2.5 Position vectors
Attempts to answer problems in areas as diverse as science, technology and economics involve solving simultaneous linear equations. In this unit we look at some of the equations that represent points, lines and planes in mathematics. We explore concepts such as Euclidean space, vectors, dot products and conics.
Author(s): The Open University

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Learning outcomes
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.
Author(s): The Open University

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2.5 Symmetry
Geometry is concerned with the various aspects of size, shape and space. In this unit, you will explore the concepts of angles, shapes, symmetry, area and volume through interactive activities.
Author(s): The Open University

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Acknowledgements
You may have met complex numbers before, but not had experience in manipulating them. This unit gives an accessible introduction to complex numbers, which are very important in science and technology, as well as mathematics. The unit includes definitions, concepts and techniques which will be very helpful and interesting to a wide variety of people with a reasonable background in algebra and trigonometry.
Author(s): The Open University

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4.2 Defining useful subsets of the complex number system, and proving the Nested Rectangles Theorem
You may have met complex numbers before, but not had experience in manipulating them. This unit gives an accessible introduction to complex numbers, which are very important in science and technology, as well as mathematics. The unit includes definitions, concepts and techniques which will be very helpful and interesting to a wide variety of people with a reasonable background in algebra and trigonometry.
Author(s): The Open University

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3. The challenge of change
In this unit, aimed at teachers of Physical Education, we begin by looking at some of the common misconceptions relating to fitness and activity levels together with accepted definitions of these concepts. We consider how active young people should actually be, and discuss how PE teachers can ensure they are making an effective contribution to this area of public health.
Author(s): The Open University

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2.3 Acquiring territory
This unit will define basic concepts and terms that are essential for an understanding of the culture and identity of the Roman empire. Terms such as ‘Roman empire’ and ‘imperium’ will be introduced in the context of the formation and expansion of the empire, and the unit will provide you with the background for further study of the Roman empire.
Author(s): The Open University

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2.2 Imperium as power: Augustus and the beginning of the empire
This unit will define basic concepts and terms that are essential for an understanding of the culture and identity of the Roman empire. Terms such as ‘Roman empire’ and ‘imperium’ will be introduced in the context of the formation and expansion of the empire, and the unit will provide you with the background for further study of the Roman empire.
Author(s): The Open University

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8 Reviewing and reflecting
From diamonds to dynamite everything involves a chemical reaction. This unit introduces you to the concepts and principles that underpin chemistry at the molecular level. Everyday experiences are used to help you to understand the more complex issues.
Author(s): The Open University

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6.3 Valence-shell electron-pair repulsion theory
From diamonds to dynamite everything involves a chemical reaction. This unit introduces you to the concepts and principles that underpin chemistry at the molecular level. Everyday experiences are used to help you to understand the more complex issues.
Author(s): The Open University

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4.5.2 Noble gas configurations under stress
From diamonds to dynamite everything involves a chemical reaction. This unit introduces you to the concepts and principles that underpin chemistry at the molecular level. Everyday experiences are used to help you to understand the more complex issues.
Author(s): The Open University

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3.5 Scattering from finite square wells and barriers
Scattering is fundamental to almost everything we know about the world, such as why the sky is blue. Tunnelling is entirely quantum-mechanical and gives rise to such phenomena as nuclear fusion in stars. Examples and applications of both these fascinating concepts are investigated in this unit.
Author(s): The Open University

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3.3 Scattering from a finite square step
Scattering is fundamental to almost everything we know about the world, such as why the sky is blue. Tunnelling is entirely quantum-mechanical and gives rise to such phenomena as nuclear fusion in stars. Examples and applications of both these fascinating concepts are investigated in this unit.
Author(s): The Open University

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3.1 Overview
Scattering is fundamental to almost everything we know about the world, such as why the sky is blue. Tunnelling is entirely quantum-mechanical and gives rise to such phenomena as nuclear fusion in stars. Examples and applications of both these fascinating concepts are investigated in this unit.
Author(s): The Open University

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2.2 Wave packets and scattering in one dimension
Scattering is fundamental to almost everything we know about the world, such as why the sky is blue. Tunnelling is entirely quantum-mechanical and gives rise to such phenomena as nuclear fusion in stars. Examples and applications of both these fascinating concepts are investigated in this unit.
Author(s): The Open University

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Acknowledgements

Grateful acknowledgement is made to the following sources for permission to reproduce material in this unit:

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Figures

Figure 2 Co
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References

Bernardes, J. (1987) ‘“Doing things with words”: Sociology and “Family Policy” debates’, Sociological Review, vol. 35, no. 4, pp. 679–702.
Bernardes, J. (1993) ‘Responsibilities in studying postmodern families’, Journal of Family Therapy, vol. 14, no. 1, pp. 35–49.
Bernardes, J. (2003[1985]) ‘Do we really
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Learning outcomes
This unit explores how information contained in DNA is used, explaining the flow of information from DNA to RNA to protein. Also introduced are the concepts of transcription (as occurs between DNA and RNA) and translation.
Author(s): The Open University

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Introduction
This unit explores how information contained in DNA is used, explaining the flow of information from DNA to RNA to protein. Also introduced are the concepts of transcription (as occurs between DNA and RNA) and translation.
Author(s): The Open University

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Vectors and conics
Attempts to answer problems in areas as diverse as science, technology and economics involve solving simultaneous linear equations. In this unit we look at some of the equations that represent points, lines and planes in mathematics. We explore concepts such as Euclidean space, vectors, dot products and conics.
Author(s): The Open University

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