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Elements of Algebra: Geometry, Numbers, Equations (Undergraduate Texts in Mathematics)

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Elements of Algebra: Geometry, Numbers, Equations (Undergraduate Texts in Mathematics) Cover

 

Synopses & Reviews

Synopsis:

This book is a concise, self-contained introduction to abstract algebra that stresses its unifying role in geometry and number theory. Classical results in these fields, such as the straightedge-and-compass constructions and their relation to Fermat primes, are used to motivate and illustrate algebraic techniques. Classical algebra itself is used to motivate the problem of solvability by radicals and its solution via Galois theory. This historical approach has at least two advantages: On the one hand it shows that abstract concepts have concrete roots, and on the other it demonstrates the power of new concepts to solve old problems. Algebra has a pedigree stretching back at least as far as Euclid, but today its connections with other parts of mathematics are often neglected or forgotten. By developing algebra out of classical number theory and geometry and reviving these connections, the author has made this book useful to beginners and experts alike. The lively style and clear exposition make it a pleasure to read and to learn from.

Table of Contents

Preface; 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; Index

Product Details

ISBN:
9780387942902
Author:
Stillwell, John C.
Publisher:
Springer
Author:
Stillwell, John
Location:
New York, NY
Subject:
Algebra
Subject:
Algebra - General
Subject:
Number Theory
Subject:
Geometry
Subject:
Mathematics - Algebra
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Copyright:
Edition Number:
1
Edition Description:
1994. Corr. 3rd
Series:
Undergraduate Texts in Mathematics
Series Volume:
1228
Publication Date:
July 2001
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
194
Dimensions:
235 x 155 mm 1020 gr

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Related Subjects

Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » Topology

Elements of Algebra: Geometry, Numbers, Equations (Undergraduate Texts in Mathematics) New Hardcover
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Product details 194 pages Springer-Verlag - English 9780387942902 Reviews:
"Synopsis" by , This book is a concise, self-contained introduction to abstract algebra that stresses its unifying role in geometry and number theory. Classical results in these fields, such as the straightedge-and-compass constructions and their relation to Fermat primes, are used to motivate and illustrate algebraic techniques. Classical algebra itself is used to motivate the problem of solvability by radicals and its solution via Galois theory. This historical approach has at least two advantages: On the one hand it shows that abstract concepts have concrete roots, and on the other it demonstrates the power of new concepts to solve old problems. Algebra has a pedigree stretching back at least as far as Euclid, but today its connections with other parts of mathematics are often neglected or forgotten. By developing algebra out of classical number theory and geometry and reviving these connections, the author has made this book useful to beginners and experts alike. The lively style and clear exposition make it a pleasure to read and to learn from.
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