Introductory Mathematics for the Life Sciences

David Phoenix

• Publisher: CRC Press
• Year: 2018
• eBook ISBN: 9781351988711
• Edition: 1
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

Introductory Mathematics for the Life Sciences offers a straightforward introduction to the mathematical principles needed for studies in the life sciences. Starting with the basics of numbers, fractions, ratios, and percentages, the author explains progressively more sophisticated concepts, from algebra, measurement, and scientific notation through the linear, power, exponential, and logarithmic functions to introductory statistics. Worked examples illustrate concepts, applications, and interpretations, and exercises at the end of each chapter help readers apply and practice the skills they develop. Answers to the exercises are posted at the end of the text.

1

Numbers

1.1 Introduction

Scientists must be able to take quantitative measurements and look for correlations within their experimental data. A scientist should therefore be able to manipulate numbers and have an appreciation of their relevance. The objectives of this chapter are:

(a) to introduce real numbers;

(b) to develop rules for the manipulation of numbers.

1.2 Real numbers

Real numbers may be represented by their position on a number line (Figure 1.1). All the numbers which lie on this line are termed real numbers and the set is represented by the symbol ℝ. Whole numbers (integers) are represented by the symbol ℤ and can be sub-grouped into positive (ℤ+) or negative (ℤ−) integers.

Negative numbers are written to the left of zero. The further a number is to the right, the bigger it is, so for example −2 is greater than −5. Addition therefore indicates that you move to the right, since the number is getting bigger; subtraction indicates that you move to the left.

On the number line, the further the number is to the right the bigger it is

Figure 1.1

ℝ represents the group of all numerical values which can be represented on the number line (i.e. the real numbers)

ℤ represents the set of intergers {…−3, −2, −1, 0, 1, 2, 3,…}

ℤ+ represents the set of positive integers, sometimes called natural numbers {1, 2, 3, 4,…}

ℤ− represents the negative integers {−1, −2, −3, −4,…}

It is obviously important that you are able to manipulate both positive and negative numbers. It is useful to remember that if you are adding a negative number to a positive number you can treat this as a subtraction, as shown in Example 1.1.

Example 1.1

$\begin{array}{l}\left(-2\right)+3\\ =3-2=1\end{array}$

It may help to remember the number line. In Example 1.1 you start at position minus two (−2) and plus three (+3) tells you to move to the right three places, which takes you to position one on the number line. In Example 1.2 you start at position minus four and move one pl...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• General Preface to the Series
• Preface
• 1 Numbers
• 2 Fractions, Percentages and Ratios
• 3 Basic Algebra and Measurement
• 4 Powers and Scientific Notation
• 5 Concentration and Accuracy
• 6 Tables, Charts and Graphs
• 7 Linear Functions
• 8 Power Functions
• 9 Exponential Functions
• 10 Logarithmic Functions
• 11 Introduction to Statistics
• Appendix: Solutions to Problems
• Index