Essential Mathematics and Statistics for Science

✍ Scribed by Dr. Graham Currell, Dr. Antony Dowman

• Publisher: Wiley
• Year: 2009
• Tongue: English
• Leaves: 405
• Edition: 2
• Category: Library

✦ Synopsis

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.

Hallmark Features:

• 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.
  • Figures from the book for downloading.

✦ Table of Contents

Essential Mathematics and Statistics for Science Second Edition......Page 3
Contents......Page 9
Preface......Page 13
On-line Learning Support......Page 17
1 Mathematics and Statistics in Science......Page 19
1.2 Experimental Variation and Uncertainty......Page 20
1.3 Mathematical Models in Science......Page 22
2 Scientific Data......Page 25
2.1 Scientific Numbers......Page 26
2.2 Scientific Quantities......Page 33
2.3 Chemical Quantities......Page 38
2.4 Angular Measurements......Page 49
3.1 Basic Techniques......Page 59
3.2 Rearranging Simple Equations......Page 71
3.3 Symbols......Page 81
3.4 Further Equations......Page 86
3.5 Quadratic and Simultaneous Equations......Page 96
4 Linear Relationships......Page 105
4.1 Straight Line Graph......Page 107
4.2 Linear Regression......Page 117
4.3 Linearization......Page 125
5 Logarithmic and Exponential Functions......Page 131
5.1 Mathematics of e, ln and log......Page 132
5.2 Exponential Growth and Decay......Page 146
6.1 Rate of Change......Page 163
6.2 Differentiation......Page 170
7 Statistics for Science......Page 179
7.1 Analysing Replicate Data......Page 180
7.2 Describing and Estimating......Page 186
7.3 Frequency Statistics......Page 194
7.4 Probability......Page 208
7.5 Factorials, Permutations and Combinations......Page 221
8 Distributions and Uncertainty......Page 229
8.1 Normal Distribution......Page 230
8.2 Uncertainties in Measurement......Page 235
8.3 Presenting Uncertainty......Page 242
8.4 Binomial and Poisson Distributions......Page 248
9.1 Scientific Systems......Page 261
9.2 The ‘Scientific Method’......Page 263
9.3 Decision Making with Statistics......Page 264
9.4 Hypothesis Testing......Page 268
9.5 Selecting Analyses and Tests......Page 274
10 t-tests and F-tests......Page 279
10.1 One-sample t-tests......Page 280
10.2 Two-sample t-tests......Page 285
10.3 Paired t-tests......Page 290
10.4 F-tests......Page 292
11.1 One-way ANOVA......Page 297
11.2 Two-way ANOVA......Page 304
11.3 Two-way ANOVA with Replication......Page 308
11.4 ANOVA Post Hoc Testing......Page 314
12 Non-parametric Tests for Medians......Page 317
12.1 One-sample Wilcoxon Test......Page 319
12.2 Two-sample Mann–Whitney U-test......Page 323
12.3 Paired Wilcoxon Test......Page 326
12.4 Kruskal–Wallis and Friedman Tests......Page 329
13 Correlation and Regression......Page 333
13.1 Linear Correlation......Page 334
13.2 Statistics of Correlation and Regression......Page 338
13.3 Uncertainty in Linear Calibration......Page 342
14 Frequency and Proportion......Page 349
14.1 Chi-squared Contingency Table......Page 350
14.2 Goodness of Fit......Page 358
14.3 Tests for Proportion......Page 361
15.1 Principal Techniques......Page 367
15.2 Planning a Research Project......Page 375
Appendix I: Microsoft Excel......Page 377
Appendix II: Cumulative z-areas for Standard Normal Distribution......Page 381
Appendix III: Critical Values: t-statistic and Chi-squared, χ2......Page 383
Appendix IV: Critical F-values at 0.05 (95 %) Significance......Page 385
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......Page 387
Appendix VI: Mann–Whitney Lower Limit, UL, at 0.05 (95 %) Significance......Page 389
Short Answers to ‘Q’ Questions......Page 391
Index......Page 397