Abstract
This chapter considers the work of George Boole and Charles Babbage who are considered grandfathers of computing. George Boole was a nineteenth-century English mathematician who made contributions to logic, probability theory and the differential and integral calculus. His calculus of logic (Boolean logic) acts as the foundation of all modern digital computers.
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- 1.
De Morgan was a nineteenth-century British mathematician based at University College London. De Morgan’s laws in set theory and logic state that (A ∪ B)c = Ac ∩ Bc and ¬ (A ∨ B) = ¬A ∧ ¬B.
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Boole was awarded the Royal Medal from the Royal Society of London in 1844 in recognition of his publications. The Irish Mathematician, Sir Rowan Hamilton (who invented Quaternions), was another famous recipient of this prize.
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Queens College Cork is now called University College Cork (UCC) and has about 18,000 students. It is located in Cork city in the south of Ireland.
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Finite differences are a numerical method used in solving differential equations.
- 5.
This is a novel about the struggle of an international revolutionary. Shostakovich wrote the score for the film of the same name that appeared in 1955.
- 6.
The power series expansion of the sine function is given by sin(x) = x − x 3/3! + x 5/5! − x 7/7! + …. The power series expansion for the cosine function is given by cos(x) = 1 − x 2/2! + x 4/4! − x6/6! + …. Functions may be approximated by interpolation and the approximation of a function by a polynomial of degree n requires n + 1 points on the curve for the interpolation. That is, the curve formed by the polynomial of degree n that passes through the n + 1 points on the function to be approximated is an approximation to the function.
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Each wheel represented a decimal digit (each wheel consisted of ten teeth).
- 8.
The Jacquard loom was invented by Joseph Jacquard in 1801. It is a mechanical loom which used the holes in punch cards to control the weaving of patterns in a fabric. The use of punch cards allowed complex designs to be woven from the pattern defined on the punch card. Each punch card corresponds to one row of the design, and the cards were appropriately ordered. It was very easy to change the pattern of the fabric being weaved on the loom, as this simply involved changing cards.
References
Menabrea, L.F.: Sketch of the Analytic Engine. Invented by Charles Babbage. Bibliothèque Universelle de Genève. Translated by Lada Ada Lovelace (1842)
Boole, G.: The calculus of logic. Camb. Dublin Math. J. III, 183–198 (1848)
Boole, G.: An Investigation into the Laws of Thought. Dover Publications, New York (1958) (First published in 1854)
McHale, D.: Boole. Cork University Press (1985)
O’Regan, G.: Mathematical Approaches to Software Quality. Springer, London (2006)
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© 2012 Springer-Verlag London Limited
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O’Regan, G. (2012). Foundations (Boole and Babbage). In: A Brief History of Computing. Springer, London. https://doi.org/10.1007/978-1-4471-2359-0_12
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DOI: https://doi.org/10.1007/978-1-4471-2359-0_12
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