Abstract
This chapter sketches the mathematical prerequisites that software engineers should be familiar with, and we discuss fundamental concepts such as sets, relations, functions, arithmetic, and trigonometry. A set is a collection of well-defined objects, and it may be finite or infinite. A relation between two sets A and B indicates a relationship between members of the two sets and is a subset of the Cartesian product of the two sets. A function is a special type of relation such that for each element in A there is at most one element in the codomain B. Number theory is the branch of mathematics that is concerned with the mathematical properties of the natural numbers and integers. Trigonometry is the branch of mathematics that deals with the measurement of sides and angles of triangles and the relationships between them, and it has many applications in science and engineering.
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Notes
- 1.
We distinguish between total and partial functions. A total function \(f{\text{:}}\,A \to B\) is defined for every element in A whereas a partial function may be undefined for one or more values in A.
- 2.
There are mathematical objects known as multi-sets or bags that allow duplication of elements. For example, a bag of marbles may contain three green marbles, two blue and one red marble.
- 3.
The British logician, John Venn, invented the Venn diagram. It provides a visual representation of a set and the various set theoretical operations. Their use is limited to the representation of two or three sets as they become cumbersome with a larger number of sets.
- 4.
Cartesian product is named after René Descartes who was a famous 17th French mathematician and philosopher. He invented the Cartesian coordinates system that links geometry and algebra, and allows geometric shapes to be defined by algebraic equations.
- 5.
We distinguish between total and partial functions. A total function is defined for all elements in the domain, whereas a partial function may be undefined for one or more elements in the domain.
- 6.
Euclid was a third century B.C. Hellenistic mathematician and is considered the father of geometry.
References
Euclid (1956) The thirteen books of the elements. Vol.1 (Trans: Sir Thomas Heath). Dover Publications (First published in 1925)
O’Regan G (2021) Guide to discrete mathematics, 2nd edn. Springer
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O’Regan, G. (2023). Mathematical Prerequisites for Software Engineers. In: Mathematical Foundations of Software Engineering. Texts in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-031-26212-8_3
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DOI: https://doi.org/10.1007/978-3-031-26212-8_3
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