### Introduction

This introductory Section reminds you of important notations and conventions used throughout engineering mathematics. We discuss the arithmetic of numbers, the plus or minus sign, $\pm $ , the modulus notation $\left|\phantom{\rule{1em}{0ex}}\right|$ , and the factorial notation !. We examine the order in which arithmetical operations are carried out. Symbols are introduced to represent physical quantities in formulae and equations. The topic of algebra deals with the manipulation of these symbols. The Section closes with an introduction to algebraic conventions. In what follows a working knowledge of the addition, subtraction, multiplication and division of numerical fractions is essential.

#### Prerequisites

- be able to add, subtract, multiply and divide fractions
- be able to express fractions in equivalent forms

#### Learning Outcomes

- recognise and use a wide range of common mathematical symbols and notations

#### Contents

1 Numbers, operations and common notations1.1 The number line

2 Calculation with numbers

2.1 Addition ( $+$ )

2.2 Subtraction ( $-$ )

2.3 The plus or minus sign ( $\pm $ )

2.4 Multiplication ( $\times $ )

2.5 Division ( $\xf7$ ) or ( $\u2215$ )

2.6 The reciprocal of a number

2.7 The modulus notation ( $\left|\right|$ )

2.8 The factorial symbol (!)

3 Rounding to $n$ decimal places

4 Rounding to $n$ significant figures

4.1 Arithmetical expressions

4.2 The BODMAS rule

5 Using symbols

6 Combining numbers together using $+,-,\times ,\xf7$

6.1 Addition ( $+$ )

6.2 Subtraction ( $-$ )

6.3 Multiplication ( $\times $ )

6.4 Division ( $\xf7$ )

6.5 Algebraic expressions

6.6 The equals sign ( $=$ )

6.7 The ‘not equals’ sign ( $\u2044=$ )

6.8 The notation for the change in a variable ( $\delta $ )

6.9 Sigma (or summation) notation ( $\sum $ )