2.8 Descriptive statistics Scientists collect many different types of information, but sets of data may be very loosely classified into two different types. In the first type, so-called ‘repeated measurement’, an individual quantity is measured a number of times. An astronomer wanting to determine the light output of a star would take many measurements on a number of different nights to even out the effects of the various possible fluctuations in the atmosphere that are a cause of stars ‘twinkling’. In the seco
2.6 Combining probabilities The probabilities described in Section 2.3 and Section 2.4 related to the outcomes of a single process, such as repeatedly tossing one coin. Now suppose you were to toss three separate coins simultaneously. What is the prob
1.4 How precise are the measurements? Scientists are always trying to get better and more reliable data. One way of getting a more precise measurement might be to switch to an instrument with a more finely divided scale. Figure 4 shows parts of two thermometers placed side by side to record the air temperature in a room. 2.1 The four rules of arithmetic You are now going to use the four operation keys (on the bottom right-hand side of the TI-84 keyboard): Does it make sense? 1.1 Mathematics and you Many people's ideas about what mathematics actually is are based upon their early experiences at school. The first two activities aim to help you recall formative experiences from childhood. Read 2.3 Section summary In this section we have seen that the complex number system is the set R × R together with the operations + and × defined by From this, one can justify the performance of ordinary algebraic operations on expressions of the form a + ib 3.2 Using scientific notation Scientific notation can be very useful when estimating the answers to calculations involving very large and/or small decimal numbers. A lottery winner won £7851 000. He put the money straight into a deposit account which earns 7.5% interest per annum (i.e. each year). If he wanted to 1.3.1 Try some yourself 1 The new home owners from Example 4 above want to price grass seed, as well as the turf (transport only). The best buy seems to be loose seed, which says ‘1 kilo covers 80 m2’. They wonder what length the side of an 80 m2 1.1.1 Try some yourself 1 Evaluate the following: (a) 62 (b) 0.52 (c) 1.52 3.2 Negative coordinates Up to now only those points with positive or zero coordinates have been considered. But the system can be made to cope with points involving negative coordinates, such as (−2, 3) or (−2, −3). Just as a number line can be extended to deal with negative numbers, the x-axis and y-axis can be extended to deal with negative coordinates. 2.4.1 Try some yourself 1 The frequency diagram below shows the numbers of people in different age groups in a sample of the UK population. (a) What is the width of each age group? (b) Which age group conta Introduction This unit shows how partial differential equations can be used to model phenomena such as waves and heat transfer. The prerequisite requirements to gain full advantage from this unit are an understanding of ordinary differential equations and basic familiarity with partial differential equations. This unit is an adapted extract from the course Mathematical methods and models (MST209 1.2.2 Choosing keywords Keywords are significant words which define the subject you are looking for. The importance of keywords is illustrated by the fact that there is a whole industry around providing advice to companies on how to select keywords for their websites that are likely to make it to the top of results lists generated by search engines. We often choose keywords as part of an iterative process; usually if we don't hit on the right search terms straight off, most of us tweak them as we go along based on t 5 Conclusion – new ways of looking at the world There is a variety of new approaches or terms that are interlinked, and have been prominent throughout this book. All of them have played a part in this book's journey through the scientific, political, philosophical and social implications of climate change. Governance of climate change is about: decision making under uncertainty; understanding and representing vulnerability even when vulnerabilities are difficult to assess or unknowable; and making every aspect of human 1.2 What determines the Earth's GMST? The Sun is the ultimate source of energy for the Earth's climate. A planet such as the Earth will have a stable temperature as long as there is a balance between the rate at which energy comes in from the Sun and the rate at which it is returned to space by the planet. If the two rates fail to match, the planet will either warm up or cool down until a balance is restored. Thus, it is appropriate to begin with a review of this global balancing act. The heart of the matter is that the energy fl Learning outcomes By the end of this unit you should be able to: understand why systems thinking might be useful and know something about how it can be applied in the context of environmental responsibility; describe the significance of environmental pragmatism and cognitive justice as tools for supporting environmental policy and action. 1.2.7 In praise of cheap offshore labour? Claims over the benefits of globalisation and the exploitation of cheap offshore labour generate strong feelings and, not surprisingly, divide opinion between those who favour the global marketplace and its detractors. The issue turns on whether the constant search for ever-cheaper manufacturing and service locations is seen as a good or a bad thing. It may appear odd, at first, to suggest that exploiting the poor of another country can, on any measure, be regarded as a good thing, but 1.1.2 Activity 1 You have already glanced at Figure 1 and some of the worki 4.3 Indirect use of solar energy The above examples illustrate the direct harnessing of the sun's radiant energy to produce heat and electricity. But the sun's energy can also be harnessed via other forms of energy that are indirect manifestations of its power. Principally, these are bioenergy and hydropower, already discussed in Section 3 above, together with wind energy and wave power.
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