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Algebra marked the beginning of modern mathematics, moving it beyond arithmetic, which involves calculations featuring given numbers, to problems where some quantities are unknown. Now, it stands as a pillar of mathematics, underpinning the quantitative sciences, both social and physical.
This Very Short Introduction explains algebra from scratch. Over the course of ten logical chapters, Higgins offers a step by step approach for readers keen on developing their understanding of algebra. Using theory and example, he renews the reader's aquaintance with school mathematics, before taking them progressively further and deeper into the subject.
Numbers and algebra
The laws of algebra
Linear equations and inequalities
Quadratic equations
The algebra of polynomials and cubic equations
Algebra and the arithmetic of remainders
Introduction to matrices
Matrices and groups
Determinants and matrices
Vector spaces