Mapping Math: Forward
Why am I writing this book?
Let me first explain why I am taking the time to write this book.
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 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 partly due to math teachers that had little sympathy for those 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 book.
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. This frustration has been shared with me by other surveyors and GIS 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 be 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.
Math is not the enemy. The enemy is those that think math should be easy for all to grasp and understand.
Who is writing this book?
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 and understand my bias when you read this book. 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. (I'm not a licensed land surveyor just yet. I'm still in training.) 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 expertize 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 of this chapter...) 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 book 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.
I'd like to finish up with some words about the style and format of this book.
The style of this book 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 book that would be accepted by one of those publishers. I'm going to go out of my way to do the following in this chapter:
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 this chapter 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 other 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.