Fats, also known as lipids, are important components of living tissues, and are used by the body for making cell membranes and for storing energy. Fats come in a variety of different biochemical types, which may be obtained from the diet or can be synthesised within the body. Many cells of the body can convert certain types of fat into others, but by preference, fats will be obtained from the diet, if available. The fatty acids that cannot be synthesised by the body and therefore must
Author(s): The Open University

Table 3 shows all the values for each step in the process of calculating a standard deviation, so that you can see what the operations encapsulated by Equation 7 actually entail, but you will probably be relieved to hear that it is not usually necessary to carry out such detailed calculations. Scientific and graphics calculators (or computer sp
Author(s): The Open University

As noted in the previous section, if the same quantity is measured repeatedly, the results will generally be scattered across a range of values. This is perhaps best illustrated using a real example. Table 2 shows 10 measurements of a quantity called the ‘unit cell constant’ for an industrial catalyst used in the refining of petrol; this is an important quantity which determines how well the catalyst works, and can be measured by X-ray diffraction techniques. Notice that the cell constant
Author(s): The Open University

This course will introduce you to a number of ways of representing data graphically and of summarising data numerically. You will learn the uses for pie charts, bar charts, histograms and scatterplots. You will also be introduced to various ways of summarising data and methods for assessing location and dispersion.

This OpenLearn course is an adapted extract from the Open University course Author(s): The Open University

This course is concerned with two main topics. In Section 1, you will learn about another kind of graphical display, the boxplot. Boxplots are particularly useful for assessing quickly the location, dispersion, and symmetry or skewness of a set of data, and for making comparisons of these features in two or more data sets. The other topic, is that of dealing with data presented in tabular form. You are, no doubt, familiar with such tables: they are common in the media and in reports an
Author(s): The Open University

This unit provides an overview of the processes involved in developing models. It starts by explaining how to specify the purpose of the model and moves on to look at aspects involved in creating models, such as simplifying problems, choosing variables and parameters, formulating relationships and finding solutions. You will also look at interpreting results and evaluating models.

This unit, the third in a series of five, builds on the ideas introduced and developed in Modelling poll
Author(s): The Open University

Examples 1 and 2

## Example 1

Author(s): The Open University

3.1 Introduction

In this section we shall develop the correspondence between C and R × R by obtaining a geometric representation of elements of C and operations on C. We shall define the polar form of a complex number and the modulus and argument of a complex number. We shall see that not only does
Author(s): The Open University

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 x the real number 2x2 − 1: it maps real numbers to real n
Author(s): The Open University

Learning outcomes

After studying this unit you should be able to:

• understand how the wave and diffusion partial differential equations can be used to model certain systems;

• determine appropriate simple boundary and initial conditions for such models;

• find families of solutions for the wave equation, damped wave equation, diffusion equation and similar homogeneous linear second-order partial differential equations, subject to simple boundary conditions, using the meth
Author(s): The Open University

1.6 Do, talk and record triad

The do–talk–record triad (DTR) is a description of what is likely to take place in collaborative mathematics classrooms. It is concerned with observable events, and with the learner rather than the teacher, though many teaching insights flow from it. Although the order of the triad suggests that it should be followed in a particular sequence, this is not necessarily the case. Sometimes talking comes before doing or recording before talking. It also takes time for a learner to move
Author(s): The Open University

Introduction

This unit is an adapted extract from the Open University course Complex analysis (M337)

This unit is devoted solely to complex numbers.

In Section 1, we define complex numbers and show you how to manipulate them, stressing the similarities with the manipulation of real numbers.

Section 2 is devoted to the geometric representation of complex numbers. You will find that
Author(s): The Open University

1.3.9 Summary

There is a lot of information available on maths and statistics via the internet. Try the activities below to start exploring what is available.

## Activity

1.3.3 Books and electronic books

Books are a good source of information. The publishing process (where a book is checked by an editor before publishing, and often reviewed by another author) means that books are reliable sources of information, although they may need to be evaluated for bias. A growing number of books can be found online.