THIS book is written primarily for undergraduate students of science and engineering, and presents an elementary introduction to some of the major branches of modern algebra - namely, matrices, sets and groups. Of these three topics, matrices are of especial importance at undergraduate level, and consequently more space is devoted to their study than to the other two. Nevertheless the subjects are interrelated, and it is hoped that this book will give the student an insight into some of the basic connections between various mathematical concepts as well as teaching him how to manipulate the mathematics itself.
Although matrices and groups, for example, are usually taught to students in their second and third year ancillary mathematics courses, there is no inherent difficulty in the presentation of these subjects which make them intractable in the first year. In the author's opinion more should be done to bring out the importance of algebraic structures early on in an undergraduate course, even if this is at the expense of some of the more routine parts of the differential calculus. Accordingly this book has been made virtually selfcontained and relies only on a minimum of mathematical knowledge such as is required for university entrance. It should therefore be suitable for physicists, chemists and engineers at any stage of their degree course.
Various worked examples are given in the text, and problems for the reader to work are included at the end of each chapter. Answers to these problems are at the end of the book. In addition, a list of further reading matter is given which should enable the student to follow the subjects discussed here considerably farther.
The author wishes to express his thanks to Dr. I. N. Baker and Mr. D. Dunn, both of whom have read the manuscript and made numerous criticisms and suggestions which have substantially improved the text. Thanks are also due to Dr. A. N. Gordon for reading the proofs and making his usual comments.