Lecture Materials, UP507
(as a supplement to, not a replacement for, in-class material.)

Week 1.

• Introductions; project interests.
• Website and syllabus
• Biosketches:  include background in GIS and project interests.
• 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.
• Synopsis
• Lab--set up website, discuss project interests.
Week 2.

Jordan Curve Theorem; implications for mapping.

The Jordan Curve Theorem (click here to see animated image of a walk in Lower Manhattan):
• permits correct assignment of addresses on either side of streets--suppose that the path is composed of two squares touching at a point.  When the path is separated into two squares, a consistent assignment procedure for addressing may be given, such as the outsides of the polygons have even numbered addresses on the north and the east sides of streets and have even numbered addresses on the insides of polygons on the south and the west edges of polygons.  If the squares were not split apart, then the south and west edges in this example would be mislabelled.  One must have the Jordan Curve Theorem built into the software if geocoding is to work.
• permits visually appropriate coloring of polygons
• illustrates the need to split complex curves apart at nodes where the curve crosses itself in order to ensure that the two properties above will hold on maps.  This fact is important in digitizing (and elsewhere).
• Synopsis
• Lab:  projects and websites.

Week 3.

• Martin Luther King Day; office hours all afternoon; no class.

Week 4.

• Guest:  Alan Levy, Director, Office of Neighborhood Commercial Revitalization, City of Detroit.
• Lab:  projects and websites

Week 5.

Week 6.

Week 7.  Focus on Spatial Transformations

• Map scale
• Latitude and longitude (related reading:  The Longitude; Mapping).
• 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.
• Spider diagrams:  one way of defining regions in the absence of regional information.
• Thiessen polygons:  another way of defining regions in the absence of regional information
• Contours:  Partitioning the plane in various ways.
• Lab:
• work on projects.  Available on machines in my office:  Animation and other extensions.
• Moving ArcView files...a time-saving maneuver
When moving a map from one computer to another, have you ever had the new file ask you, over and over again, to locate all the shape files and .dbf files?  If so, consider the following approach, particularly when there are many shape files in a single project.  When you go to File|Save Project As  in ArcView, you create an .apr file that is a "project" file.  This file is a template that brings back the shape files you chose with the themes colored the way you chose them to be colored, and so forth. It is the
top level of a spatial hierarchy!  The .apr file is a text file.  Text files can be edited in text editors, such as Windows NotePad. First, open up the .apr file in ArcView and set the working directory to something you want.  Then, save the .apr file again, from ArcView.  Next, open up the .apr file in NotePad (it may ask to put the file in WordPad if the file is too large--that is fine).  Use the "find" command to find the first occurence of "path c:\esri" or wherever the shape files were saved.  Then, use the replace command to replace c:\esri with d:\esri (or whatever you need).  You may or may not wish to use a global replace command. You retain the most control simply by repeating use of the "find" command and typing in suitable changes.

Week 8.  Spring Break

Week 9.  Midterm Presentations

Week 10.  Guest:  Karen Popek Hart, Planning Director, City of Ann Arbor.

Week 11.  Spatial Hierarchy and Fractal Transformations.

Week 12.
• Finish material from week 11.
• Break for 5 minutes
• Number-theoretic properties were used to give precise information about size and shape of fractal generator, above.  In that case, knowing the structure of the number completely determined the spatial result.  Numbers can also create spatial pattern.  Consider the following locational model of Hagerstrand.
• GIS software:  The GIS may also be used to illustrate similar ideas:  spatial infill and extent.
• Put down a dot for each adopter.  Thus, one shape file has 22 dots.
• Create a new field in the attribute table and insert associated random numbers.
• Partition these dots into the six different categories of the mean information field.
• Use "Analysis" | "Neighborhood Statistic" to build neighborhoods based on position of cell in relation to center of MIF.

Week 13.

• Perspective on conceptual material and its long-range importance
• Short-range views--world wide web--huge resource
• Standards for inclusion on the web