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

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conformity

Cryptography,This chapter discusses cryptography, which is an important application of number theory. The codebreaking work done at Bletchley Park in England during the Second World War is discussed, and the fundamentals of cryptography, including private and public-key cryptosystems, are discussed.

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Coding Theory,This chapter presents coding theory and is concerned with error detection and error correction codes. The underlying mathematics includes abstract mathematics such as group theory, rings, fields and vector spaces.

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intolerance

Matrix Theory,This chapter discusses matrices including 2 × 2 and general . × . matrices. Various operations such as the addition and multiplication of matrices are considered, and the determinant and inverse of a square matrix are discussed. The application of matrices to solving a set of linear equations using Gaussian elimination is considered.

arcane

A Short History of Logic,This chapter presents a short history of logic, and we discuss Greek contributions to syllogistic logic, stoic logic, fallacies and paradoxes. Boole’s symbolic logic and its application to digital computing are discussed, and we consider Frege’s work on predicate logic.

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Pudendal-Nerve

Software Engineering Mathematics,Chapter 19 discusses software engineering and the mathematics to support software engineering. We discuss traditional software engineering including the activities in the waterfall lifecycle model. We discuss early mathematical work in software engineering including Floyd’s work on assertions which influenced C. A. R. Hoare.

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mechanism

Foundations of Computing, by Leibniz. The difference engine was designed by Babbage to evaluate polynomials and to produce accurate mathematical tables. Babbage’s design of the analytic engine provided the vision of a modern computer, and he envisaged that it would be analogous to the operation of the ., which is designed t