Key ideas

In this course, we will take an introductory look at two key ideas: forms of data handled by a software system, and the processes that may be applied to that data. These ideas are illustrated by a particular application — a supermarket till — but they are of general relevance in designing software systems. Important terminology will be highlighted in bold.

In this course we will look at some commonly occurring forms of data. We start with fundamental forms, such as numbers and characters (which are symbols that may be typed at a keyboard). We then go on to look at more complicated data structures.

A second crucial feature of data is the processes available to handle it. The processes needed in any particular application are a particular focus in software design. Here, we shall look at how in principle we can describe a process that manipulates data. This initial description will not be concerned with how the process is executed, but only with its effect.

This course will introduce two important mathematical ideas that help in offering clear and precise descriptions of software components relating to data and processes. These ideas are set and function.

Section 1 gives a brief introduction to how data and processes may arise in an application situation. Section 2 is concerned with fundamental forms of data, and the mathematical idea of a set. Section 3 looks briefly at some more structured forms of data. In Section 4 we look at processes, and the mathematical idea of function. Section 5 is concerned with processes of a particular sort. Examples of these processes are the addition of numbers (as in 5 + 6) and a comparison of two numbers (as in 3