The module begins by introducing some basic notation from set theory and how describing ‘sets’ or ‘events’ in this way can be used to define and calculate probabilities. This leads onto further investigation of some particular probability distributions (discrete and continuous) and their applications. Ways of exploring and illustrating data is also examined, before studying some statistical techniques that can be used to draw conclusions to observations or hypotheses.

Prerequisites: GCSE mathematics or equivalent

• Produce and interpret Venn Diagrams.
• Use and interpret set notation to determine various events and apply this knowledge to solve problems in basic probability theory.
• Recall and use the axioms of probability.
• Solve problems involving the concepts of conditional probability and statistical independence.
• State the differences between discrete and continuous random variables and calculate their means and variances.
• Analyse the properties of some important probability distributions and use them to determine probabilities.
• Produce graphical representations of data and calculate basic statistical measures of numerical data sets.
• Hypothesis testing.

22 - 50 minute lectures: Two lectures each week are used to present the theory together with examples and applications

11 - 50 minute lectures: The weekly tutorials provide further opportunity for students to tackle problems and discuss any aspects of the material introduced during the lectures.

Handouts will be provided containing essential parts of material and students are expected to add their own notes and solutions to examples. Opportunity will be provided to students in lectures to attempt and discuss mathematical problems. Students are also expected to undertake at least 40 hours private study including preparation of worked solutions prior to the tutorial classes. Further resources will also be made available via Learning Central.

Data handling – Production of graphical illustrations and basic statistical analyses   

General problem solving – Application of the mathematics/statistics introduced to solve simple problems in science

Communication – To produce clear and accurate written work communicating how results are obtained

Summative assessment for the module will take the form of continuous assessment and written examination.

The continuous assessment will be in two parts:

1. Group Presentation and Report
2. Individual homework exercise

This is designed to be formative, in that feedback will be provided and items discussed to aid progress towards achieving the learning outcomes of the module. Further formative assessment will also be provided via weekly tutorial exercises.

The major component of the summative assessment is the written examination. The examination is structured into two sections of equal weight. Section A contains a number of (short) compulsory questions and is intended to assess a student’s ability on the methods introduced. Section B presents a choice (two from three questions) of more detailed questions and tests both basic skills and their application.

• Set theory and probability
  • including Venn diagrams, conditional probability and statistical independence.

• Discrete and continuous probability distributions.

• Introductory Statistics
  • including data representation, statistical measures, hypothesis testing

Please see Background Reading List for an indicative list.

Foundation Mathematics (3rd Ed), Booth, D. J., Pearson, 1998