A Map-ematical Framework for Quantitative Analysis of Mapped Data


   Map Analysis and GIS Modeling for Understanding and Communicating Spatial Patterns and Relationships within STEM Discipline Contexts


University of Denver — February 20, 2015

Center for Statistics and Visualization and Department of Geography and the Environment


Joseph K. Berry

Adjunct Faculty in Geosciences, University of Denver

Adjunct Faculty in Natural Resources, Colorado State University

Principal, Berry and Associates // Spatial Information Systems, Fort Collins, Colorado


This presentation describes a comprehensive framework for map analysis and modeling concepts and procedures as direct spatial extensions of traditional mathematics and statistics enabling individuals with minimal or no GIS background to develop spatial reasoning and problem solving skills—thinking with maps. (50 minute presentation and 40 minute follow-on informal discussion)  


The intent of the presentation is two-fold— 1) to get the Geospatial community to look beyond its traditional mapping and geoquery roles and 2) to engage the STEM disciplines in the validity of quantitative analysis of spatial data. The thesis is that there is common ground in the recognition that “maps are numbers first, pictures later” and that the spatial distribution of these numbers is as important as their numerical distribution in explaining relationships among variables be they scalar or mapped.  The presentation describes the direct extension of traditional math/stat procedures into the spatial realm thereby infusing understanding and communication of spatial patterns into quantitative data analysis.



Handout describing the presentation and listing of online references (.pdf)


PowerPoint supporting formal presentation (11.5MB)


Summary of follow-on informal discussion (available after the presentation)




References: (PowerPoint slides and live URL links to references are at www.innovativegis.com/basis/Present/Mapematics_2015/)


-         Simultaneously Trivializing and Complicating GIS — white paper describing a mathematical structure for Spatial Analysis/ Statistics.


-         SpatialSTEM: a mathematical/statistical framework for understanding and communicating grid-based map analysis, paper presented at ASPRS 2013 Annual Conference, Baltimore, Maryland, March 28, 2013.


-         A Math/Stat Framework for Grid-based Map Analysis and Modeling — Topic 10, book IV GIS Modeling in the online Beyond Mapping Compilation Series of the Beyond Mapping columns published in GeoWorld since 1989.


-         A Brief History and Probable Future of Geotechnology white paper on the evolution and future directions of GIS technology.


-         Education Outside the Traditional Lines Topic 6, book IV GIS Modeling in the online Beyond Mapping Compilation Series of the Beyond Mapping columns published in GeoWorld since 1989.


-         Beyond Mapping Compilation Series a compilation of over 300 “Beyond Mapping” columns appearing in GeoWorld 1989 to 2013 organized into three online books.