An Introduction to Abstract Algebra

This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and in the information and physical sciences. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility and relevance of algebra today. In particular applications to Polya coloring theory, latin squares, Steiner systems and error correcting codes are described. Another feature of the book is that group theory and ring theory are carried further than is often done at this level.

There is ample material here for a two semester course in abstract algebra.

The importance of proof is stressed and rigorous proofs of almost all results are given. But care has been taken to lead the reader through the proofs by gentle stages. There are nearly 400 problems, of varying degrees of difficulty, to test the reader's skill and progress. The book should be suitable for graduate students.

Reviews

"Altogether, this book represents a very gentle, user-friendly and skillful introduction to undergraduate abstract algebra for students in various fields of science. [...] a very experienced teacher has here presented a valuable introductory text on abstract algebra that can universally be used as a source for a one or two semester course on the subject for students in their second or third year of study: Without any doubt, this text is also very suitable for private study and exam preparation of undergraduates."

--Werner Kleinert in: Zentralblatt MATH 10/2003

Contents

1.Sets, relations and functions
2. The integers
3. Introduction to groups
4. Cosets, quotient groups and homomorphisms
5. Groups acting on sets
6. Introduction to rings
7. Division in rings
8. Vector spaces
9.The structure of groups
10. Introduction to the theory of fields
11. Galois theory
12. Further topics
Bibliography
Index of notation
Index