John Stillwell: Elements of Algebra | Buch

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Cover: 9780387942902 | Elements of Algebra | Geometry, Numbers, Equations | John Stillwell

Bild: 9780387942902 | Elements of Algebra | Geometry, Numbers, Equations | John Stillwell

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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.

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.

Erscheinungsjahr:	1994
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	200
Reihe:	Undergraduate Texts in Mathematics
Inhalt:	xii 184 S. 34 s/w Illustr. 34 s/w Zeichng.
ISBN-13:	9780387942902
ISBN-10:	0387942904
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Stillwell, John
Auflage:	1994
Hersteller:	Springer US Springer New York Undergraduate Texts in Mathematics
Maße:	241 x 160 x 17 mm
Von/Mit:	John Stillwell
Erscheinungsdatum:	19.08.1994
Gewicht:	0,471 kg

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