This page contains supporting material
for the textbook Introduction to Algebra, by Peter J. Cameron,
published by
Oxford University Press in April 1998.
The ISBNs for the book are - 019 850195 1 (hardback)
- 019 850194 3 (paperback)
This site will contain solutions to the exercises, further material, problems, corrections, and links to other sites of interest to algebraists. |

... a very good textbook in Algebra... The lecturers who are going to decide to use this book for their classes will make a good choice; they and their students will benefit a lot from this book.

Expand (1+1)(*x*+*y*) in two different ways:

- (1+1)(
*x*+*y*) = 1(*x*+*y*)+1(*x*+*y*) =*x*+*y*+*x*+*y* - (1+1)(
*x*+*y*) = (1+1)*x*+(1+1)*y*=*x*+*x*+*y*+*y*

2. Can you explain what the following is about?

Curiously enough, the twelve-tone system has no zero in it. Given a series: 3, 5, 2, 7, 10, 8, 11, 9, 1, 6, 4, 12 and the plan of obtaining its inversion by numbers which when added to the corresponding ones of the original series will give 12, one obtains 9, 7, 10, 5, 2, 4, 1, 3, 11, 6, 8 and 12. For in this system 12 plus 12 equals 12. There is not enough of zero in it.John Cage, "Eric Satie", in

3. Hermann Weyl on Proposition 2.12(c), the statement that
(*ST*)^{-1}=*T*^{-1}*S*^{-1}:

With this rule, although perhaps not with its mathematical expression, you are all familiar. When you dress, it is not immaterial in which order you perform the operations; and when in dressing you start with the shirt and end up with the coat, then in undressing you observe the opposite order; first take off the coat and the shirt comes last.Hermann Weyl,

- Peter Cameron's homepage at Queen Mary, University of London
- Group-Pub-Forum homepage at the University of Bath
- Permutation groups resources at Queen Mary, University of London
- ATLAS of Finite Group Representations at the University of Birmingham
- GAP homepage at St Andrews University
- Overview of MAGMA (mirror site at the University of Bath - original at the University of Sydney)
- History of Matrices and Determinants and History of Group Theory from the MacTutor History of Mathematics Archive at St Andrews University
- A Survey of Venn diagrams by Frank Ruskey, from the Electronic Journal of Combinatorics
- A Brief History of Algebra and Computing: An Eclectic Oxonian View by Jonathan P. Bowen at the University of Reading
- The Art of Algebra from Al-Khwarizmi to Viete by Karen Hunger Parshall at the University of Virginia
- 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)

GAP and MAGMA are systems for computation with algebraic structures including groups and rings.

Peter J. Cameron

4 January 2001.