Abstract
This chapter discusses algebra, and we discuss simple and simultaneous equations, including the method of elimination and the method of substitution to 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 domains, fields and vector spaces.
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Notes
- 1.
Recall that ℤ/nℤ = ℤn = {[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.
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O’Regan, G. (2020). Algebra. In: Mathematics in Computing. Undergraduate Topics in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-030-34209-8_6
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DOI: https://doi.org/10.1007/978-3-030-34209-8_6
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-030-34209-8
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