Abstract
This chapter presents an informal overview of the relationship between computing and mathematics. In order to study this relationship, a brief history of mathematics is given, followed by illustrative examples of the use of mathematics in computing. The chapter closes with a note about the terminology used in the rest of the book.
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- 1.
Some analogue devices can calculate values in a continuous manner. For example, one can build a device that, given two numbers encoded as voltages, outputs their sum as a voltage. This is an analogue device since its inputs and outputs can be varied in an infinitude of ways in arbitrarily small steps. Normal computers calculate things by first expressing them in terms of ones and zeros, thus allowing us to only change things in steps by changing ones to zeros and vice versa.
- 2.
Well, of course, if we model the transistors which make up the computer, the program would just be an instance of the transistors being set with particular voltages. However, we would be committing the cardinal sin of not abstracting away unnecessary detail, resulting in a precise description of the behaviour of a computer, but one too big to be of any practical use.
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© 2012 Springer-Verlag Berlin Heidelberg
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Pace, G.J. (2012). Why Mathematics?. In: Mathematics of Discrete Structures for Computer Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29840-0_1
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DOI: https://doi.org/10.1007/978-3-642-29840-0_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29839-4
Online ISBN: 978-3-642-29840-0
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