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Essential Mathematics and Statistics for Science. Edition No. 1

  • ID: 5225090
  • Book
  • April 2009
  • 404 Pages
  • John Wiley and Sons Ltd
Essential Mathematics and Statistics for Science, Second Edition 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, supported by revision material and on-line self-assessments. The book then progresses to cover topics relevant to both first and second year level study as well as supporting data analysis for final year projects. The practical applications of the theory are developed by numerous worked examples and practice questions. 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 all the 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 less confident students, as well as an easily accessible resource for students of all abilities. - 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. - Extensive use of video for all worked answers now provides a very successful style of learning support for students via the website. - Website also incorporates Excel and Minitab tutorials in addition to self-assessment tests and other resources:
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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.

3.5 Quadratic and Simultaneous 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, ?2.

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.

Short Answers to ‘Q’ Questions.

Index.
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Graham Currell Bristol Polytechnic, UK; University of the West of England.

Dr. Antony Dowman University of the West of England.
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