An Introduction to Abstract Algebra

This two-volume course on abstract algebra provides a broad introduction to the subject.

F. M. Hall (Author)

9780521298612, Cambridge University Press

Paperback, published 14 February 1980

316 pages
23 x 15.5 x 1.5 cm, 0.372 kg

This two-volume course on abstract algebra provides a broad introduction to the subject for those with no previous knowledge of it but who are well grounded in ordinary algebraic techniques. It starts from the beginning, leading up to fresh ideas gradually and in a fairly elementary manner, and moving from discussion of particular (concrete) cases to abstract ideas and methods. It thus avoids the common practice of presenting the reader with a mass of ideas at the beginning, which he is only later able to relate to his previous mathematical experience. The work contains many concrete examples of algebraic structures. Each chapter contains a few worked examples for the student - these are divided into straightforward and more advanced categories. Answers are provided. From general sets, Volume 1 leads on to discuss special sets of the integers, other number sets, residues, polynomials and vectors. A chapter on mappings is followed by a detailed study of the fundamental laws of algebra, and an account of the theory of groups which takes the idea of subgroups as far as Langrange's theorem. Some improvements in exposition found desirable by users of the book have been incorporated into the second edition and the opportunity has also been taken to correct a number of errors.

Preface
1. Introduction
2. Sets
3. Elementary set theory
4. The set of integers
5. Other sets of numbers
6. Residue classes
7. Polynomials
8. Vectors
9. Functions and mappings
10. The fundamental laws of algebra
11. Groups
12. Examples of groups
13. Subgroups
Answers to exercises
Index.

Subject Areas: Mathematics [PB]