Elements of Algebra by John Stillwell
This book is intended to complement my Elements oi Algebra, and it is similarly motivated by the problem of solving polynomial equations. However, it is independent of the algebra book, and probably easier. In Elements oi Algebra we sought solution by radicals, and this led to the concepts of fields and groups and their fusion in the celebrated theory of Galois. In the present book we seek integer solutions, and this leads to the concepts of rings and ideals which merge in the equally celebrated theory of ideals due to Kummer and Dedekind. Solving equations in integers is the central problem of number theory, so this book is truly a number theory book, with most of the results found in standard number theory courses. However, numbers are best understood through their algebraic structure, and the necessary algebraic concepts- rings and ideals-have no better motivation than number theory. The first nontrivial examples of rings appear in the number theory of Euler and Gauss. The concept of ideal-today as routine in ring the- ory as the concept of normal subgroup is in group theory-also emerged from number theory, and in quite heroic fashion. Faced with failure of unique prime factorization in the arithmetic of certain generalized inte- gers, Kummer created in the 1840s a new kind of number to overcome the difficulty. He called them ideal numbers because he did not know exactly what they were, though he knew how they behaved."..The book is written in a very clear and pleasing style. Each of the 9 chapters of the book concludes with a section called "Discussions", which contains very interesting and valuable historical information and comments on the topics presented in the respective chapter. We strongly recommend this nice volume not only to beginners but also to experts."--MATHEMATICAL REVIEWS
| SKU | Unavailable |
| ISBN 13 | 9781441928399 |
| ISBN 10 | 1441928391 |
| Title | Elements of Algebra |
| Author | John Stillwell |
| Series | Undergraduate Texts In Mathematics |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer-Verlag New York Inc. |
| Year published | 2010-12-01 |
| Number of pages | 184 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |