Elements of Algebra: Geometry, Numbers, Equations - Brossura

Stillwell, John

 
9781441928399: Elements of Algebra: Geometry, Numbers, Equations
Brossura
ISBN 10: 1441928391 ISBN 13: 9781441928399
Casa editrice: Springer New York, 2010

Sinossi

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.

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Recensione

"...The book is written in a very clear and pleasing style. Each of the 9 chapters of the book concludes with a section called "Discussions", which contains very interesting and valuable historical information and comments on the topics presented in the respective chapter. We strongly recommend this nice volume not only to beginners but also to experts."--MATHEMATICAL REVIEWS

Contenuti

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

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Editore
Springer New York
Data di pubblicazione
2010
Lingua
Inglese
ISBN 10 
1441928391
ISBN 13 
9781441928399
Rilegatura
Copertina flessibile
Numero di pagine
196
Contatto del produttore
non disponibile
Persona responsabile
CMN Printpool Inh. Mathis Neumann
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Hamburg
Germania

Altre edizioni note dello stesso titolo

9780387942902: Elements of Algebra: Geometry, Numbers, Equations

Edizione in evidenza

ISBN 10:  0387942904 ISBN 13:  9780387942902
Casa editrice: Springer Nature, 2001
Rilegato