 The institutions of the EU work towards objectives related to the three pillars and the creation of a body of Community law that applies

• uniformly

• in all member states.

The institutions having legal rule-making powers include the European Council, the Council of the European Union, the European Parliament and the European Commission. Finally, there is the European Court of Justice (ECJ), which has the power to settle lega
Author(s): The Open University

The EU operates through institutions created in the treaties. These institutions can have decision-making powers, law-making powers or may act as part of a checking and consultation procedure.

The institutions include:

1. The European Parliament (represents the people of the EU).

2. The Council of the European Union (represents the member states of the EU).

3. The European Commission (represents the interests of the EU).

<
Author(s): The Open University

This course provides an overview of John Napier and his work on logarithms. It discusses his approach to this lasting invention and looks at the key players who worked with him, including Briggs, Wright and Kepler.

This OpenLearn course provides a sample of Level 2 study in Mathematics

Author(s): The Open University

Vectors and conics
Attempts to answer problems in areas as diverse as science, technology and economics involve solving simultaneous linear equations. In this free course, Vectors and conics, 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. First
Author(s): Creator not set

For many calculations you use a calculator. The main aim of this course is to help you to do this in a sensible and fruitful way. Using a calculation to solve a problem involves four main stages:

• Stage 1: working out what calculation you want to do;

• Stage 2: working out roughly what size of answer to expect from your calculation;

• Stage 3: carrying out the calculation;

• Stage 4: interpreting the answer – D
Author(s): The Open University

After studying this course, you should be able to:

• divide one number by another

• divide using decimals

• practise division skills learnt.

Author(s): The Open University

Introduction to differential equations
Differential equations are any equations that include derivatives and arise in many situations. This free course, Introduction to differential equations, considers three types of first-order differential equations. Section 1 introduces equations that can be solved by direct integration and section 2 the method of separation of variables. Section 3 looks at applications of differential equations for solving real world problems. Section 4 introduces the integrating factor method for solving linear
Author(s): Creator not set

Modelling and estimation
This free course is concerned with modelling and estimation and looks in particular at the binomial distribution. Section 1 starts by defining probability, introduces relevant notation and briefly discusses basic properties of probabilities. The section concludes by considering some of the general features of and ideas about modelling discrete random variables. Section 2 looks at one particular probability model for discrete data, the binomial distribution. Section 3 investigates how data can be
Author(s): Creator not set

Modelling events in time
This free course develops ideas about probability and random processes. Sections 1 and 2 introduce the fundamental ideas of random processes through a series of examples. Section 3 describes a model that is appropriate for events occurring ‘at random’ in such a way that their rate of occurrence remains constant. Section 4 derives the main results from Section 3. Section 5 introduces the multivariate Poisson process in which each event may be just one of several different types of event. Sect
Author(s): Creator not set

Except for third party materials and otherwise stated in the acknowledgements section, this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence.

Course image: russellstreet in Flickr made available under
Author(s): The Open University ## Study another free course

There are more than 800 courses on OpenLearn for you t
Author(s): The Open University

The rules for multiplying positive and negative numbers can be illustrated by the table below.

Multiplying a positive number by a positive number gives a positive answer.

Multiplying a negative number by a positive number gives a negative answer.

Multi
Author(s): The Open University

Next consider subtraction of a negative number. In terms of Thomas’s piggy bank, subtracting a negative number is the same as taking away one of his IOUs. If his mother says ‘you have been a good boy today so I’ll take away that IOU for £3’ this is equivalent to him being given £3.

So, − (3) = 3. Does this correspond with the number line interpretation of subtracting a negative number?

Consider the evaluation of 8 − 3. Continue to think o
Author(s): The Open University

## Activity 56

Evaluate each of the following and give an example from everyday life to illustrate the sum (e.g. Thomas's piggy bank).

• (a) 4 − 6

• (b
Author(s): The Open University

In order to understand arithmetic with negative numbers, it is helpful to see how arithmetic can be represented on the number line. The strategy is to start with simple examples of whole positive numbers and then generalise to negative numbers. The same principles must apply!

Author(s): The Open University

How about other fractions? What is 6 ÷ ? This means how many [Image_Link]https://www.open.edu/openlearn/ocw/pluginfile.php/117429/mod_ou
Author(s):
The Open University

## Activity 46

Evaluate each of the following.

• [Image_Link]https://www.open.edu/openlearn/ocw/pluginfile.php/11742
Author(s):
The Open University

The same rules about the order of calculations apply to decimals as apply to whole numbers.

## Calculations are performed in the following order:

Brackets;

Powers (e.g. squaring or cubing a number);

Division and Multiplication (performed in the order written, left to
Author(s): The Open University

## Activity 31

Insert brackets in the following calculations to emphasise the order in which a scientific calculator would perform them, then do the calculations by hand and on your calculator, with and without the bracke
Author(s): The Open University

You may have noticed that sometimes the order in which calculations are carried out seems to matter and sometimes it does not. When using a calculator, it is very important to know the order in which it will do calculations. It is not always the order in which you enter them.

Although written English is read from left to right, this is not the case for all written languages (Chinese is read top to bottom, right to left). With mathematics, the order of the written operations does not alw
Author(s): The Open University