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.
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- Date Published: February 1980
- format: Paperback
- isbn: 9780521298612
- length: 316 pages
- dimensions: 230 x 155 x 15 mm
- weight: 0.372kg
- availability: Available
Table of Contents
3. Elementary set theory
4. The set of integers
5. Other sets of numbers
6. Residue classes
9. Functions and mappings
10. The fundamental laws of algebra
12. Examples of groups
Answers to exercises
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