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Craig Adam has over twenty years experience in teaching mathematics within the context of science at degree level. Initially this was within the physics discipline, but more recently he has developed and taught courses in mathematics and statistics for students in forensic science. As head of natural sciences at Staffordshire University in 1998, he led the initial development of forensic science degrees at that institution. Once at Keele University he worked within physics before committing himself principally to forensic science from 2004. His current research interests are focused on the use of chemometrics in the interpretation and evaluation of data from the analysis of forensic materials, particularly those acquired from spectroscopy. His teaching expertise areas within forensic science, apart from mathematics and statistics, include blood dynamics and pattern analysis, enhancement of marks and impressions, all aspects of document analysis, trace evidence analysis and evidence evaluation.
1 Getting the basics right.
Introduction: Why forensic science is a quantitative science.
1.1 Numbers, their representation and meaning.
Self-assessment exercises and problems.
1.2 Units of measurement and their conversion.
Self-assessment problems.
1.3 Uncertainties in measurement and how to deal with them.
1.4 Basic chemical calculations.
Chapter summary.
2 Functions, formulae and equations.
Introduction: Understanding and using functions, formulae and equations.
2.1 Algebraic manipulation of equations.
Self-assessment exercises.
2.2 Applications involving the manipulation of formulae.
2.3 Polynomial functions.
2.4 The solution of linear simultaneous equations.
2.5 Quadratic functions.
2.6 Powers and indices.
3 The exponential and logarithmic functions and their applications.
Introduction: Two special functions in forensic science.
3.1 Origin and definition of the exponential function.
3.2 Origin and definition of the logarithmic function.
3.3 Application: the pH scale.
3.4 The "decaying" exponential.
3.5 Application: post-mortem body cooling.
3.6 Application: forensic pharmacokinetics.
4 Trigonometric methods in forensic science.
Introduction: Why trigonometry is needed in forensic science.
4.1 Pythagoras's theorem.
4.2 The trigonometric functions.
4.3 Trigonometric rules.
4.4 Application: heights and distances.
4.5 Application: ricochet analysis.
4.6 Application: aspects of ballistics.
4.7 Suicide, accident or murder?
4.8 Application: bloodstain shape.
4.9 Bloodstain pattern analysis.
5 Graphs - their construction and interpretation.
Introduction: Why graphs are important in forensic science.
5.1 Representing data using graphs.
5.2 Linearizing equations.
5.3 Linear regression.
5.4 Application: shotgun pellet patterns in firearms incidents.
Self-assessment problem.
5.5 Application: bloodstain formation.
5.6 Application: the persistence of hair, fibres and flints on clothing.
5.7 Application: determining the time since death by fly egg hatching.
5.8 Application: determining age from bone or tooth material
5.9 Application: kinetics of chemical reactions.
5.10 Graphs for calibration.
5.11 Excel and the construction of graphs.
6 The statistical analysis of data.
Introduction: Statistics and forensic science.
6.1 Describing a set of data.
6.2 Frequency statistics.
6.3 Probability density functions.
6.4 Excel and basic statistics.
7 Probability in forensic science.
Introduction: Theoretical and empirical probabilities.
7.1 Calculating probabilities.
7.2 Application: the matching of hair evidence.
7.3 Conditional probability.
7.4 Probability tree diagrams.
7.5 Permutations and combinations.
7.6 The binomial probability distribution.
8 Probability and infrequent events.
Introduction: Dealing with infrequent events.
8.1 The Poisson probability distribution.
8.2 Probability and the uniqueness of fingerprints.
8.3 Probability and human teeth marks.
8.4 Probability and forensic genetics.
8.5 Worked problems of genotype and allele calculations.
8.6 Genotype frequencies and subpopulations.
9 Statistics in the evaluation of experimental data: comparison and confidence.
How can statistics help in the interpretation of experimental data?
9.1 The normal distribution.
9.2 The normal distribution and frequency histograms.
9.3 The standard error in the mean.
9.4 The t-distribution.
9.5 Hypothesis testing.
9.6 Comparing two datasets using the t-test.
9.7 The t -test applied to paired measurements.
9.8 Pearson's ¿2 test.
10 Statistics in the evaluation of experimental data: computation and calibration.
Introduction: What more can we do with statistics and uncertainty?
10.1 The propagation of uncertainty in calculations.
10.2 Application: physicochemical measurements.
10.3 Measurement of density by Archimedes' upthrust.
10.4 Application: bloodstain impact angle.
10.5 Application: bloodstain formation.
10.6 Statistical approaches to outliers.
10.7 Introduction to robust statistics.
10.8 Statistics and linear regression.
10.9 Using linear calibration graphs and the calculation of standard error.
11 Statistics and the significance of evidence.
Introduction: Where do we go from here? - Interpretation and significance.
11.1 A case study in the interpretation and significance of forensic evidence.
11.2 A probabilistic basis for interpreting evidence.
11.3 Likelihood ratio, Bayes' rule and weight of evidence.
11.4 Population data and interpretive databases.
11.5 The probability of accepting the prosecution case - given the evidence.
11.6 Likelihood ratios from continuous data.
11.7 Likelihood ratio and transfer evidence.
11.8 Application: double cot-death or double murder?
References.
Bibliography.
Answers to self-assessment exercises and problems.
Appendix I: The definitions of non-SI units and their relationship to the equivalent SI units.
Appendix II: Constructing graphs using Microsoft Excel.
Appendix III: Using Microsoft Excel for statistics calculations.
Appendix IV: Cumulative z -probability table for the standard normal distribution.
Appendix V: Student's t -test: tables of critical values for the t -statistic.
Appendix VI: Chi squared ¿2 test: table of critical values.
Appendix VII: Some values of Qcrit for Dixon's Q test.
Some values for Gcrit for Grubbs' two-tailed test.
Index.
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