Mathematics and statistics

This is the foundation course on which subsequent, more specialised quantitative courses in Mathematics and Statistics are based. The course offers an overview of key mathematical methods and statistical concepts frequently applied to economics, management, finance and related areas.

Topics covered

• Arithmetic and algebra: The mathematics part of the course begins with a review of arithmetic (including the use of fractions and decimals). The manipulation of algebraic expressions (including the use of brackets and the power laws). Identities, equations and inequalities. Solving linear and quadratic equations. Solving simultaneous linear equations.
• Functions: Some common functions (including polynomials, exponentials, logarithms and trigonometric functions) and their graphs. Inverse functions and how to find them (if they exist). The laws of logarithms and their uses.
• Calculus: The meaning of the derivative and how to find it (including the product, quotient and chain rules). Using derivatives to find approximations and solve simple optimisation problems with economic applications. Curve sketching. Integration of simple functions and using integrals to find areas.
• Financial mathematics: Percentages and compound interest over different compounding intervals. Arithmetic and geometric sequences. The sum of arithmetic and geometric series. Investment schemes and ways of assessing the value of an investment.
• Data exploration: The statistics part of the course begins with basic data analysis through the interpretation of graphical displays of data. Univariate, bivariate and categorical situations are considered, including time series plots. Distributions are summarised and compared and their patterns discussed. Descriptive statistics are introduced to explore measures of location and dispersion.
• Probability: The world is an uncertain place and probability allows this uncertainty to be modelled. Probability distributions are explored to describe how likely different values of a random variable are expected to be. The Normal distribution is introduced and its importance in statistics is discussed. The concept of a sampling distribution is explored.
• Sampling and experimentation: An overview of data‐collection methods is followed by how to design and conduct surveys and experiments in the social sciences. Particular attention is given to sources of bias and conclusions that can be drawn from observational studies and experiments.
• Fundamentals of regression: An introduction to modelling a linear relationship between variables. Interpretation of computer output to assess model adequacy.

Learning outcomes

If you complete the course successfully, you should be able to:

• Manipulate algebraic expressions
• Graph, differentiate and integrate simple functions
• Calculate basic quantities in financial mathematics
• Interpret and summarise raw data on social science variables graphically and numerically
• Appreciate the concepts of a probability
• Distribution, modelling uncertainty and the Normal distribution
• Design and conduct surveys and experiments in a social science context
• Model a linear relationship between variables and interpret computer output to assess model adequacy.

Assessment

Unseen written exam (Two-hour 15 minutes).