You may be studying this unit because you â€“ or a member of your family or a friend â€“ have been personally affected by cardiovascular diseases in some way. You may be professionally involved in looking after people with one of these diseases. Perhaps you are interested in health issues in general. Whatever your motivation or underlying reasons for studying this unit, you will gain valuable insights into the extent of cardiovascular diseases and their treatment in the early twenty-first cen
Author(s): The Open University

In everyday terms, everybody is familiar with the word â€˜averageâ€™, but in science and statistics there are actually several different kinds of average used for different purposes. In the kind of situation exemplified by Table 2, the sort to use is the mean (or more strictly the â€˜arithmetic meanâ€™) For a set of measurements, this is de
Author(s): The Open University

You may have met complex numbers before, but not had experience in manipulating them. This course gives an accessible introduction to complex numbers, which are very important in science and technology, as well as mathematics. The course includes definitions, concepts and techniques which will be very helpful and interesting to a wide variety of people with a reasonable background in algebra and trigonometry.

This OpenLearn course provides a sample of Level 3 study in Author(s): The Open University

Numbers
This unit will help you understand more about real numbers and their properties. It will explain the relationship between real numbers and recurring decimals, explain irrational numbers and discuss inequalities. The unit will help you to use the Triangle Inequality, the Binomial Theorem and the Least Upper Bound Property. First published on Wed, 2
Author(s): Creator not set

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

This course looks at Babylonian mathematics. You will learn how a series of discoveries have enabled historians to decipher stone tablets and study the various techniques the Babylonians used for problem-solving and teaching. The Babylonian problem-solving skills have been described as remarkable and scribes of the time received a training far in advance of anything available in medieval Christian Europe 3000 years later.

This OpenLearn course provides a sample of Level 2 study in
Author(s): The Open University

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

All materials included in this unit are derived from content originated at the Open University.

Author(s): The Open University

After studying this unit you should be able to:

• create simple models, given a clear statement of the problem;

• write down the simplifying assumptions that underpin a model;

• identify the key variables and the parameters of a model;

• apply the inputâ€“output principle to obtain a mathematical model, where appropiate;

• obtain mathematical relationships between variables, based on or linking back to the simplifying assumptions
Author(s): The Open University

Having discussed nth roots, we are now in a position to define the expression ax, where a is positive and x is a rational power (or exponent).

## Definition

If aÂ >Â 0, m Author(s): The Open University

Just as we usually take for granted the basic arithmetical operations with real numbers, so we usually assume that, given any positive real number a, there is a unique positive real number bÂ =Â  such that b2Â =Â a. We now discuss the justification
Author(s): The Open University

This unit is devoted to the real numbers and their properties. In particular, we discuss inequalities, which play a crucial role in analysis.

Author(s): The Open University

Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

Grateful acknowledgement is made to the following sources for permission to reproduce material in this unit:

The content ackno
Author(s): The Open University

The calculator does not make mistakes in the way that human brains tend to. Human fingers do, however, make mistakes sometimes; and the calculator may not be doing what you think you have told it to do. So correcting errors and estimating the approximate size of answers are important skills in double-checking your calculator calculations. (Just as they are for checking calculations done in your head or on paper!)

Author(s): The Open University

Very small and very large numbers can be difficult to comprehend. Nothing in our everyday experience helps us to get a good feel for them. For example numbers such as 1099 are so big that if Figure 1 was drawn to scale, you would be dealing with enormous distances. How big is big?

First express 1â€‰000â€‰000â€‰000 in scientific notation as 109. Next, to find out how many times bigger 1099 is, use your calculator to divide 1099 by 109
Author(s): The Open University

While reading a newspaper article, I noticed some examples of how prices changed in the 10 years from 1984 to 1994. The table below shows the typical prices that you would have expected to pay in 1984 and in 1994 for a pint of milk and a Ford Fiesta motor car.

Price in 1984 Price in 1994
Pint o
Author(s): The Open University

Many people see calculators only as a way of producing answersâ€”indeed some people see them almost as a means of cheating, of short-cutting procedures that can and should be carried out in one's head or on paper. However, the calculator can also be a means of learning mathematics more effectively, something you will come to appreciate more. Many previous mathematics students have found that their graphics calculator, used with understanding and intelligence, has become a most effective aid t
Author(s): The Open University

After studying this unit 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.

Author(s): The Open University

In Section 5 we show how functions may be used to sketch curves in the plane, even when these curves are not necessarily the graphs of functions.

Click 'View document' below to open Section 5 (8 pages, 151KB).

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 'View document' below to open Section 4 (5 pages, 104KB).

In Section 1 we formally define real functions and describe how they may arise when we try to solve equations. We remind you of some basic real functions and their graphs, and describe how some of the properties of these functions are featured in their graphs.

Click 'View document' below to open Section 1 (12 pages, 1.8MB).