Textbook

# Essential Mathematics and Statistics for Science, 2nd Edition

This book is a completely revised and updated version of this invaluable text which allows science students to extend necessary skills and techniques, with the topics being developed through examples in science which are easily understood by students from a range of disciplines. The introductory approach eases students into the subject, progressing to cover topics relevant to first and second year study and support data analysis for final year projects.

The revision of the material in the book has been matched, on the accompanying website, with the extensive use of video, providing worked answers to over 200 questions in the book plus additional tutorial support. The second edition has also improved the learning approach for key topic areas to make it even more accessible and user-friendly, making it a perfect resource for students of all abilities. The expanding website provides a wide range of support material, providing a study environment within which students can develop their independent learning skills, in addition to providing resources that can be used by tutors for integration into other science-based programmes.

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Preface

On-line Learning Support

1 Mathematics and Statistics in Science

1.1 Data and Information

1.2 Experimental Variation and Uncertainty

1.3 Mathematical Models in Science

2 Scientific Data

2.1 Scientific Numbers

2.2 Scientific Quantities

2.3 Chemical Quantities

2.4 Angular Measurements

3 Equations in Science

3.1 Basic Techniques

3.2 Rearranging Simple Equations

3.3 Symbols

3.4 Further Equations

4 Linear Relationships

4.1 Straight Line Graph

4.2 Linear Regression

4.3 Linearization

5 Logarithmic and Exponential Functions

5.1 Mathematics of e, ln and log

5.2 Exponential Growth and Decay

6 Rates of Change

6.1 Rate of Change

6.2 Differentiation

7 Statistics for Science

7.1 Analysing Replicate Data

7.2 Describing and Estimating

7.3 Frequency Statistics

7.4 Probability

7.5 Factorials, Permutations and Combinations

8 Distributions and Uncertainty

8.1 Normal Distribution

8.2 Uncertainties in Measurement

8.3 Presenting Uncertainty

8.4 Binomial and Poisson Distributions

9 Scientific Investigation

9.1 Scientific Systems

9.2 The ‘Scientific Method’

9.3 Decision Making with Statistics

9.4 Hypothesis Testing

9.5 Selecting Analyses and Tests

10 t -tests and F-tests

10.1 One-sample t -tests

10.2 Two-sample t -tests

10.3 Paired t -tests

10.4 F-tests

11 ANOVA – Analysis of Variance

11.1 One-way ANOVA

11.2 Two-way ANOVA

11.3 Two-way ANOVA with Replication

11.4 ANOVA Post Hoc Testing

12 Non-parametric Tests for Medians

12.1 One-sample Wilcoxon Test

12.2 Two-sample Mann–Whitney U-test

12.3 Paired Wilcoxon Test

12.4 Kruskal–Wallis and Friedman Tests

13 Correlation and Regression

13.1 Linear Correlation

13.2 Statistics of Correlation and Regression

13.3 Uncertainty in Linear Calibration

14 Frequency and Proportion

14.1 Chi-squared Contingency Table

14.2 Goodness of Fit

14.3 Tests for Proportion

15 Experimental Design

15.1 Principal Techniques

15.2 Planning a Research Project

Appendix I: Microsoft Excel

Appendix II: Cumulative z -areas for Standard Normal Distribution

Appendix III: Critical Values: t -statistic and Chi-squared, χ2

Appendix IV: Critical F-values at 0.05 (95 %) Significance

Appendix V: Critical Values at 0.05 (95 %) Significance for: Pearson’s Correlation Coefficient, r , Spearman’s Rank Correlation Coefficient, rS, and Wilcoxon Lower Limit, WL

Appendix VI: Mann–Whitney Lower Limit, UL, at 0.05 (95 %) Significance

Index

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• Additional help for weaker students making text more accessible.
• Moving some sections from the printed book and making them available as pdf downloads onto the web site to help engage students on a more interactive level.
• All existing chapters fully revised and updated to include new literature.
• Website – additional changes have been made and will be revised – to inform students of revised online matieral such as new animated screen captions.
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• Applied approach providing mathematics and statistics from the first to final years of undergraduate science courses.
• Second edition substantially revised to improve the learning approach to key topics and the organisation of resources for ease of use in teaching.
• Companion website at www.wiley.com/go/currellmaths2 providing:
• Over 200 videos showing step-by-step workings of problems in the book.
• Additional materials including related topic areas, applications, and tutorials on Excel and Minitab.
• Interactive multiple-choice questions for self-testing, with step-by-step video feedback for any wrong answers.
• A developing resource of study plans for useful topics and applications.