Titlebook: Mathematics in Computing; An Accessible Guide Gerard O’Regan Textbook 2020Latest edition Springer Nature Switzerland AG 2020 Calculus.Codi

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Overview of Mathematics in Computing,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

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Number Theory,erties of the natural numbers and integers. We discuss prime number theory where prime numbers are fundamental in arithmetic where every integer can be factored as a product of primes. Euclid’s algorithm may be employed to determine the greatest common divisor of two numbers. There are many applicat

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Algebra,o solve simultaneous equations. We show how quadratic equations may be solved by factorization, completing the square or using the quadratic formula. We present the laws of logarithms and indices. We discuss several structures used in abstract algebra, including monoids, groups, rings, integral doma

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Computability and Decidability,ine. Church and Turing showed that mathematics is not decidable. In other words, there is no mechanical procedure (i.e. algorithm) to determine whether an arbitrary mathematical proposition is true or false, and so the only way to determine the truth or falsity of a statement is trying to solve the

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Advanced Topics in Logic, the applications of logic to AI. Fuzzy logic is an extension of classical logic that acts as a mathematical model for vagueness. Temporal logic is concerned with the expression of properties that have time dependencies, and it allows temporal properties about the past, present and future to be expr

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