Spatial Mathematics: Theory and Practice through Mapping

by Sandra Lach Arlinghaus, Joseph J. Kerski

Overview

In terms of statistics, GIS offers many connections. With GIS, data are gathered, displayed, summarized, examined, and interpreted to discover patterns. Spatial Mathematics: Theory and Practice through Mapping uses GIS as a platform to teach mathematical concepts and skills through visualization of numbers. It examines theory and practice from disparate academic disciplines such as geography, mathematics, physics, and general social science. This approach allows students to grapple with biodiversity, crime, natural hazards, climate, energy, water, and other relevant real-world issues of the twenty-first century.

Includes QR Codes Linked to Animated Maps, a Mapping Activity Site, or to an Interactive Webpage, Creating an Interactive Resource That Stays Relevant

The book integrates competing philosophical views of the world: synthesis and analysis. These two approaches yield different results and employ different tools. This book considers both approaches to looking at real-world issues that have mathematics as a critical, but often unseen, component. This approach shows readers how to use mathematics to consider the broad problem at hand and to explore diverse realms in the worlds of geography and mathematics and in their interface.

A truly interdisciplinary text, the book bridges the worlds of mathematics and geography and demonstrates how they are inextricably linked. It takes advantage of the convergence in citizen science, STEM education, and mapping that help readers become critical consumers of data—understanding its content, quality, limitations, and benefits. It provides thorough grounding in the analytical, statistical, and computational skills required for working in any field that uses geospatial technologies—not just surveyors and remote sensing analysts.

Product Details

ISBN-13:	9780367867041
Publisher:	CRC Press
Publication date:	12/12/2019
Edition description:	Reprint
Pages:	300
Product dimensions:	6.12(w) x 9.19(h) x (d)

About the Author

Sandra Lach Arlinghaus is an American educator who is Adjunct Professor in the School of Natural Resources and Environment at the University of Michigan.

Table of Contents

Geometry of the Sphere. Location, Trigonometry, and Measurement of the Sphere. Transformations: Analysis and Raster/Vector Formats. Replication of Results: Color and Number. Scale. Partitioning of Data: Classification and Analysis. Visualizing Hierarchies. Distribution of Data: Selected Concepts
Map Projections. Integrating Past, Present, and Future Approaches. Glossary. References, Further Reading, and Related Materials.

What People are Saying About This

From the Publisher

In this important work, Drs. Arlinghaus and Kerski fill an important need in the geospatial literature with their accessible introduction to spatial mathematics. … this book frames concepts in a way that is accessible to new learners who may not have an advanced math background. This accessibility should not be confused with simplicity, however. In successive chapters, the authors build an intellectually challenging description of the math underlying geospatial analysis. Throughout, easy-to-follow activities help make the concepts clear and relevant. If we are to build a generation of spatial thinkers (and not just people trained in GIS and GPS), we need foundational understanding like this book supports. Highly recommended!
—Bob Coulter, Missouri Botanical Garden

Two ancient texts had a profound and lasting impact on the literate world. … Now, in this book, additional insight for the mathematical solution of geographical tasks is provided. The pedagogical orientation is especially worthy of comment.
—Waldo Tobler, Professor Emeritus of Geography, University of California at Santa Barbara

If a picture is worth a thousand words, then a map is worth exponentially more. Underneath the colors of a modern electronic map is an enormous amount of math and science, from how to represent a three dimensional globe on a two dimensional surface to how to produce and represent color itself in a way to communicate meaning and make sense of complex data.
This book is both all about the map and all about the math behind the map, using what has become ubiquitous on our smart phones and in our vehicles as a vehicle itself to teach complex math concepts in accessible ways. The book’s use of modern, socially pressing issues as the basis of understanding spatial math further augments its goal to make complex concepts accessible, meaningful, and useful for students.
—Marc Schlossberg, Professor of Planning, Public Policy & Management, University of Oregon

Teaching mathematics can be tough but here is a book that is a gentle introduction to the mathematics of the spatial world through the medium of mapping. The use of QR codes to access additional map-based material is clever and innovative, and provides a nice link to the very technologies that this mathematics supports.
—Michael Batty, University College London

An excellent textbook mainstreaming geoinformation perspectives through mathematical education, Spatial Mathematics has a clearly developed theoretical approach with great exercises and practical hands-on activities.
—Karl Donert, President, European Association of Geographers (EUROGEO)

Editorial Reviews

"…this book does not contain any equations or math, as one would expect from the title… As such, this book will be of use to those who want to start out with an effort to learn GIS, without having to struggle through the actual mathematics behind it all."
—Harold Schuch, GeoCounsel, Inc., Littleton, Colorado, USA

"this colourful book should be useful for complementing technical geography lectures using Google Earth and Esri’s software explorations in view of attracting high-school and general science students to spatial geography and computer mapping."
—Rod Blais, GEOMATICA, Vol. 67, No. 4, 2013

"In this important work, Drs. Arlinghaus and Kerski fill an important need in the geospatial literature with their accessible introduction to spatial mathematics. … this book frames concepts in a way that is accessible to new learners who may not have an advanced math background. This accessibility should not be confused with simplicity, however. In successive chapters, the authors build an intellectually challenging description of the math underlying geospatial analysis. Throughout, easy-to-follow activities help make the concepts clear and relevant. If we are to build a generation of spatial thinkers (and not just people trained in GIS and GPS), we need foundational understanding like this book supports. Highly recommended!"
—Bob Coulter, Missouri Botanical Garden

"Two ancient texts had a profound and lasting impact on the literate world. … Now, in this book, additional insight for the mathematical solution of geographical tasks is provided. The pedagogical orientation is especially worthy of comment."
—Waldo Tobler, Professor Emeritus of Geography, University of California at Santa Barbara

"If a picture is worth a thousand words, then a map is worth exponentially more. Underneath the colors of a modern electronic map is an enormous amount of math and science, from how to represent a three dimensional globe on a two

From the Publisher