August 16 - 20

## 2010

**Mathematical Principles of GIS**

Geographic information systems have been around for about 35 years and we have seen many developments towards a better understanding of how they should work and function. Many data structures and algorithms have been developed and a lot of insight has been gained on the inner structure of spatial data and relationships. This workshop gives a brief overview of the nature of spatial information and the historic development of our understanding of space and time as well as the basic concepts of geography, cartography, and related sciences.

The major part of the workshop deals with the mathematical basis of spatial information handling. For this purpose we will look into various branches of mathematics and explain where they are being used or when they are useful for the representation and manipulation of spatial data.

First, we will discuss mathematical logic as the language of mathematics and how propositional and predicate logic as well as reasoning is being used in many applications. Set theory, relations, and functions will be explained with relation to GIS. The three major mathematical structures of algebra, topology, and ordered sets will be discussed. Algebra is known in GIS in the context of map algebra, relational algebra in databases, and calculations. Topology is a core concept in GIS for the structuring of spatial data and relationships. We will explain on what mathematical concepts topology in GIS is based and why we use certain representations for redundancy free storage of spatial data. Ordered sets play an important role in the comparison of elements or objects such as in ¡°containment¡± and ¡°part of¡± relationships. We will explain the theory of ordered sets and their application in answering certain spatial queries by translating a spatial query into a mathematical problem, and use the mathematical solution in the spatial context.

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