## Free courses

Produced by The Open University, a world leader in open and distance learning, all OpenLearn courses are free to study. We offer nearly 1000 free courses across 9 different subject areas. Our courses are available to start right away.

- All topics

Science, Maths & Technology

### Metric spaces and continuity

This free course contains an introduction to metric spaces and continuity. The key idea is to use three particular properties of the Euclidean distance as the basis for defining what is meant by a general distance function, a metric. Section 1 introduces the idea of a metric space and shows how this concept allows us to generalise the notion of ...

Science, Maths & Technology

### Rings and polynomials

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 a ring ...

Science, Maths & Technology

### Introduction to the calculus of variations

This 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 ...

Science, Maths & Technology

### An introduction to web applications architecture

This free course, An introduction to web applications architecture, provides an overview of the design and implementation of computer software that runs on web servers, instead of those running solely on desktop computers, laptops or mobile devices.

Science, Maths & Technology

### Surfaces

Surfaces are a special class of topological spaces that crop up in many places in the world of mathematics. In this free course, you will learn to classify surfaces and will be introduced to such concepts as homeomorphism, orientability, the Euler characteristic and the classification theorem of compact surfaces.

Science, Maths & Technology

### IT: Information

BBC News 24, Sky News, CNN. We live in an era where news has become almost instantaneous. This free course, IT: Information, will look at how news is gathered and the technology that's used for its dissemination. You will also be encouraged to examine how information might be manipulated by questioning its reliability.

Science, Maths & Technology

### IT in everyday life

We now live in a global village where distance is no longer a barrier to commercial or social contact. This free course, IT in everyday life, will enable you to gain an understanding of the information and communication technologies that drive our networked world and how they now permeate our everyday lives.

Science, Maths & Technology

### IT: device to device communication

Are you a technophobe? Bluetooth, Ethernet, WiFi; are they terms that mean nothing to you? IT: device to device communication, is a free course that will gently guide you to an understanding of how devices 'talk' to each other and what technologies and processes are involved. You will also look at wired and wireless communication technologies, ...

Science, Maths & Technology

### Modelling and estimation

This 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 ...

Science, Maths & Technology

### Introduction to algebra

This 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 ...

Science, Maths & Technology

### Introduction to linear equations and matrices

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 equations....

Science, Maths & Technology

### Introduction to group theory

This 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 ...