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Elements of Algebra Geometry, Numbers, Equations

ISBN-10: 0387942904
ISBN-13: 9780387942902
Edition: 3rd 1994
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Description: This book is a concise, self-contained introduction to abstract algebra which 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,  More...

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Book details

Edition: 3rd
Copyright year: 1994
Publisher: Springer
Publication date: 7/20/2001
Binding: Hardcover
Pages: 184
Size: 6.25" wide x 9.25" long x 0.75" tall
Weight: 0.946
Language: English

This book is a concise, self-contained introduction to abstract algebra which 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. Classical results of geometry and number theory (such as straightedge-and-compass construction and its relation to Fermat primes) are used to motivate and illustrate algebraic techniques, and classical algebra itself (solutions of cubic and quartic equations) is used to motivate the problem of solvability by radicals and its solution via Galois theory. Modern methods are used whenever they are clearer or more efficient, but technical machinery is introduced only when needed. The lively style and clear expositions make this book a pleasure to read and to learn from.

Algebra and Geometry
The Rational Numbers
Numbers In General
Polynomials
Fields
Isomorphisms
Groups
Galois Theory of Unsolvability
Galois Theory of Solvability
References
Index

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