4.3 The Euler characteristic
Surfaces are a special class of topological spaces that crop up in many places in the world of mathematics. In this unit, you will learn to classify surfaces and will be introduced to such concepts as homeomorphism, orientability, the Euler characteristic and the Classification Theorum.
4.2 Subdivisions
Surfaces are a special class of topological spaces that crop up in many places in the world of mathematics. In this unit, you will learn to classify surfaces and will be introduced to such concepts as homeomorphism, orientability, the Euler characteristic and the Classification Theorum.
4.1 Nets on surfaces
Surfaces are a special class of topological spaces that crop up in many places in the world of mathematics. In this unit, you will learn to classify surfaces and will be introduced to such concepts as homeomorphism, orientability, the Euler characteristic and the Classification Theorum.
3.3 The projective plane
Surfaces are a special class of topological spaces that crop up in many places in the world of mathematics. In this unit, you will learn to classify surfaces and will be introduced to such concepts as homeomorphism, orientability, the Euler characteristic and the Classification Theorum.
3.2.1 Remarks
Surfaces are a special class of topological spaces that crop up in many places in the world of mathematics. In this unit, you will learn to classify surfaces and will be introduced to such concepts as homeomorphism, orientability, the Euler characteristic and the Classification Theorum.
3.2 Orientability
Surfaces are a special class of topological spaces that crop up in many places in the world of mathematics. In this unit, you will learn to classify surfaces and will be introduced to such concepts as homeomorphism, orientability, the Euler characteristic and the Classification Theorum.
3.1.1 Inserting half-twists
Surfaces are a special class of topological spaces that crop up in many places in the world of mathematics. In this unit, you will learn to classify surfaces and will be introduced to such concepts as homeomorphism, orientability, the Euler characteristic and the Classification Theorum.
3.1 Surfaces with twists
Surfaces are a special class of topological spaces that crop up in many places in the world of mathematics. In this unit, you will learn to classify surfaces and will be introduced to such concepts as homeomorphism, orientability, the Euler characteristic and the Classification Theorum.
4.2.1 Eco-efficiency = money in the bank
Human societies have to take urgent action to end their dependences on fossil fuels. We have to alter the whole path of our development and decision making in order to make our societies both environmentally adaptable and sustainable. This unit takes on the task of trying to chart some of the ways in which it might be possible.
3.3.1 Too late for the nation state?
Human societies have to take urgent action to end their dependences on fossil fuels. We have to alter the whole path of our development and decision making in order to make our societies both environmentally adaptable and sustainable. This unit takes on the task of trying to chart some of the ways in which it might be possible.
3.3 Green governance needs citizens
Human societies have to take urgent action to end their dependences on fossil fuels. We have to alter the whole path of our development and decision making in order to make our societies both environmentally adaptable and sustainable. This unit takes on the task of trying to chart some of the ways in which it might be possible.
Next steps After completing this unit you may wish to study another OpenLearn Study Unit or find out more about this topic. Here are some suggestions:
5 Rhyme If a poem rhymes, then considering how the rhyme works is always important. Rhyme schemes can be simple or highly intricate and complex; it will always be worth considering why a particular rhyme pattern was chosen and trying to assess its effects. 1 Overview 2.1 Culture as socialisation The cultural perspective has become popular in business studies because it offers a way of explaining performance and understanding difference. It is only one way of analysing business, but it is an interesting one as it focuses particularly on the insider point of view, or on what it is ‘really’ like to work in an organisation. There have been many definitions of organisational culture. One definition that is often cited is: 1 Developing your problem solving skills This Key Skill Assessment Unit offers an opportunity for you to select and prepare work that demonstrates your key skills in the area of problem solving. This unit provides you with advice and information on how to go about presenting your key skills work as a portfolio. In presenting work that demonstrates your key skills you are taking the initiative to show that you can develop and improve a particular set of skills, and are able to use your skills more generally in your studi Summarising text 1.3.12 Summary 1 Unit overview IDS Big Question: Stephen Devereux (IDS) & Thandika Mkandawire (LSE) speak about Social Protecti
Activity 4
Does the recruitment and selection process fill you with dread? Discrimination and equal opportunities legislation can make this area feel like a minefield. If you are faced with appointing a new employee, then this unit will provide a straight-forward guide to the process: from writing job descriptions to finally assessing who to appoint.
In this unit you will learn how to summarise. Summarising is useful both when completing assignments and while studying.
This unit will help you to identify and use information in health and lifestyle, whether for your work, study or personal purposes. Experiment with some of the key resources in this subject area, and learn about the skills which will enable you to plan searches for information, so you can find what you are looking for more easily. Discover the meaning of information quality, and learn how to evaluate the information you come across. You will also be introduced to the many different ways of organ
What do we mean by ‘wellbeing’ for young people? How is it shaped by social differences and inequalities, and how can we improve young people's mental and physical health? This unit will examine the range of factors affecting young people’s wellbeing, such as obesity, binge drinking, depression and behavioural problems.
This month's Big Questions for Development coincides with the Social Protection Conference being held at IDS. We interviewed IDS Research Fellow, Stephen Devereux and
Thandika Mkandawire, Chair in African Development for the London School of Economics on what are the challenges in delivering social protection?
