I am always looking for material that enhances my people’s mathematics and computer science proficiency so I stumbled onto some information compiled by Alex Tereshenkov which is very helpful. Hope you enjoy it and also visit Alex’s Blog.

A lot of people who are studying GIS at school or already working as GIS analysts or GIS consultants often wonder what kind of competence will help to be attractive for employers and what domains of expertise are going to be in demand in the foreseeable future.

Usually the kind of questions GIS professionals ask is how much a GIS analyst should learn from other domains. So, we are wondering how much math, statistics, programming, and computer science should GIS analysts learn. Naturally, knowing what kind of GIS specific expertise is in demand is also very helpful. I have several posts on how get better at GIS here, here, and here.

To know what kind of GIS tools can do what kind of job is definitely helpful. This is much like a woodworker should know what kind of tools he has in his toolbox and what tools are available in the woodworking shop. Finding an appropriate tool for a certain job is not so hard nowadays with the Internet search engine and QA sites. However, the ability to understand both how data processing tools work and what happens behind the scenes to be able to interpret the analysis results is indispensable.

What is often true for many GIS analysts is that during their studies the main focus was on the GIS techniques and tools while math and CS courses were supplementary. This makes sense and the graduates are indeed most often competent GIS professionals capable of operating various GIS software suites, provide user support, and perform all kind of spatial analysis. However, it is also possible that in a career change, a person who hasn’t done any studies on GIS, is working as a GIS analyst and needs to catch up a bit. For those people who feel that they lack background GIS competence that they should had a chance to learn during their studies, or for you who just want to learn something that could help to have a broader view and give a deeper understanding of the GIS, I have compiled a list of useful links and books. Please enjoy!

There are lots of **great questions answered on the GIS.SE** web site; here is just a few:

- How important is knowledge of computer science in GIS analysis?
- How much math does a GIS Analyst need to know?
- Recommend topics to be included in a Computer Science for Geospatial Technologies course
- Advice for someone considering a career in GIS (without software development)

**Great books:**

**Spatial Mathematics: Theory and Practice through Mapping (2013)**

This book provides gentle introduction into some mathematical concepts with focus on mapping and might be a good book to start learning math in GIS. No advanced background in math is required and high-school math competence will be sufficient.

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

**Mathematical Techniques in GIS, Second Edition (2014)**

This book gives you a fairly deep understanding of the math concepts that are applicable in GIS. To follow the first 5 chapters, you don’t need any math except high school math. Later on, the book assumes that you have good knowledge of math at the level of a college Algebra II course. If you feel that it gets hard to read, take an Algebra II course online at Khan Academy or watch some videos from MIT to catch up first and then get back to the book. What I really liked about this book is that there are plenty of applicable examples on how to implement certain mathematical algorithms to solve the basic GIS problems such as point in polygon problem, finding if lines are intersecting and calculating area of overlap between two polygons. This could be particularly useful for GIS analysts who are trying to develop own GIS tools and are looking for some background on where to get started with the theory behind the spatial algorithms.

Table of contents

- Characteristics of Geographic Information
- Numbers and Numerical Analysis
- Algebra: Treating Numbers as Symbols
- The Geometry of Common Shapes
- Plane and Spherical Trigonometry
- Differential and Integral Calculus
- Matrices and Determinants
- Vectors
- Curves and Surfaces
- 2D/3D Transformations
- Map Projections
- Basic Statistics
- Correlation and Regression
- Best-Fit Solutions

**GIS: A Computing Perspective, Second Edition (2004)**

The book is a bit dated, but it is probably the best book in computer science for a GIS professional. It provides very deep understanding of the computational aspects that are used in GIS.

Table of contents

- Introduction
- Fundamental database concepts
- Fundamental spatial concepts
- Models of geospatial information
- Representation and algorithms
- Structures and access methods
- Architectures
- Interfaces
- Spatial reasoning and uncertainty
- Time

This book is a unique example of a book for GIS professionals who want to see how the basic GIS algorithms and tools work. The exercises that follow give readers a chance to execute many common GIS algorithms by hand which let truly understand even some complex operations such as generating TIN or finding the shortest path on a street network. The software used as a reference is ArcView GIS 3, but it is still relevant as the GIS concepts haven’t changed much since then.

Table of contents

- GIS Data Models
- GIS Tabular Analysis
- Point Analysis
- Line Analysis
- Network Analysis
- Dynamic Segmentation
- Polygon Analysis
- Grid Analysis
- Image Analysis Basics
- Vector Exercises
- Grid Exercises
- Saving Time in GIS Analysis

I haven’t read this book so don’t have anything to comment on this. Sorry!

Table of contents

- Plane Geometry
- Trigonometry
- Plane Coordinates
- Problems in Three Dimensions
- Areas and Volumes
- Matrices
- Vectors
- Conic Sections
- Spherical Trigonometry
- Solution of Equations
- Least Squares Estimation
- References
- Least Squares models for the general case
- Notation for Least Squares

**Exploring Spatial Analysis in GIS (1996)**

I haven’t read this book either. I guess this one might be hard to find, but have listed it here just in case.