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2016 | OriginalPaper | Chapter

6. Algebra

Author: Gerard O’Regan

Publisher: Springer International Publishing

Published in: Guide to Discrete Mathematics

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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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Recall from Chap. 3 that ℤ/ nℤ = ℤ _n = {[ a] _n: 0 ≤ a ≤ n − 1} = {[0] _n, [1] _n, …., [ n − 1] _n}.

A finite division ring is actually a field (i.e. it is commutative under multiplication), and this classic result was proved by Wedderburn.

Mathematics in Computing. Second Edition, Gerard O’ Regan. Springer. 2012.

Title

Algebra

Book

Guide to Discrete Mathematics

Print ISBN: 978-3-319-44560-1

Electronic ISBN: 978-3-319-44561-8

https://doi.org/10.1007/978-3-319-44561-8

DOI

https://doi.org/10.1007/978-3-319-44561-8_6

Author:

Gerard O’Regan

Publisher

Springer International Publishing

Sequence number

Chapter number

Chapter 6