# The A to Z of mathematics a basic guide - Sidebotham T.H.

ISBN 0-471-15045-2

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X PREFACE

The material in the book falls into three categories.

1. There are processes that explain specific skills; a typical example is the entry Algebra.

2. There are straightforward definitions of words with applications in the world around us, as in the entry Proportion.

3. There is a variety of enrichment material that has good entertainment value, like Hexomino.

I believe there is something of interest for everyone. If you are curious about mathematics and it intrigues you, now may be the time to take the initiative and discover that you indeed have skills in this area of knowledge. Some people need the maturity of a few more years before they achieve success. If you are making a career change and need to revise your mathematical knowledge, then this book is for you. The book will appeal to everyone, even students, who may be interested in, or need to catch up on, basic mathematics. If you are a parent who desires to help your son or daughter and lack the expertise, then this book is for you also. The style and presentation of the book are chosen specifically to suit the lay reader. It is a useful resource for home schooling situations. I hope it is a rich source of ideas for mathematics teachers and also those who are in teacher training, whatever subject in which they are specializing.

You will need a scientific calculator to follow through the steps of working in some of the examples. In statistical topics the reader is referred to the calculator handbook for its use, because brands of calculators can vary so much. The whole book is cross-referenced. If readers are not familiar with the explanations given in a specific entry, they are advised to first read the references at the end of the entry to prepare the groundwork. This book contains an abundance of diagrams, equations, tables, graphs, and worked examples. An emphasis is placed on SI units throughout.

If you are keen to acquire the basic skills of mathematics in this book, I offer the following advice. Do not read it like you may read a novel in which you can skim and still enjoy the book and have a good grasp of the story and plot. To grasp mathematics you must examine the detail of every word and symbol. Have a pen, a calculator, and paper at hand to try out the processes and verify them for yourself.

It is my hope that this book will be on a bookshelf in every home, and will be used by family members as a reference and guide. I am sure you will find it useful, interesting, and entertaining.

Tom Sidebotham

Acknowledgments

I take this opportunity to thank the following persons, without whose help and guidance this book would not have been possible: Steve Quigley, for encouraging, enthusing, and redirecting me, and for sharing the vision; Heather Haselkom, for all her efforts on my behalf to keep the project afloat and for maintaining the lines of communication; David Byatt, for scrutinizing the text and offering judicious alternatives (the accuracy is entirely the responsibility of the author); Dr. David Sidebotham, for his computer skills in enabling me to transplant the book in New York; Stephanie Lentz and her team at TechBooks for transforming my manuscript so wonderfully well; and lastly, the Angel at my elbow throughout the writing.

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A

ABSOLUTE VALUE

The absolute value of a number is the distance of the number from the origin 0, measured along the number line. In the accompanying figure the absolute value of 3 at point B is the distance of point B from 0, which is 3. The absolute value of 2 at point A is the distance of point A from 0, which is 2.

The symbol for the absolute value of a number is two vertical parallel lines placed around the number. At the point B, the absolute value of 3 is written as

IpointS point 0| = 13 0|

= |3|

= 3

If the subtraction had taken place in the opposite way, the answer would still be 3, but the working would be

Absolute value of 3 = |point 0 points |

= |0 3|

= l-3|

= 3 as before

Similarly for the point A:

Absolute value of 2 = |point A point 0|

= |-2-0|

= |-2|

= 2

1

2 ABSTRACT

The absolute value of the line segment AS is obtained in the following way:

Absolute value of AB = | point A β point B | or | point B β point A | = |-2-3|

= |-5|

= 5

When an absolute value is applied to a subtraction, it is safe to subtract the two numbers on the number line in either direction; one gets the same answer for the length of the line segment that joins them.

References: Integers, Number Line.

ABSTRACT

βAbstractβ means separated from practical problems in the real world. Mathematics is an abstract subject and is practiced using symbols, but these symbols can represent real-life things. Real problems can be solved using abstract mathematics, and then the symbols used can be related back to solve the practical problem. In the example that follows the practical problem is about finding the width of a lawn. In the abstract, the symbol representing this width is x. The value of x is found using abstract mathematics, and so the width of the lawn is known and the problem solved.

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