Abstract
Algebra is the branch of mathematics that uses letters in the place of numbers, where the letters stand for variables or constants that are used in mathematical expressions. Algebra is the study of such mathematical symbols and the rules for manipulating them, and it is a powerful tool for problem solving in science and engineering.
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Notes
- 1.
Recall from Chap. 3 that ℤ/nℤ = ℤ n = {[a] n : 0 ≤ a ≤ n − 1} = {[0] n , [1] n , …., [n − 1] n }.
- 2.
A finite division ring is actually a field (i.e. it is commutative under multiplication), and this classic result was proved by Wedderburn.
Reference
Mathematics in Computing. Second Edition, Gerard O’ Regan. Springer. 2012.
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© 2016 Springer International Publishing Switzerland
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O’Regan, G. (2016). Algebra. In: Guide to Discrete Mathematics. Texts in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-44561-8_6
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DOI: https://doi.org/10.1007/978-3-319-44561-8_6
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