Spatial Mathematics: Theory and Practice through Mapping
Spatial Mathematics: Theory and Practice through Mapping is a book on the mathematics that underlies geographic information systems and spatial analysis. It was written by Sandra Arlinghaus and Joseph Kerski, and published in 2013 by the CRC Press.
Topics[edit]
The book has 10 chapters, divided into two sections on geodesy and on techniques for visualization of spatial data; each chapter has separate sections on theory and practice.[1] For practical aspects of geographic information systems it uses ArcGIS as its example system.[2]
In the first part of the book, Chapters 1 and 2 covers the geoid, the geographic coordinate system of latitudes and longitudes, and the measurement of distance and location. Chapter 3 concerns data structures for geographic information systems, data formatting based on raster graphics and vector graphics, methods for buffer analysis,[3] and its uses in turning point and line data into area data. Later in the book, but fitting thematically into this part,[1][4] chapter 9 covers map projections.[3]
Moving from geodesy to visualization,[1] chapters 4 and 5 concern the use of color and scale on maps. Chapter 6 concerns the types of data to be visualized, and the types of visualizations that can be made for them. Chapter 7 concerns spatial hierarchies and central place theory, while chapter 8 covers the analysis of spatial distributions in terms of their covariance. Finally, chapter 10 covers network and non-Euclidean data.[1][3]
Additional material on the theoretical concepts behind the topics of the book is provided on a web site, accessed through QR codes included in the book.[1]
Audience and reception[edit]
Reviewer reactions to the book were mixed. Several reviewers noted that, for a book with "mathematics" in its title, the book was surprisingly non-mathematical, with both Azadeh Mousavi and Paul Harris calling the title "misleading".[1][4] Harris complains that "the maths is treated quite lightly and superficially".[4] Alfred Stein notes the almost total absence of mathematical equations,[2] and Daniel Griffith similarly notes the lack of proof of its mathematical claims.[5]
Mousavi also writes that, although the book covers a broad selection of topics, it "suffers from lack of necessary depth" and that it is confusingly structured.[1] Sang-Il Lee points to a lack of depth as the book's principal weakness.[3] Stein notes that its reliance on a specific version of ArcGIS makes it difficult to reproduce its examples, especially for international users with different versions or for users of versions updated after its publication.[2] Another weakness highlighted by Griffith is "its limited connection to the existing literature, with its citations far too often being only those works by its authors".[5] Harris sees a missed opportunity in the omission of spatial statistics, movement data, and spatio-temporal data, the design of spatial data structures, and advanced techniques for visualizing geospatial data.[4]
Nevertheless, Mousavi recommends this book as an "introductory text on spatial information science" aimed at practitioners, and commends its use of QR codes and word clouds.[1] Stein praises the book's attempt to bridge mathematics and geography, and its potential use as a first step towards that bridge for practitioners.[2] Harris suggests it "in an introductory and applied context", and in combination with a more conventional textbook on geographic information systems. Lee argues that the overview of fundamental concepts and cross-disciplinary connections forged by the book make it "worth reading by anyone interested in the geospatial sciences".[3] And Griffith concludes that the book is successful in motivating its readers to "explore formal mathematical subject matter that interfaces with geography".[5]
References[edit]
- ^ a b c d e f g h Mousavi, Azadeh (December 2014), "Review of Spatial Mathematics", Journal of Spatial Information Science, 2014 (9): 125–127, doi:10.5311/josis.2014.9.210
- ^ a b c d Stein, Alfred (December 2014), "Review of Spatial Mathematics", International Journal of Applied Earth Observation and Geoinformation, 33: 342, Bibcode:2014IJAEO..33..342S, doi:10.1016/j.jag.2014.06.014
- ^ a b c d e Lee, Sang-Il (September 2014), "Review of Spatial Mathematics", Geographical Analysis, 46 (4): 456–458, doi:10.1111/gean.12066
- ^ a b c d Harris, Paul (July 2016), "Review of Spatial Mathematics", Environment and Planning B: Planning and Design, 43 (5): 963–964, doi:10.1177/0265813515621423, S2CID 63886416
- ^ a b c Griffith, Daniel A. (April 2014), "Review of Spatial Mathematics", The AAG Review of Books, 2 (2): 65–67, doi:10.1080/2325548x.2014.901863