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.
http://www.innovativegis.com/basis/Papers/Other/SpatialSTEM/TrivializingComplicating_GIS.pdf
-
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.
http://www.innovativegis.com/basis/Papers/Other/ASPRS13_sSTEM/
-
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.
http://www.innovativegis.com/basis/BeyondMappingSeries/Beyondmapping_IV/Topic10/BM_IV_T10.htm
-
A
Brief History and Probable Future of Geotechnology — white
paper on the evolution and future directions of GIS technology.
http://www.innovativegis.com/basis/Papers/Other/Geotechnology/Geotechnology_history_future.htm
-
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.
http://www.innovativegis.com/basis/BeyondMappingSeries/Beyondmapping_IV/Topic6/BM_IV_T6.htm
-
Beyond
Mapping Compilation Series — a compilation of over 300 “Beyond
Mapping” columns appearing in GeoWorld 1989 to
2013 organized into three online books.
http://www.innovativegis.com/basis/BeyondMappingSeries/