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##### FC-21 - Resolution

Resolution in the spatial domain refers to the size of the smallest measurement unit observed or recorded for an object, such as pixels in a remote sensing image or line segments used to record a curve. Resolution, also called the measurement scale, is considered one of the four major dimensions of scale, along with the operational scale, observational scale, and cartographic scale. Like the broader concept of scale, resolution is a fundamental consideration in GIScience because it affects the reliability of a study and contributes to the uncertainties of the findings and conclusions. While resolution effects may never be eliminated, techniques such as fractals could be used to reveal the multi-resolution property of a phenomenon and help guide the selection of resolution level for a study.

##### FC-11 - Set Theory

Basic mathematical set theory is presented and illustrated with a few examples from GIS. The focus is on set theory first, with subsequent interpretation in some GIS contexts ranging from story maps to municipal planning to language use. The breadth of interpretation represents not only the foundational universality of set theory within the broad realm of GIS but is also reflective of set theory's fundamental role in mathematics and its numerous applications. Beyond the conventional, the reader is taken to see glimpses of set theory not commonly experienced in the world of GIS and asked to imagine where else they might apply. Initial broad exposure leaves room for the mind to grow into deep and rich fields flung far across the globe of academia. Direction toward such paths is offered within the text and in additional resources, all designed to broaden the horizons of the open-minded reader.

##### FC-26 - Problems of Scale and Zoning

Spatial data are often encoded within a set of spatial units that exhaustively partition a region, where individual level data are aggregated, or continuous data are summarized, over a set of spatial units. Such is the case with census data aggregated to enumeration units for public dissemination. Partitioning schemes can vary by scale, where one partitioning scheme spatially nests within another, or by zoning, where two partitioning schemes have the same number of units but the unit shapes and boundaries differ. The Modifiable Areal Unit Problem (MAUP) refers to the fact the nature of spatial partitioning can affect the interpretation and results of visualization and statistical analysis. Generally, coarser scales of data aggregation tend to have stronger observed statistical associations among variables. The ecological fallacy refers to the assumption that an individual has the same attributes as the aggregate group to which it belongs. Combining spatial data with different partitioning schemes to facilitate analysis is often problematic. Areal interpolation may be used to estimate data over small areas or ecological inference may be used to infer individual behaviors from aggregate data. Researchers may also perform analyses at multiple scales as a point of comparison.

##### FC-20 - The power of maps
• Describe how maps such as topographic maps are produced within certain relations of power and knowledge
• Discuss how the choices used in the design of a road map will influence the experience visitors may have of the area
• Explain how legal issues impact the design and content of such special purpose maps as subdivision plans, nautical charts, and cadastral maps
• Exemplify maps that illustrate the provocative, propagandistic, political, and persuasive nature of maps and geospatial data
• Demonstrate how different methods of data classification for a single dataset can produce maps that will be interpreted very differently by the user
• Deconstruct the silences (feature omissions) on a map of a personally well known area
• Construct two maps about a conflict or war producing one supportive of each side’s viewpoint
##### FC-15 - Shape

Shape is important in GI Science because the shape of a geographical entity can have far-reaching effects on significant characteristics of that entity. In geography we are mainly concerned with two-dimensional shapes such as the outlines of islands, lakes, and administrative areas, but three-dimensional shapes may become important, for example in the treatment of landforms. Since the attribute of shape has infinitely many degrees of freedom, there can be no single numerical measure such that closely similar shapes are assigned close numerical values. Therefore different shape descriptors have been proposed for different purposes. Although it is generally desirable for a shape descriptor to be scale invariant and rotation invariant, not all proposed descriptors satisfy both these requirements. Some methods by which a shape is described using a single number are described, followed by a discussion of moment-based approaches. It is often useful to represent a complex shape by means of a surrogate shape of simpler form which facilitates storage, manipulation, and comparison between shapes; some examples of commonly used shape surrogates are presented. Another important task is to compare different shapes to determine how similar they are. The article concludes with a discussion of a number of such measures of similarity.

##### FC-08 - Time

Time is a fundamental concept in geography and many other disciplines. This article introduces time at three levels. At the philosophical level, the article reviews various notions on the nature of time from early mythology to modern science and reveals the dual nature of reality: external (absolute, physical) and internal (perceived, cognitive). At the analytical level, it introduces the measurement of time, the two frames of temporal reference: calendar time and clock time, and the standard time for use globally. The article continues to discuss time in GIS at the practical level. The GISystem was first created as a “static” computer-based system that stores the present status of a dynamic system. Now, GISystems can track and model the dynamics in geographical phenomena and human-environment interactions. Representations of time in dynamic GISystems adopt three perspectives: discrete time, continuous time and Minkowski’s spacetime, and three representations: ordinal, interval, and cyclical. The appropriate perspective and representation depend on the observed temporal patterns, which can be static, oscillating, chaotic, or stochastic. Recent progress in digital technology brings us opportunities and challenges to collect, manage and analyze spatio-temporal data to advance our understanding of dynamical phenomena.

##### FC-07 - Space
• Differentiate between absolute and relative descriptions of location
• Define the four basic dimensions or shapes used to describe spatial objects (i.e., points, lines, regions, volumes)
• Discuss the contributions that different perspectives on the nature of space bring to an understanding of geographic phenomenon
• Justify the discrepancies between the nature of locations in the real world and representations thereof (e.g., towns as points)
• Select appropriate spatial metaphors and models of phenomena to be represented in GIS
• Develop methods for representing non-cartesian models of space in GIS
• Discuss the advantages and disadvantages of the use of cartesian/metric space as a basis for GIS and related technologies
• Differentiate between common-sense, Cartesian/metric, relational, relativistic, phenomenological, social constructivist, and other theories of the nature of space
##### FC-25 - Error
• Compare and contrast how systematic errors and random errors affect measurement of distance
• Describe the causes of at least five different types of errors (e.g., positional, attribute, temporal, logical inconsistency, and incompleteness)
##### FC-16 - Area and Region
• List reasons why the area of a polygon calculated in a GIS might not be the same as the real world object it describes
• Demonstrate how the area of a region calculated from a raster data set will vary by resolution and orientation
• Outline an algorithm to find the area of a polygon using the coordinates of its vertices
• Explain how variations in the calculation of area may have real world implications, such as calculating density
• Delineate regions using properties, spatial relationships, and geospatial technologies
• Exemplify regions found at different scales
• Explain the relationship between regions and categories
• Identify the kinds of phenomena commonly found at the boundaries of regions
• Explain why general-purpose regions rarely exist
• Differentiate among different types of regions, including functional, cultural, physical, administrative, and others
• Compare and contrast the opportunities and pitfalls of using regions to aggregate geographic information (e.g., census data)
• Use established analysis methods that are based on the concept of region (e.g., landscape ecology)
• Explain the nature of the Modifiable Areal Unit Problem (MAUP)