Algebra: A Very Short Introduction

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Oxford University Press, 2015 - Algebra - 144 pages
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.
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
Chapter 8 Matrices and groups
101
Chapter 9 Determinants and matrices
111
Chapter 10 Vector spaces
126
Further reading
139
Index
141
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About the author (2015)


Peter M. Higgins is a Professor in Pure Mathematics at the University of Essex. He is the inventor of the Circular Sudoku puzzle type that now features in numerous newspapers, magazines and computer games. He has written extensively on the subject of mathematics, including Numbers: A Very Short Introduction (OUP, 2011) and Nets, Puzzles, and Postmen (OUP, 2007), which won the 2012 Premio Peano prize for the best book on mathematics, published in Italian.

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