地理信息系统（GIS）起源于1960年代，发展至今已成为处理空间数据的主要工具和科学。GIS中的许多基础理论和核心思想，如对时间和空间概念的理解、对空间特征的描述、对空间数据的处理等，均对GIS从业者的数学基础提出了一定的要求。本书介绍与GIS相关的必备数学知识，包括数理逻辑、几何、代数、拓扑学、集合论、图论、概率与统计以及不确定性理论，这些内容涉及GIS数据建模、几何计算、拓扑分析、空间推绎等，对于理解诸如怎样表达空间特征模型、怎样从给定的事实得出逻辑结论、怎样进行坐标变换，乃至遥感图像分类和机器学习等方面都有所帮助。书中还给出了这些数学知识在GIS中的应用实例，便于读者加深对所学内容的理解。
本书可作为地理信息、遥感、测绘等专业高年级本科生和研究生教材，也适合GIS从业者阅读。学习本书的基本要求是掌握高中数学基本知识。

Prolog
Preface
About the Authors
Chapter 1 Spatial Modeling in GIS
1.1 Real World Phenomena and Their Abstractions
1.1.1 Spatial Data and Information
1.2 Concepts of Space and Time
1.2.1 Pre-Newtonian Concepts of Space and Time
1.2.2 Classical Concepts of Space and Time
1.2.3 Contemporary Concepts of Space and Time
1.2.4 Concepts of Space and Time in Spatial Information Systems
1.3 The Real-World and Its Models
1.3.1 Maps
1.3.2 Databases
1.3.3 Space and Time in Real-World Models
1.4 Real-World Models and Their Representation
1.4.1 Spatial Data Models
1.4.2 Spatiotemporal Data Models
1.5 Summary
Chapter 2 Propositional Logic
2.1 Assertion and Proposition
2.2 Logical Operators
2.3 Types of Propositional Forms
2.4 Applications in GIS
2.5 Exercises
Chapter 3 Predicate Logic
3.1 Predicates
3.2 Quantifers
3.3 Quantifers and Logical Operators
3.4 Compact Notation
3.5 Applications in GIS
3.6 Exercises
Chapter 4 Logical Inference
4.1 Logical Arguments
4.2 Proving Arguments Valid in Propositional Logic
4.2.1 Proving Arguments Valid with Truth Tables
4.2.2 Proving Arguments Valid with Rules of Inference
4.3 Proving Arguments Valid in Predicate Logic
4.4 Applications in GIS
4.5 Exercises
Chapter 5 Set Theory
5.1 Sets and Elements
5.2 Relations between Sets
5.3 Operations on Sets
5.4 Applications in GIS
5.5 Exercises
Chapter 6 Relations and Functions
6.1 Cartesian Product
6.2 Binary Relations
6.2.1 Relations and Predicates
6.2.2 Graphic Representation of Binary Relations
6.2.3 Special Properties of Relations
6.2.4 Composition of Relations
6.3 Functions
6.3.1 Composition of Functions
6.3.2 Classes of Functions
6.4 Applications in GIS
6.5 Exercises
Chapter 7 Coordinate Systems and Transformations
7.1 Coordinate Systems
7.1.1 Cartesian Coordinate System
7.1.2 Polar Coordinate System
7.1.3 Transformations between Cartesian and Polar Coordinate Systems
7.1.4 Geographic Coordinate System
7.2 Vectors and Matrices
7.2.1 Vectors
7.2.2 Matrices
7.3 Transformations
7.3.1 Geometric Transformations
7.3.2 Combination of Transformations
7.3.3 Homogeneous Coordinates
7.3.4 Transformation between Coordinate Systems
7.4 Applications in GIS
7.5 Exercises
Chapter 8 Algebraic Structures
8.1 Components of An Algebra
8.1.1 Signature and Variety
8.1.2 Identity and Zero Elements
8.2 Varieties of Algebras
8.2.1 Group
8.2.2 Field
8.2.3 Boolean Algebra
8.2.4 Vector Space
8.3 Homomorphism
8.4 Applications in GIS
8.5 Exercises
Chapter 9 Topology
9.1 Topological Spaces
9.1.1 Metric Spaces and Neighborhoods
9.1.2 Topology and Open Sets
9.1.3 Continuous Functions and Homeomorphisms
9.1.4 Alternate Definition of A Topological Space
9.2 Base, Interior, Closure, Boundary, and Exterior
9.3 Classification of Topological Spaces
9.3.1 Separation Axioms
9.3.2 Compactness
9.3.3 Size
9.3.4 Connectedness
9.4 Simplicial Complexes and Cell Complexes
9.4.1 Simplexes and Polyhedra
9.4.2 Cells and Cell Complexes
9.5 Applications in GIS
9.5.1 Spatial Data Sets
9.5.2 Topological Transformations
9.5.3 Topological Consistency
9.5.4 Spatial Relations
9.6 Exercises
Chapter 10 Ordered Sets
10.1 Posets
10.1.1 Order Diagrams
10.1.2 Upper and Lower Bounds
10.2 Lattices
10.3 Normal Completion
10.3.1 Special Elements
10.3.2 Normal Completion Algorithm
10.4 Applications in GIS
10.5 Exercises
Chapter 11 Graph Theory
11.1 Introducing Graphs
11.1.1 Basic Concepts
11.1.2 Path, Circuit, Connectivity
11.2 Important Classes of Graphs
11.2.1 Direct