Essential mathematics and statistics for science

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, 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---- Short Answers to 'Q' Questions.