You can see the calculations that you have entered as well as the answers. This means you can easily check whether you have made any mistakes.

Author(s): The Open University

Having set out on her mathematical journey, Dawn suddenly remembered that she had forgotten to pack any sandwiches

There are many re
Author(s): The Open University

In Section 2 we develop an algebraic notation for recording symmetries, and demonstrate how to use the notation to calculate composites of symmetries and the inverse of a symmetry.

Click 'View document' below to open Section 2 (9 pages, 504KB).

## Unit image

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All other material contained within this unit originated at the Open University.

Author(s): The Open University

In Section 2 we give the general definition of a function, and illustrate how functions can be used to describe a variety of mathematical concepts, such as transformations of the plane. We discuss the idea of composing two functions, and the idea of forming the inverse of a function.

Click 'View document' below to open Section 2 (16 pages, 366KB).

All written material contained within this unit originated at the Open University

1. Join the 200,000 students currently studying withThe Open University.

Author(s): The Open University

1 What are the following?

• (a) 10

• (b) 01

• (c) 20

• (d) 02

Author(s): The Open University

Assuming that both the content of mathematics and the processes need to be included in programmes and curricula, the problem becomes one of how a suitable curriculum can be structured. One possibility is to construct a very specific curriculum with clearly defined objectives for both content and processes separately, and possibly with suggested learning activities. However, content and process are two complementary ways of viewing the subject.

An alternative is to see the curriculum in
Author(s): The Open University

The idea underlying complementary currencies â€“ that there is a great well of social capital waiting to be drawn upon to make society more sustainable â€“ is an idea that is becoming quietly influential. â€˜Social capitalâ€™ is a term frequently used by those mainstream politicians and civil servants tasked with addressing the widening gap between rich and poor people within societies throughout the world. Indeed, investing in and enhancing social capital is now the starting point in
Author(s): The Open University

Of course, the picture changes when you consider total CO2 emissions for different countries rather than emissions per person. Figure 8(b) is another chart that shows that America was by far the greatest total emitter of CO2 in 2002, but, owing to their huge population
Author(s): The Open University

I've focused on two studies of the carbon footprint of UK individuals and households, but there are many others (e.g. WWF, 2006; Goodall, 2007 and Marshall, 2007a).

Author(s): The Open University

The instrumental record referred to above is based on direct temperature measurements (using thermometers), and extends back only 150 years or so. Temperatures further back in time are reconstructed from a variety of proxy data. These include historical documents, together with natural archives of climate-sensitive phenomena, such as the growth or retreat of glaciers, tree rings, corals, sediments and ice cores (see Author(s): The Open University

One issue that might be added by a workers' organisation or trade union, for instance, might be that of freedom of association and the right of workers to organise. Another might be the right to collective bargaining. In fact, the coverage of the codes of conduct vary considerably depending on who instigated the code and the parties involved (Pearson and Seyfang, 2001). Most codes of conduct, it seems, are top-down affairs, drawn up by the companies involved or by trade associations. Some hav
Author(s): The Open University

You have already glanced at Figure 1 and some of the worki
Author(s): The Open University

The content acknowledged below is Proprietary (see terms and conditions) and is used under licence.

Grateful acknowledgement is made to the following sources for permission to reproduce material within this unit.

## Table

Box 4: Four Scenarios for 2050, Royal Commission on Environmental Pollution, 22nd Report, Energyâ€“ The Changing Climate, June 2000. Crown copyright material is reproduced under class licence number C01W0000065 with the p
Author(s): The Open University

Renewable energy sources are generally sustainable in the sense that they cannot â€˜run outâ€™ â€“ although, as noted above, both biomass and geothermal energy need wise management if they are to be used sustainably. For all of the other renewables, almost any realistic rate of exploitation by humans would be unlikely to approach their rate of replenishment by nature, though of course the use of all renewables is subject to various practical constraints.

Renewable energies are also rela
Author(s): The Open University

Ecological economics, which formally came to prominence in the mid-1980s, represents a departure from reliance on the use of mainstream economic modelling. Instead, it branches out to actively engage with and incorporate the ethical, social and behavioural dimensions of environmental issues. In short, ecological economics attempts to provide an interdisciplinary approach to environmental issues, whereas environmental economics maintains the primacy of economic modelling.

Mark Sag
Author(s): The Open University

In economic terms, green consumerism is typically expressed using measures based on the willingness to pay (WTP) principle. As mentioned above, this takes two main forms: eco-taxation, in which environmental costs are estimated and added to the price of commodities (e.g. vehicles with high carbon emissions); and eco-labelling, in which products are labelled with relevant environmental information, such as is now required by the food industry and governments in many industrialised count
Author(s): The Open University

Environmental economics emerged as a sub-discipline in the 1960s, following a tradition that began in the early twentieth century with â€˜agriculturalâ€™ economics and continued in the 1950s with â€˜resourceâ€™ economics. In each case, natural resources are treated as environmental assets in the same way as other resource inputs, using the classical mainstream supply and demand economic models. David Pearce, who at one stage was at the forefront of environmental economics and was an ac
Author(s): The Open University

The blue whale could have supplied indefinitely a sustainable yield of 6000 individuals a year.

This is one of the earliest references to sustainability in the literature, taken from the 1971 edition of the science journal Nature (cited in Senge et al., 2006, p. 45). Here, the blue whale is given instrumental value â€“ a means of measuring not the survival of the blue whale for its intrinsic v
Author(s): The Open University