| Math, in a Nutshell |
| Introduction Numbers, mathematics, algebra and geometry give everyone a warm feeling inside. It is one of the easiest, most basic parts of life to understand. The simple fact of the matter is that life as it is now would not exist without mathematics. Numbers do indeed form the foundation upon which technology is built. Ok, so maybe you are one of the millions of people who shudder at the very word. It is not hard to agree to the necessity of math, but enjoying it is not as easy. This is understandable. From day one in school people are thrown to the wolves as it were and told they had to learn math. For the most part all training in the manipulation of numbers is done the same way. You get a book and have chapter after chapter of problems to work out. As soon as you learn how to count, some fool always wants to know the answer when you take two sets of those numbers and add them. It’s not enough that you have to learn how to do this, they inundate you with page after page of numbers to add. After a few chapters of this they reverse themselves and want you to subtract numbers. They repeat this with multiplication and division. This process is repeated for all mathematical operations. The bottom line is that it gets tedious. It can get to be so mechanical that a persons mind gets turned off. No excitement. This is supposed to be remedied by the famous or rather infamous, story problem. However, these do not just give the numbers and say do this or do that. There are key words that indicate what operation or operations are to be performed. The key is to understand what these words are. Story problems have scared off more students than anything that could be thrown at them in a history class. You graduate from high school and apply for college. In many cases you are given a set of tests to determine the classes you need. The math test tells you what grade level your skills are. Where do you fit in? Maybe you know ahead of time that your math skills are not as strong as they should be, so you decide to work on raising them. Where do you start? The first thing you notice is that all math books tend to be divided by grade level. Maybe you take a pretest and find out that your math skills are lower than you think. It is hard for a person to pick up a book designed for grade seven when you are much older than that and realize you are unable to solve many of the given problems. This book is about skills, not grade levels. As you age, many of the techniques learned earlier tend to get rusty. This book is designed to be steel wool for the basics. There are a few assumptions being applied. The first of course is that the basic operations are understood. How to add, subtract, divide, and multiply is known, but there are complications of these that will be pursued here. The other assumption is that people reading this want a book that does not over or under whelm. Start at chapter one, but if that is easy and well understood, skip and go to the next chapter. A suggestion is that when you find the chapter that is not understood, start reading at the chapter just previous. Chapter one will be an overview of the basic operations. What will make this different is the approach. There are many books on the market that give problem after problem. One learns by rote repetition. There won’t be any problems like traditional math books have. These can be made up by the reader or found in other books. The idea of this book is to show what and how the various operations work. Chapter two will deal with the advanced form of addition and subtraction, that is, multiplication and division. In both chapters I will include decimals. There will be a few stray algebraic equations in this chapter just to show how they look. The reader at this point will be familiar with the operations but that does not mean the work is done. We need to discuss units. Although the problem is stated in inches, once we get over twelve, it needs to be broken down to the lowest terms. This will of course imply more division, and subtraction. All units are English, metric will be described and a brief explanation will be given, but nothing detailed. This will be in chapter four, devoted to the conversion between metric and what is commonly referred to as English. Actually, English, or the feet, inches, pound, units used in the United States, is called Imperial. Each by itself is relatively easy to convert, say from inches to feet or meters to kilometers. The problem comes in when converting from inches to meters or the other way around. There will be a conversion table and instructions on how it is used, and when. Most complaints about math appear to stem from story problems. I hope a novel approach will ease some of the pain when these are encountered. Most math books take situations that are easy to set up in story fashion but are not realistic. Most people don’t go down to the train station and try to judge when one train will arrive as compared to another. In the modern world we calculate how long it takes to get to work based on certain situations. We go to the store and need to ascertain how much clothes will cost based on the sale prices. These are real world story problems. Algebra, in chapter six, is almost as scary. Looking at an algebra book for the first time you suddenly see that you will be doing operations with letters. Now how in the heck did they ever come up with that crazy idea? Numbers are bad enough. Closer to the back of the book it gets worse, not only are they using letters, but now some idiot has thrown in a bunch of Greek letters. We don’t have enough, now they start using foreign alphabets. Besides, algebra isn’t used in the ordinary real life day-to-day existence, is it? It is and I intend to show where and how. Chapter seven will present a new angle. It will also show squares and rectangles. Here is where we enter the world of geometry. Some of the basic equations for area and circumference could have been covered earlier, but it is easier to understand these concepts after a basic understanding of working equations is established. It is also better to go from the simple to the more complex in the same location without having to constantly refer back to earlier chapters or other books. By the end of the geometry chapter, we will enter the modern digital world. Now carpentry is a lot of sawing and hammering. All that’s needed is to know how many boards to cut, how many nails will be needed and what holes need to be cut, right? That’s true if you want a square house with a flat roof and don’t care that the hole for the sewer pipe and electrical lines are only twice as big as they need to be. In reality however, most roofs are designed at an angle so water can run off and the squirrels can have a slide to play on. Very few carpenters actually grab a pile of lumber and build their house. Most use something called blueprints. It is here that the person has to know geometry to figure out all the angles and hole sizes. Some of the basic equations are first learned in algebra, but anything beyond the simple angles requires a different division of mathematics. There are more advanced forms of math but to go from addition to calculus, a higher form of algebra, in one book is a little much. Each chapter will have a summary and at the end of the book will be an appendix that contains abbreviations and the Greek alphabet. This book is for entertainment first and learning second. So let’s round up those numbers and get them corralled, we have mathematical operations to perform! |