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3.1.6 (F) Creativity

Pupils should appreciate that science is an activity that involves creativity and imagination as much as many other human activities and that some scientific ideas are enormous intellectual achievements. Scientists, as much as any other profession, are passionate and they (and their work) rely on inspiration and imagination.

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3.1.5 (E) Historical development of scientific knowledge

Pupils should be taught some of the historical background to the development of scientific knowledge.


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2.4What is ‘capital’?

Before we move on to look at the different types of business organisation, we will introduce one more concept. It is the concept of capital. It has, historically, been a very important concept in company law. But it is a concept not limited to company law. The next activity will allow you to reflect on your own ideas of what ‘capital’ means, without you needing to have any prior legal knowledge, or, for that matter, knowledge of any other discipline.

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1.1 ‘Company law’

Before embarking on this course, it is important to take some time to think about the implications of its title: Company law in context. In particular, what constitutes ‘company law’, and what is the context in which we are thinking about it?

At this point, you might like to pause for a moment and contemplate what this phrase means to you. In particular, what do you understand by the concept of a ‘company’?

At first, this may seem like a ludicrously straightforward questio
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Learning outcomes

After studying this course, you should be able to:

  • understand the historical growth of the idea of human rights

  • demonstrate an awareness of the international context of human rights

  • demonstrate an awareness of the position of human rights in the UK prior to 1998

  • understand the importance of the Human Rights Act 1998

  • analyse and evaluate concepts and ideas.


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2.3 What is a ‘business’?

The vast majority of companies are, indeed, set up and run with ‘commercial objects’ – in other words, they are business enterprises, or ‘undertakings’, set up to trade and make a profit. It is principally in the context of the company as a form of business organisation (or ‘business medium’) that we will be studying it. So, before we start to look in detail at what companies are, it is a good idea to have a grasp of what companies do, which will lead us on to consider why they
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Working mathematically
This free course, Working mathematically, is aimed at teachers who wish to review how they go about the practice of teaching mathematics, those who are considering becoming mathematics teachers, or those who are studying mathematics courses and would like to understand more about the teaching and learning process. First published
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Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2

2.2 Geometric shapes – quadrilaterals

A quadrilateral is a shape with four straight sides.
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4.4 Self-assessment questions and problems

SAQ 26

Find the distance between the numbers 2 − i and 1 + 3i.

Answer

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1.2 Representation and language

Consider some of the many different things we can do with language: express ourselves in metaphor, issue commands, ask questions, fill in crosswords, write shopping lists and diary entries, repeat nursery rhymes by rote, solve logical or arithmetical problems, make promises, tell stories, sign our names, etc. Impressive though it is, this variety in the uses of language is a potential distraction from our main interest, which is in the use of language to represent. It will therefore help if w
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3.2 Relationship between complex numbers and points in the plane

We have seen in Section 2.2 that the complex number system is obtained by defining arithmetic operations on the set R × R. We also know that elements of R × R can be represented as points in a plane. It seems reasonable to ask what insight can be obtained by representing complex numbers as
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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
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1 Introduction

You have almost certainly met complex numbers before, but you may well not have had much experience in manipulating them. In this course we provide you with an opportunity to gain confidence in working with complex numbers by working through a number of suitable problems.

Perhaps the most striking difference between real numbers and complex numbers is the fact that complex numbers have a two-dimensional character, arising from our definition of a complex number as an ordered pair of
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Learning outcomes

After studying this course, you should be able to:

  • perform basic algebraic manipulation with complex numbers

  • understand the geometric interpretation of complex numbers

  • know methods of finding the nth roots of complex numbers and the solutions of simple polynomial equations.


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Acknowledgements

These extracts are from M208 © 2006 The Open University.

All material contained within this course originated at The Open University.

Course image: Matt in Flickr made available under Creative Commons Attribution 2.0 Licence.

Don't miss out:

If reading
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Conclusion

This free course provided an introduction to studying Mathematics. It took you through a series of exercises designed to develop your approach to study and learning at a distance and helped to improve your confidence as an independent learner.


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5 Hyperbolic functions

In Section 4 we introduce the hyperbolic functions sinh, cosh and tanh, which are constructed from exponential functions. These hyperbolic functions share some of the properties of the trigonometric functions but, as you will see, their graphs are very different.

Click the link below to open Section 4 (5 pages, 104KB).

Section 4
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1 Overview

A fundamental concept in mathematics is that of a function.

Consider, for example, the function f defined by

This is an example of a real function, because it associates with a given real number
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Keep on learning

Study another free course

There are more than 800 courses on OpenLearn for you t
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3.2 Converting to a percentage

Fractions and decimals can also be converted to percentages, by multiplying by 100%.

So, for example, 0.17, 0.3 and can be expressed as percentages as follows:

  0.17 × 100% = 17%;

<
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