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...free course is concerned with modelling and estimation and looks in particular at the binomial distribution. Section 1 starts by defining probability, introduces relevant notation and briefly discusses basic properties of probabilities. The section concludes by considering some of the general features of and ideas about modelling discrete random variables. Section 2 looks...

...free course is an introduction to algebra which builds on the idea of using letters to represent numbers. Section 1 looks at finding, simplifying and using formulas and includes useful tips on learning algebra. Section 2 introduces some of the terminology used in algebra and techniques such as evaluating and checking equivalence of expressions, identifying terms in an...

...free course is concerned with some of the statistical methods used in epidemiology and more widely in medical statistics. Section 1 introduces cohort studies in which individuals are classified according to their exposure and followed forward in time to evaluate disease outcomes. Section 2 looks at models for cohort studies. Section 3 introduces case-control studies in...

...free course is an introduction to Number Theory. Section 1 provides a brief introduction to the kinds of problem that arise in Number Theory. Section 2 reviews and provides a more formal approach to a powerful method of proof, mathematical induction. Section 3 introduces and makes precise the key notion of divisibility. The Division Algorithm, concerning the division of...

...free course is an introduction to analysis which looks at real numbers and their properties, with a particular emphasis on inequalities. Section 1 starts by revising rational numbers and their decimal representations. Then, real numbers are introduced as infinite decimals. Section 2 looks at rules for manipulating inequalities and finding the solution set of an...

...free course is an introduction to group theory, one of the three main branches of pure mathematics. Section 1 looks at the set of symmetries of a two-dimensional figure which are then viewed as functions. Section 2 introduces an algebraic notation for recording symmetries and calculating composites and inverses of symmetries. Section 3 introduces definitions and looks at...

...free course consolidates and builds on group theory studied at OU level 2 or equivalent. Section 1 describes how to construct a group called the direct product of two given groups, and then describes certain conditions under which a group can be regarded as the direct product of its subgroups. Section 2 describes the key properties of the structure of cyclic groups....

...free course concerns the calculus of variations. Section 1 introduces some key ingredients by solving a seemingly simple problem – finding the shortest distance between two points in a plane. The section also introduces the notions of a functional and of a stationary path. Section 2 describes basic problems that can be formulated in terms of functionals. Section 3 looks...