## Peter J. Cameron
## Second edition, Oxford University Press, 2008What is algebra? | Exercises | Other material | The first edition |

You can see the preface and table of contents here.

This page will point you to a list of misprints, solutions to odd-numbered exercises, further exercises, additional material, etc.

To criticize mathematics for its abstraction is to miss the point entirely.
Abstraction is what makes mathematics work. If you concentrate
too closely on too limited an application of a mathematical idea, you rob
the mathematician of his most important tools: analogy, generality, and
simplicity. Mathematics is the ultimate in technology transfer.
Ian Stewart, |

In other words, in algebra, we can prove a theorem in (say) ring theory and apply it to integers, polynomials, matrices, and so on. We don't need to do the work over again in each new situation we meet. Also, the more general theorem may be easier, since inessential detail is stripped away.

Here is Doctor Johnson's definition of algebra in his dictionary:

This is a peculiar kind of arithmetick, which takes the quantity sought, whether it be a number or a line, or any other quantity, as if it were granted, and by means of one or more quantities given, proceeds by consequence, till the quantity at first only supposed to be known, or at least some power thereof, is found to be equal to some quantity or quantities which are known, and consequently itself is known.He clearly thought that algebra means solving equations! Read the book to find out what algebra is nowadays.

Read what other people have said about algebra here.

- Here are course notes for four algebra courses I have taught recently:
- Here are web pages for my other textbooks:
- Combinatorics: Topics, Techniques, Algorithms, published by Cambridge University Press;
- Sets, Logic and Categories, published by Springer-Verlag.
- Permutation Groups, published by Cambridge University Press.

- Permutation groups resources at Queen Mary, University of London
- ATLAS of Finite Group Representations at Queen Mary, University of London
- Two systems for computational algebra:
- GAP homepage at St Andrews University
- MAGMA homepage at the University of Sydney

- From the MacTutor History of Mathematics Archive at St Andrews University:
- A Survey of Venn diagrams by Frank Ruskey and Mark Weston, from the Electronic Journal of Combinatorics
- Solving the quintic (worked example in Mathematica)
- Semigroups directory at the University of Southampton
- Nearrings homepage at the University of Linz
- Theory and Applications of Categories (electronic journal)

Peter J. Cameron

`p.j.cameron(at)qmul.ac.uk`

17 December 2007.