Computing
Computing is any goal-oriented activity requiring, benefiting from, or creating computers. Computing includes designing, developing and building hardware and software systems; designing a mathematical sequence of steps known as an algorithm; processing, structuring, and managing various kinds of information; doing scientific research on and with computers; making computer systems behave intelligently; and creating and using communications and entertainment media. The field of computing includes computer engineering, software engineering, computer science, information systems, and information technology.
Software
Computer software, or simply software, is a part of a computer system that consists of data or computer instructions, in contrast to the physical hardware from which the system is built. In computer science and software engineering, computer software is all information processed by computer systems, programs and data. Computer software includes computer programs, libraries and related non-executable data, such as online documentation or digital media. Computer hardware and software require each other and neither can be realistically used on its own.
Software
One of the difficulties in thinking about software is its huge variety. A function definition in a spreadsheet cell is software. A smartphone app is software. The flight management system for an Airbus A380 is software. A word processor is software. We shouldn't expect a single discipline of software engineering to cover all of these, any more than we expect a single discipline of manufacturing to cover everything from the Airbus A380 to the production of chocolate bars, or a single discipline of social organization to cover everything from the United Nations to a kindergarten. Improvement in software engineering must come bottom-up, from intense specialized attention to particular products.
Michael A. Jackson in: K. De Grave (ed.) Formalism & Intuition in Software Development; A conversation with Michael A. Jackson conducted by Edgar G. Daylight and Bas van Vlijmen. 2015