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Algebra: A Very Short Introduction

Peter M. Higgins
Publisher: 
Oxford University Press
Publication Date: 
2015
Number of Pages: 
144
Format: 
Paperback
Series: 
Very Short Introductions
Price: 
11.95
ISBN: 
9780198732822
Category: 
General
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Underwood Dudley
, on
01/18/2016
]

Yes, the book is short: its height is only 6-7/8” and it contains a mere 144 pages. Its width, 4-3/8”, is also modest. It is one a series of Very Short Introductions, now including more than 400 titles.

Its author teaches at the University of Essex. His Techniques of Semigroup Theory appeared in 1992; when I looked it was in 9,260,448th place in Amazon’s list of best sellers. He has since turned to popular mathematics, which sells better, and written several books in the field, including another in the VSI series and one that won a prize in 2012 for being the best book on mathematics published in Italian.

Its contents are not drawn only from Algebra 1 and Algebra 2. The quadratic formula is here, and what it means for a fraction to be in its lowest terms, but so are groups, rings, fields, modular arithmetic, matrices, and eigenvectors. The book has no prerequisites. The author covers an amazing amount of ground with clarity and liveliness. The book and its author are altogether admirable. Reading some books, I think “I could do that better”. That is not the case here.

The subtitle of the VSI series is “stimulating ways into new subjects”. That is probably accurate for most readers when the subject is, for example, structural engineering or Buddhist ethics, but everyone has encountered some algebra in school. Even so, those who have been away from the subject for some time (perhaps twenty years, but a year or two may be enough) can, if they are so inclined, read the book with enjoyment and, maybe, profit.

There is a period missing at the end of a displayed line on page 59. Tsk, tsk.


Woody Dudley thinks that short books should have short reviews and short reviewer descriptions.

1. Numbers and algebra
2. The laws of algebra
3. Linear equations and inequalities
4. Quadratic equations
5. The algebra of polynomials
6. Introduction to matrices
7. Matrices and groups
8. Determinants and matrices
9. Algebra and the arithmetic of remainders
10. Vector spaces
Further Reading
Index