We next establish some general results about Euler characteristics. We start with a theorem that tells us what happens to the Euler characteristic of a surface when we remove an open disc.

## Theorem 10: Disc Removal Theorem

The Euler characteristic of a surface with an open disc removed is one le
Author(s): The Open University

Now that we have studied a variety of sources of evidence from Africa, it is possible to reconsider how well our four models of cultural interaction fit the evidence.

Author(s): The Open University

1. The term â€˜addictionâ€™ carries a number of different meanings. The word is generally used with reference to drugs (e.g. heroin, nicotine, alcohol), where a person is described as being â€˜dependent onâ€™ or â€˜addicted toâ€™ a substance. Also, substances are described as â€˜addictiveâ€™ or â€˜non-addictiveâ€™, implying that addiction is an intrinsic property of the substance. Some people are addicted to food. Given that food is necessary, in what sense is
Author(s): The Open University

Carlisle Scholars, Army Strategy Conference 2015
Description not set
Author(s): No creator set

After completing this unit you may wish to study another OpenLearn Study Unit or find out more about this topic. Here are some suggestions:

## course Question A

Foxes eat rabbits and rabbits eat dandelions. Predict what will happen if rabbit numbers are severely reduced (e.g. by disease). How confident are you about your predictions?

Author(s): The Open University

Virtual Maths - Numbers, Geometry 3D shapes
Diagrams and forumulas for calculating area and volume of 3D shapes cube, cuboid, cylinder, sphere, hemisphere, triangular prism, frustrum, cone, pyramid
Author(s): Leeds Metropolitan University

Up to now I have focused on the claims of the antisweatshop movement and the counter-claims of those who contest the purely negative conclusions drawn about the exploitation of another country's poor. To that end, I have, at various moments, touched on issues of demands to take responsibility: whether, for instance, responsibility for sweatshops should be divided up in some way between all those connected to the market system which gives rise to them, or placed firmly at the door of the big r
Author(s): The Open University

By the end of this guide you should be able to:

• conduct your own searches efficiently and effectively;

• find references to material in bibliographic databases;

• make efficient use of full text electronic journals services;

• critically evaluate information from a variety of sources;

• understand the importance of organising your own information;

• identify some of the systems available;

• describe ho
Author(s): The Open University

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

Course image: INTVGene in Flickr made available under Creative Commons Attribution-ShareAlike 2.0 Licence.

All other materials included in this course ar
Author(s): The Open University

Towering ambition: William Beckford and his buildings in Wiltshire and Bath
Dr Amy Frost investigates all of the architectural wonders that William Beckford spent his life constructing in this detailed biography.
Author(s): No creator set

One Dutch family was found to have a history of antisocial (aggressive) behaviour. Genetic studies were conducted and a potential culprit gene MAOA, monoamine oxidase A, identified. The aggressive individuals in the family appeared to have a mutant gene which produced no MAOAP, an enzyme involved in the breakdown of certain neurotransmitters, including serotonin. A knockout mouse model, in which the MAOA gene was inactive, was also found to be aggressive, apparently confirming the role of MAO
Author(s): The Open University

Now try to answer the following questions, to remind you of some of the things you have learned and test your understanding of them.

## Question 9

To the nearest order of magnitude, how much greater is the estimated
Author(s): The Open University

This subsection looks at two ways of finding an â€˜averageâ€™. The first produces the mean, which is what was originally meant by â€˜averageâ€™, and what most people think of when they talk about an average. The second gives the median, which might more accurately be described as a â€˜typicalâ€™ or middle value. They will be illustrated using the following batch of heights.

The heights in metres (measured to the nearest centimetre) of a group of seven people are as follows
Author(s): The Open University

For information on changes to flora, click on Science magazine.

For changes to fauna, and economic effects, go to Information Sheet 4, or for the paper quoted at the top of the screen, Information Sheet 1, both at Climatic Research Unit.

Click on the link below to open the data-smoothing information

Data-smoothing