The module covers major topics of probability theory and statistics. We will introduce theoretical concepts through simple experiments and games, before moving on to some important probability distributions: what kind of distribution shall we use for the lifetime of light bulbs, or for the number of mistyping errors on the pages of a newspaper, etc; how can we describe a probability distribution: a density function versus characteristic function; the law of large numbers in a mathematical formulation; the central limit theorem 7; or why the Gaussian (Normal) distribution is special. These concepts are used in financial mathematics, and they form the basis of statistics, thus providing tools for appraising the world around us, in the form of estimates, hypothesis testing, correlations, and regressions. These techniques are used in the social sciences as well.
We are going to use calculus on a basic level only, but mathematical thinking is important. The course will show the theoretical background as well as the practice of statistics. It is an introductory course to a branch of applied mathematics. (In Cambridge, it is called “applicable maths”, and it falls under the group of pure maths subjects.)