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Elements of Algebra: Geometry, Numbers, Equations
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Elements of Algebra: Geometry, Numbers, Equations Hardcover - 2001

by John Stillwell


From the publisher

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.

First line

The purpose of this chapter is to sketch the classical background of abstract algebra.

From the rear cover

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.

Details

  • Title Elements of Algebra: Geometry, Numbers, Equations
  • Author John Stillwell
  • Binding Hardcover
  • Edition 1st
  • Pages 184
  • Volumes 1
  • Language ENG
  • Publisher Springer, Berlin/Heidelberg/New York/Tokyo
  • Date July 20, 2001
  • Illustrated Yes
  • Features Illustrated
  • ISBN 9780387942902 / 0387942904
  • Weight 1.03 lbs (0.47 kg)
  • Dimensions 9.56 x 6.42 x 0.61 in (24.28 x 16.31 x 1.55 cm)
  • Library of Congress subjects Algebra
  • Library of Congress Catalog Number 94010015
  • Dewey Decimal Code 512.02
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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)

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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)

by Stillwell, John

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Elements of Algebra: Geometry, Numbers, Equations

Elements of Algebra: Geometry, Numbers, Equations

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New. Algebra is abstract mathematics - let us make no bones about it - yet it is also applied mathematics in its best and purest form. It is not abstraction for its own sake, but abstraction for the sake of efficiency, power and insight. Algebra emerged from the struggle to solve concrete, physical problems in geometry, and succeeded after 2000 years of failure by other forms of mathematics. It did this by exposing the mathematical structure of geometry, and by providing the tools to analyse it. This is typical of the way algebra is applied; it is the best and purest form of application because it reveals the simplest and most universal mathematical structures. The present book aims to foster a proper appreciation of algebra by showing abstraction at work on concrete problems, the classical problems of construction by straightedge and compass. These problems originated in the time of Euclid, when geometry and number theory were paramount, and were not solved until th the 19 century, with the advent… Read More
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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)

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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)

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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)

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