detroit

• Fractal construction:  self-similarity
• Fractal application:  marina
• I-maps
• The Relationship between Bicycle Accidents and Lanes of Travel at Downtown Ann Arbor Intersections
• Bus Stops and Bus Users in the City of Detroit

• Dot density maps
• Clustering of regions
• I-maps
• The Relationship between Bicycle Accidents and Lanes of Travel at Downtown Ann Arbor Intersections
• Bus Stops and Bus Users in the City of Detroit

• Spider Diagrams
• Summary--look over website and think about where we have been (also in connection with "five themes":  Location; Place; Human/Environment Interaction; Movement; Regions).
• Older equipment--how maps were once made (not all that long ago!)--hands-on with older equipment--Rapidographs, Leroy Lettering Set, Zip-A-Tone (dry transfer lettering and screening),...