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Describe how linear functions are used to fuzzify input data (i.e., mapping domain values to linguistic variables)
Support or refute the statement by Lotfi Zadeh, that “As complexity rises, precise statements lose meaning and meaningful statements lose precision,” as it relates to GIS&T
Explain why fuzzy logic, rather then Boolean algebra models, can be useful for representing real world boundaries between different tree species

Define various terms used to describe topological relationships, such as disjoint, overlap, within, and intersect
List the possible topological relationships between entities in space (e.g., 9-intersection) and time
Use methods that analyze topological relationships
Recognize the contributions of topology (the branch of mathematics) to the study of geographic relationships
Describe geographic phenomena in terms of their topological relationships in space and time to other phenomena

Define the following terms pertaining to a network: Loops, multiple edges, the degree of a vertex, walk, trail, path, cycle, fundamental cycle
List definitions of networks that apply to specific applications or industries
Create an adjacency table from a sample network
Explain how a graph can be written as an adjacency matrix and how this can be used to calculate topological shortest paths in the graph
Create an incidence matrix from a sample network
Explain how a graph (network) may be directed or undirected
Demonstrate how attributes of networks can be used to represent cost, time, distance, or many other measures
Demonstrate how the star (or forward star) data structure, which is often employed when digitally storing network information, violates relational normal form, but allows for much faster search and retrieval in network databases
Discuss some of the difficulties of applying the standard process-pattern concept to lines and networks
Demonstrate how a network is a connected set of edges and vertices

Evaluate methods used by contemporary GIS software to resample raster data on-the-fly during display
Select appropriate interpolation techniques to resample particular types of values in raster data (e.g., nominal using nearest neighbor)
Resample multiple raster data sets to a single resolution to enable overlay
Resample raster data sets (e.g., terrain, satellite imagery) to a resolution appropriate for a map of a particular scale
Discuss the consequences of increasing and decreasing resolution

Define “metadata” in the context of the geospatial data set
Use a metadata utility to create a geospatial metadata document for a digital database you created
Formulate metadata for a graphic output that would be distributed to the general public
Formulate metadata for a geostatistical analysis that would be released to an experienced audience
Compose data integrity statements for a geostatistical or spatial analysis to be included in graphic output
Identify software tools available to support metadata creation
Interpret the elements of an existing metadata document
Explain why metadata production should be integrated into the data production and database development workflows, rather than treated as an ancillary activity
Outline the elements of the U.S. geospatial metadata standard
Explain the ways in which metadata increases the value of geospatial data

Illustrate the GBF/DIME data model
Describe a Freeman-Huffman chain code
Describe the relationship of Freeman-Huffman chain codes to the raster model
Discuss the impact of early prototype data models (e.g., POLYVRT and GBF/DIME) on contemporary vector formats
Describe the relationship between the GBF/DIME and TIGER structures, the rationale for their design, and their intended primary uses, paying particular attention to the role of graph theory in establishing the difference between GBF/DIME and TIGER files
Discuss the advantages and disadvantages of POLYVRT
Explain what makes POLYVRT a hierarchical vector data model

Differentiate between a controlled vocabulary and an ontology
Describe a domain ontology or vocabulary (i.e., land use classification systems, surveyor codes, data dictionaries, place names, or benthic habitat classification system)
Describe how a domain ontology or vocabulary facilitates data sharing
Define “thesaurus” as it pertains to geospatial metadata
Describe the primary focus of the following content standards: FGDC, Dublin Core Metadata Initiative, and ISO 19115
Differentiate between a content standard and a profile
Describe some of the profiles created for the Content Standard for Digital Geospatial Metadata (CSDGM)

Illustrate the quadtree model
Describe the advantages and disadvantages of the quadtree model for geographic database representation and modeling
Describe alternatives to quadtrees for representing hierarchical tessellations (e.g., hextrees, rtrees, pyramids)
Explain how quadtrees and other hierarchical tessellations can be used to index large volumes of raster or vector data
Implement a format for encoding quadtrees in a data file

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