Arlinghaus / Kerski Spatial Mathematics

Theory and Practice through Mapping
1. Auflage 2013
ISBN: 978-1-4665-0533-9
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 300 Seiten

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.

Zielgruppe

Professionals and graduate students working in geography, specifically GIS, remote sensing, and GPS; undergraduate and graduate students in environmental sciences, social sciences, and engineering; math educators; and students studying to be teachers of any discipline involving mathematics.

Autoren/Hrsg.

Arlinghaus, Sandra Lach

Kerski, Joseph J.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Geowissenschaften Geologie Geodäsie, Kartographie, Fernerkundung
• Geowissenschaften Geographie | Raumplanung Geodäsie, Kartographie, GIS, Fernerkundung
• Interdisziplinäres Wissenschaften Wissenschaften Interdisziplinär Naturwissenschaften, Technik, Medizin
• Geowissenschaften Geologie GIS, Geoinformatik

Inhaltsverzeichnis

Geometry of the Sphere
Introduction
Theory: Earth Coordinate Systems
Theory: Earth’s Seasons—A Visual Display
Theory: Precision of Latitude and Longitude Values
Other Earth Models
Practice Using Selected Concepts from This Chapter
Related Theory and Practice: Access through QR Codes

Location, Trigonometry, and Measurement of the Sphere
Introduction: Relative and Absolute Location
Location and Measurement: From Antiquity to Today
Practice: Measuring the Circumference of the Earth Using GPS
Measuring Positions on the Earth Surface, and Fractions
Other Common Coordinate Systems
Practice: Coordinates Using Different Systems
Theory: Visual Trigonometry Review
Practice: Find the Length of One Degree on the Earth-Sphere
Practice: Determine Sun Angles at Different Seasons of the Year
Practice: Work with Measurement, the Graticule, and Map Projections
Summary and Looking Ahead
Related Theory and Practice: Access through QR Codes

Transformations: Analysis and Raster/Vector Formats
Transformations
Partition: Point-Line-Area Transformations
Set Theory
Raster and Vector Mapping: Know Your File Formats
Practice Using Selected Concepts from this Chapter
Related Theory and Practice: Access through QR Codes

Replication of Results: Color and Number
Introduction
Background—Color
Color Straws and Color Voxels
Color Ramps: Alternate Metrics
Algebraic Aspects of Ratios
Pixel Algebra
Preservation of the Aspect Ratio
Image Security
Theory Finale
Practice Using Selected Concepts from This Chapter
Related Theory and Practice: Access through QR Codes

Scale
Introduction
Scale Change
The Dot Density Map: Theory and Example
Practice Using Selected Concepts from This Chapter
Related Theory and Practice: Access through QR Codes

Partitioning of Data: Classification and Analysis
Introduction
The Choice of Data Ranges
Normalizing Data
Inside, Outside, Wrong Side Around
Making Something From Nothing?
Practice Using Selected Concepts from This Chapter
Related Theory and Practice: Access through QR Codes

Visualizing Hierarchies
Introduction
Hierarchies: Census Data
Thinking Outside the Pixel
Practice Using Selected Concepts from This Chapter
Related Theory and practice: Access through QR Codes

Distribution of Data: Selected Concepts
Introduction
Ann Arbor, Michigan—Tornado Siren Infill Project
Educational and Marketing Efforts to the Public
Examining the Distribution of Tornado Data
Activity: Examining the Distribution of Tornado Data
Mean Center and Standard Deviational Ellipse
Activities Using Mean Center and Standard Deviational Ellipse
Related Theory and Practice: Access through QR Codes
Appendix of Media Commentary

Map Projections
Introduction
In the news
Looking at Maps and Their Underlying Projections
Sampling Projection Distortion
Some Projection Characteristics
Pseudo or Miscellaneous Projections
Contemporary Approach: Web Mercator Auxiliary Sphere Projection
Sampling the Environment: The Degree Confluence Project
Practice Using Selected Concepts from This Chapter
Around the Theoretical Corner?
Exercises
Related Theory and Practice: Access through QR Codes

Integrating Past, Present, and Future Approaches
Introduction
From the Classics to the Modern: Past and Present
A Non-Euclidean Future?
Practice Using Selected Concepts from the Chapter
Graph Theory and Topology: Discrete and Continuous Spatial Mathematics
Putting It All Together: Theory
Related Theory and Practice: Access through QR Codes
Glossary

References, Further Reading, and Related Materials