Elements of Algebra

This book is a concise, self-contained introduction to abstract algebra that stresses its unifying role in geometry and number theory. There is a strong emphasis on historical motivation - both to trace abstract concepts to their concrete roots, but also to show the power of new ideas to solve old problems. This approach shows algebra as an integral part of mathematics and makes this text more informative to both beginners and experts than others.

Zusammenfassung

"...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

Inhalt

1. Algebra and Geometry.- 2. The Rational Numbers.- 3. Numbers in General.- 4. Polynomials.- 5. Fields.- 6. Isomorphisms.- 7. Groups.- 8. Galois Theory of Unsolvability.- 9. Galois Theory of Solvability.- References.