Essential mathematics & 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 Angular measurements.

3. Equations in Science.

3.1 Basic equation handling.

3.2 Introduction to rearranging equations.

3.3 Rearranging complicated equations.

3.4 Solving equations.

3.5 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 and Information.

7.1 Describing and inferring.

7.2 Frequency statistics.

7.3 Probability.

7.4 Bayesian odds.

7.5 Factorials, permutations and combinations.

8. Distributions and Uncertainty.

8.1 Normal distribution.

8.2 Uncertainties in measurement.

8.3 Experimental uncertainty.

8.4 Binomial distribution.

8.5 Poisson distribution.

9. Scientific Investigation.

9.1 Scientific systems.

9.2 The 'scientific method.

9.3 Hypothesis testing.

10. Parametric Tests.

10.1 Sample variances: F test.

10.2 Sample means: Students t test.

10.3 Linear correlation.

10.4 Test for proportion.

11. Chi squared Tests.

11.1 Test for frequencies.

11.2 Contingency tests.

11.3 Goodness of fit.

12. Non parametric Tests.

12.1 Wilcoxon tests.

12.2 Mann Whitney test.

12.3 Kruskal Wallis and Friedman tests.

12.4 Sign test.

12.5 Spearmans rank correlation.

13. Experimental Design and Analysis.

13.1 Data variance.

13.2 Analysis of variance (ANOVA).

13.3 Experiment design.

Appendixes.

Review Questions.

Short Answers to In text Questions.

Index.