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Mathematics in computing : an accessible guide to by Gerard O'Regan

By Gerard O'Regan

Arithmetic in Civilization units, kinfolk and features common sense software program Engineering Formal tools Z Formal Specification Language quantity conception Cryptography Coding concept Language concept and Semantics Computability and Decidability chance, information and software program Reliability Matrix concept advanced Numbers and Quaternions Calculus Graph idea

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Extra resources for Mathematics in computing : an accessible guide to historical, foundational and application contexts

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R n ∪ . . , there exists c1 ,c2 , . . cn ∈ A such that: aRc1 , c1 Rc2 , . . , cn Rb. Parnas6 introduced the concept of the limited domain relation (LD-relation), and a LD relation L consists of an ordered pair (RL , CL ) where RL is a relation and CL is a subset of Dom RL . The relation RL is on a set U and CL is termed the competence set of the LD relation L. A description of LD relations and a discussion of their properties are in Chap. 2 of [Par:01]. The importance of LD relations is that they may be used to describe program execution.

A a b Sets may be defined by using a predicate to constrain set membership. For example, the set S = {n : N : n ≤ 10 ∧ n mod 2 = 0} also represents the set {2, 4, 6, 8, 10}. That is, the use of a predicate allows a new set to be created from an existing set by using the predicate to restrict membership of the set. The set of even natural numbers may be defined by a predicate over the set of natural numbers that restricts membership to the even numbers. It is defined by: Evens = {x|x ∈ N ∧ even(x)}.

7 “Archimedes in thought” by Fetti Archimedes’ made good contributions to mathematics including developing a good approximation to π, as well as contributions to the positional numbering system, geometric series and to maths physics. g. the calculation of the composition of cattle in the herd of the Sun god by solving a number of simultaneous Diophantine equations. The herd consisted of bulls and cows with one part of the herd consisting of white, the second part black, the third spotted and the fourth brown.

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