Maths from Scratch for Biologists

by Alan J. Cann

Overview

Numerical ability is an essential skill for everyone studying the biological sciences; but many students are frightened by the 'perceived' difficulty of mathematics, and are nervous about applying mathematical skills in their chosen field of study. Having taught introductory maths and statistics for many years, Alan Cann understands these challenges, and just how invaluable an accessible, confidence building textbook could be to the fearful student. Unable to find a book pitched at the right level that concentrated on why numerical skills are useful to biologists, he wrote his own. The result is Maths from Scratch for Biologists, a highly instructive, informal text that explains step by step how and why you need to tackle maths within the biological sciences.

Product Details

ISBN-13:	9781118685709
Publisher:	Wiley
Publication date:	04/25/2013
Sold by:	JOHN WILEY & SONS
Format:	eBook
Pages:	240
File size:	10 MB

About the Author

Alan Cann has worked in both the UK and USA, and in addition to teaching undergraduate and postgraduate biologists and medical students, he runs an active research laboratory at the University of Leicester, UK, studying the molecular biology and pathogenesis of viruses. He has been awarded numerous grants for educational research and was the inaugural winner of the Society for General Microbiology UK Wildy prize for Education in 2001.

Table of Contents

	Preface	xi
1	Maths in Biology	1
1.1	What can go wrong?	1
1.2	Estimating	5
1.3	How to use this book	6
1.4	Mathematical conventions used in this book	6
2	Manipulating Numbers	7
2.1	Manipulating numbers	8
2.2	Solving equations	9
2.3	Why do you need to know all this?	12
2.4	Fractions	14
2.5	The number 1	15
2.6	Lowest common multiple and greatest common factor	16
2.7	Adding and subtracting fractions	17
2.8	Multiplying fractions	18
2.9	Dividing fractions	18
2.10	Fractions, decimals and percentages	19
2.11	Ratios and proportions	20
3	Units and Conversions	25
3.1	The SI system of units	25
3.2	SI prefixes	27
3.3	SI usage	28
3.4	Measuring energy	29
3.5	Temperature	31
4	Molarities and Dilutions	35
4.1	Avogadro's number	35
4.2	Molecular weight	36
4.3	Solutions	37
4.4	Spectroscopy	40
4.5	Dilutions	42
5	Areas and Volumes	49
5.1	Geometry	49
5.2	Calculating areas and volumes	49
6	Exponents and Logs	57
6.1	Exponents	57
6.2	Exponential functions	60
6.3	Logarithms	62
7	Introduction to Statistics	69
7.1	What is statistics?	69
7.2	Statistical variables	70
7.3	Statistical methods	71
7.4	Frequency distributions	73
7.5	Frequency distribution graphs	76
8	Descriptive Statistics	83
8.1	Populations and samples	83
8.2	The central tendency	84
8.3	Variability	85
8.4	Standard error	88
8.5	Confidence intervals	88
8.6	Parametric and non-parametric statistics	90
8.7	Choosing an appropriate statistical test	91
8.8	Exploratory data analysis	92
9	Probability	99
9.1	Probability theory	99
9.2	Replacing vs not replacing selections	100
9.3	Calculating the probability of multiple events	101
9.4	The binomial distribution	103
9.5	Coincidences	106
10	Inferential Statistics	111
10.1	Statistical inference	111
10.2	Procedure for hypothesis testing	113
10.3	Standard scores (z-scores)	114
10.4	Student's t-test (t-test)	115
10.5	Analysis of variance (ANOVA)	121
10.6	x[superscript 2]-test	125
10.7	Fisher's exact test	131
11	Correlation and Regression	135
11.1	Regression or correlation?	135
11.2	Correlation	136
11.3	Regression	141
Appendix 1	Answers to Problems	147
Appendix 2	Software for Biologists	195
	E-mail	195
	Word processors	197
	Presentation and graphics	198
	Internet resources	198
	Statistics software	200
Appendix 3	Statistical Formulae and Tables	203
	Critical values of the x[superscript 2] distribution	206
	Critical values of student's t-Test	207
	Table of critical values of the F-statistic	208
	Table of critical values of the correlation coefficient, r	213
	Table of binomial probabilities	214
Appendix 4	Glossary	221
	Index	227