Geometry
Overview Geometry is concerned with the various aspects of size, shape and space. In this free course you will explore the concepts of angles, shapes, symmetry, area and volume through interactive activities. Syllabus
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Number theory
Overview This 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 …
Mathematics for science and technology
Overview Maths is intimately entwined with science and technology, whether it is used to analyse data collected on plants in the Amazon rainforest, to calculate the trajectory of a comet or design a bridge to connect two countries. This means that science and technology go hand-in-hand with maths, and that a firm grasp of maths …
Introduction to differential equations
Overview Differential equations are any equations that include derivatives and arise in many situations. This free course, Introduction to differential equations, considers three types of first-order differential equations. Section 1 introduces equations that can be solved by direct integration and section 2 the method of separation of variables. Section 3 looks at applications of differential …
Introduction to number theory
Overview This free course, Introduction to number theory, is a branch of mathematics concerned with the properties of integers. Section 1 introduces Euclid’s algorithm, which is used to find the HCF of two integers, and the idea of congruences, mathematical statements used to compare remainders when two integers are each divided by another integer. Section …
Introduction to linear equations and matrices
Overview In this free course, matrices are used as a concise way of representing systems of linear equations which occur frequently in mathematics. Section 1 looks at simultaneous linear equations in two and three unknowns and then generalises the ideas to systems of linear equations. Section 2 develops a strategy for solving systems of linear …
Bayesian statistics
Overview This free course is an introduction to Bayesian statistics. Section 1 discusses several ways of estimating probabilities. Section 2 reviews ideas of conditional probabilities and introduces Bayes’ theorem and its use in updating beliefs about a proposition, when data are observed, or information becomes available. Section 3 introduces the main ideas of the Bayesian …
Rings and polynomials
Overview This free course contains an introduction to rings and polynomials. We see that polynomial rings have many properties in common with the integers; for example, we can define a division algorithm, and this enables us to develop the analogue of the highest common factor for two polynomials. Section 1 explores the abstract definitions of …
Everyday maths 1
Overview Have you ever noticed how often you need maths skills in everyday life? This free course serves as good preparation for Level 1 Functional Skills in maths, and whilst it doesnot cover all aspects of the current curriculum, it is designed to inspire you to improve your current maths skills and help you to remember any …
Medical statistics
Overview This 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 …