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.
CV-04 - Scale and Generalization
Scale and generalization are two fundamental, related concepts in geospatial data. Scale has multiple meanings depending on context, both within geographic information science and in other disciplines. Typically it refers to relative proportions between objects in the real world and their representations. Generalization is the act of modifying detail, usually reducing it, in geospatial data. It is often driven by a need to represent data at coarsened resolution, being typically a consequence of reducing representation scale. Multiple computations and graphical modication processes can be used to achieve generalization, each introducing increased abstraction to the data, its symbolization, or both.