Mapping Math: Introduction

Mapping Math: Introduction

What is Mapping Math?

Mapping Math is a series of articles I hope to write as part of my work with the OSGeo Education Committee. The articles will teach the mathematical concepts used by land surveyors and other geospatial professionals. Each article will discuss a single topic on this greater subject. All of the articles will follow the same basic template.

What are the goals of Mapping Math?

I have the following goals for this series of articles:

• Collect together in a single place the mathematical concepts needed by land surveyors and geospatial professionals.
• Teach these concepts in an informal style and easy-to-understand manner.
• Release this content under an “open” license that allows it to be freely copied, distributed, and translated into other languages.
• Make basic computer programming in a modern programming language (and the application of computer programming to math problems) a central part of the articles.

Background

This series of articles started out as the idea for a book. After the “book” had suffered from a lack of my attention for many months, I decided it might be more successful if I wrote the material as a series of related, but independent articles. I discussed this idea with Charlie Schweik, the chairman of the OSGeo Education Committee, and he seemed open to letting me explore it. I believe writing the material for Mapping Math as a series of articles instead of a book will accomplish several things:

• It will make the task seem less overwhelming.
• It will allow me to actually accomplish something, even if “something” comes in small packages.
• It will make it easier for other authors to contribute.

Why is Mapping Math needed?

I have found that there is a big difference between the type of people that understand math, and the type of people that can teach math in a way that is easily understood by others. It seems like there are a lot more of the first type of people than there are the second type. This presents a serious problem for some students of mathematics.

I struggled with math growing up. I know this was partly due to my own lack of ability, but I think it was also due to math teachers that had little sympathy for students to whom math did not just “make sense”. My introduction to algebra as a young teenager was a surprise, because it was the first type of math I had encountered that I didn't despise. Even so, I struggled with algebra as I had all the other types of math before it. I would consistently score lower in math than in any other subject on standardized tests. I am telling you as the reader this small part of my own history because I want you to know that I understand what it is like to fight math and loose the brawl. I am finally winning this fight in my own life, and I now use math every single day. In my own life Math has been transformed from a frustrating obstacle to a powerful tool. I hope this background will help me to be a better math teacher, and will make it easier for you to benefit from this series of articles.

I wanted to write some instructions on the math used in mapping that could be understood by all types of people, even by those who found math difficult. I personally think that traditional math books are horrible creatures that should be forever banned from the classroom. (My two favorite math books are “Idiot's Guide to Calculus” and “Calculus for Dummies.) I have also found that there is not a great deal of material available about the math used by mapping professionals, and certainly none as freely available as I hope the content of this book will be. (The book “The 3-D Global Spatial Data Model” is the first thing I have seen that comes close to providing a collection of the math needed by mappers.) This frustration has been shared with me by other surveyors and geospatial professionals. I hope this will fill what I see as a serious void in the material on math for the professional that works with spatial data or maps, whether that is a Land Surveyor or GIS Professional.

I found that I really enjoyed math and its ability to solve problems when I could see how it was practically applied in land surveying. That transition from “purely conceptual math” to math in its role as a practical tool made a big difference for me as a math student. I want to show others how math concepts are applied to the making of maps and spatial data. Perhaps others will come to love math as I have when they see how math can be used as a tool in their own work. In the Mapping Math series of articles I hope to avoid the abstract as much as possible and focus on the practical whenever possible.

Math is not the enemy. The enemy is those that think math should be easy for all to grasp and understand.

Author Bias

All authors taint their written works with a bias or slant that is as unique as they are unique as individuals. I am no exception to this rule. I want to provide you with a little bit of information about myself, so that you can recognize and understand my bias when you read this series of articles. I'm sure this bias will creep in despite by efforts to remain objective. This will also help the reader understand why some other mapping professionals may disagree with my style or portions of the material, and be justified in doing so.

First of all, the reader should understand that my day job is as a Land Surveyor. As I mentioned earlier, I use math in my work every day, and in my world trigonometry rules as King. I deal mostly with the making and analyzing measurements, and with the act of creating spatial data. As a result some of the material in this book may focus on the math used in those processes. Land Surveyors also tend to be a little more particular about the accuracy and precision of spatial data than other mapping professionals, and this may be evident in this book occasionally.

Secondly, I should let you know that most of my experience with GIS is as a programmer or software developer. (Although I have embarked on a couple of projects that I hope will help to remedy this.) This means my expertise in the math behind spatial analysis will be a little weaker. (What a great opportunity this would be for a fellow mapping professional with a noble heart to step in as a contributing author.) I still understand the concepts of this area of GIS and I hope to discuss it in some sections of the book.

Finally, I must tell you that I'm not a highly educated man by the standards of “modern society”, for lack of a better term. I learned about land surveying and GIS at my community college in Montana, but did not have any “higher” education after that. All of my other knowledge has been gained through practical experience on the job or by self instruction and volunteer projects. I personally think that “higher” education can be overrated, and that practical experience and self instruction can be just as, or more, beneficial. At any rate, I have no fancy degrees, diplomas, certifications, or titles, and I don't have any letters that follow my name. I thought I would warn those among my readers who feel that is important.

Who is this series of articles written for?

Although I hope it appeals to all kinds of people, I am targeting two (2) types of people specifically with this book. The first type of person is new to process of map making and digital maps. The second type of person may have some experience in one of these areas, but would like to tackle more of the math behind the work they do. For everyone else, this material will hopefully serve as a good review.

Style and Format

The style of this series of articles will be very informal. I've already mentioned how I feel about stuffy and mechanical math text books, and I definitely won't be writing a articles that would be approved of by one of those publishers. I'm going to go out of my way to do the following in each article:

1. Show every single step when solving a math problem.
2. Clearly define and explain unfamiliar terms.
3. Clearly indicate and highlight important terms and formulas.
4. Explain the concept and practical application of the math, not just have you memorize rules and formulas.
5. Use lots of diagrams and pictures.

The informal style I hope to use does not mean that I want to have mistakes or errors. I want each article to be as grammatically and technically correct as possible. I also don't want any math mistakes. (Yes, I do make math mistakes and I have seen them in math books.)

How can you help?

If you find a mistake, please send an e-mail to sunburned.surveyor@gmail.com and let me know about it. I'll get it fixed as soon as I can. While we are on the subject, let me also add that you are welcome to send me suggestions and ideas for the book. Also do not hesitate if you want to help me with the writing of the book, or with translation into a language other than English.