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Elements of Algebra
Geometry, Numbers, Equations
Buch von John Stillwell
Sprache: Englisch

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Beschreibung
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 of abstract algebra. As we now know, alge­ bra brings about a unification of geometry, number theory and indeed most branches of mathematics. This is not really surprising when one has a historical understanding of the subject, which I also hope to impart.
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 of abstract algebra. As we now know, alge­ bra brings about a unification of geometry, number theory and indeed most branches of mathematics. This is not really surprising when one has a historical understanding of the subject, which I also hope to impart.
Zusammenfassung
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.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 1994
Fachbereich: Arithmetik & Algebra
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xii
184 S.
34 s/w Illustr.
34 s/w Zeichng.
ISBN-13: 9780387942902
ISBN-10: 0387942904
Sprache: Englisch
Einband: Gebunden
Autor: Stillwell, John
Hersteller: Springer US
Springer New York
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 17 mm
Von/Mit: John Stillwell
Erscheinungsdatum: 19.08.1994
Gewicht: 0,471 kg
Artikel-ID: 101267330
Zusammenfassung
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.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 1994
Fachbereich: Arithmetik & Algebra
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xii
184 S.
34 s/w Illustr.
34 s/w Zeichng.
ISBN-13: 9780387942902
ISBN-10: 0387942904
Sprache: Englisch
Einband: Gebunden
Autor: Stillwell, John
Hersteller: Springer US
Springer New York
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 17 mm
Von/Mit: John Stillwell
Erscheinungsdatum: 19.08.1994
Gewicht: 0,471 kg
Artikel-ID: 101267330
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