## Algebra: A Very Short IntroductionAlgebra 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. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable. |

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### Contents

Chapter 1 Numbers and algebra | 1 |

Chapter 2 The laws of algebra | 11 |

Chapter 3 Linear equations and inequalities | 25 |

Chapter 4 Quadratic equations | 40 |

Chapter 5 The algebra of polynomials and cubic equations | 53 |

Chapter 6 Algebra and the arithmetic of remainders | 75 |

Chapter 7 Introduction to matrices | 87 |

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### Common terms and phrases

abelian group abstract algebra arithmetic associated Binomial brackets calculation cancel Chapter column common factor commutative commutative law completing the square complex numbers congruence conjugate cubic cyclic group David denominator denoted det(A determinant diagonal distributive law eigenvalues eigenvector entry equal example expression finite field follows fractions full rank gives graph inequality integral domain inverse Kirchhoff matrix laws of algebra linear combination linear equations linear transformation mathematics meaning Michael Modular arithmetic modulo negative number node non-zero number line number system original pair particular Peter plane polynomial equation positive integer positive number problem properties quadratic equation quadratic formula rational numbers Rational Root Theorem rational roots real numbers rectangle remainder represent ring rotation rules scalar solution solve square matrix square root substitution subtraction symbols unique unknown vector space write zero