Lecture Materials, UP402
(as a supplement to, not a replacement for, in-class material.)

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.

Week 2.
• Coloring of maps;
• 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.

Week 4.
Matt Naud, guest lecturer, for two hours.
Lab--visit to City of Ann Arbor Planning Commission (or substitute), time to be announced, later.

Week 5.
Field evidence.  Use of GIS in an integrated report.

Week 6.

Week 7.
• 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
• 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.

Week 8.
Midterm Presentations:
1.  Paul Perrault
2.  Dan Burt
3.  Tina Meltzer
4.  Chris Eckman
5.  Alzena Saleem
6.  Sarah Velarde
7.  Kara Huizdos, Jennifer Gillis
9.  Ron Keolian, Rachel Hornstein, Vanessa Reisin

Week 9.
• Syria MIS, see pop-up menu on main page
• Bromley NIS, see pop-up menu on main page

Week 10.
Centrality and Hierarchy -- from the classical to the modern.  Using the classical for alignment to extend into the modern setting--a strategy useful in a wide range of theoretical and applied research.
• Material on a geometric model of Central Place Theory (Christaller/Lösch).
• Classical central place theory--basic triangular lattice.
• K=3 hierarchy, marketing principle
• K=4 hierarchy, transportation principle
• Fractal central place theory.
• Illustration of exact fit of the two approaches, showing that the fractally-generated tiles fit together precisely to form the classical central place landscapes.
• Interactivity

Week 11.

Week 12.

Week 13.  No class, Thanksgiving recess begins at 5:00p.m.

Week 14.
• 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),...