Abstract Algebra and Famous Impossibilities: Squaring the Circle, Doubling the Cube, Trisecting an Angle, and Solving Quintic Equations - Couverture rigide
Livre 163 sur 168: Undergraduate Texts in Mathematics
Synopsis
The famous problems of squaring the circle, doubling the cube and trisecting an angle captured the imagination of both professional and amateur mathematicians for over two thousand years. Despite the enormous effort and ingenious attempts by these men and women, the problems would not yield to purely geometrical methods. It was only the development. of abstract algebra in the nineteenth century which enabled mathematicians to arrive at the surprising conclusion that these constructions are not possible. In this book we develop enough abstract algebra to prove that these constructions are impossible. Our approach introduces all the relevant concepts about fields in a way which is more concrete than usual and which avoids the use of quotient structures (and even of the Euclidean algorithm for finding the greatest common divisor of two polynomials). Having the geometrical questions as a specific goal provides motivation for the introduction of the algebraic concepts and we have found that students respond very favourably. We have used this text to teach second-year students at La Trobe University over a period of many years, each time refining the material in the light of student performance.
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À propos de l?auteur
Sidney A. Morris is Emeritus Professor at the Federation University, Australia (formerly University of Ballarat) and Adjunct Professor at La Trobe University, Australia. His primary research is in topological groups, topology, and transcendental number theory, with broader interests including early detection of muscle wasting diseases, health informatics, and predicting the Australian stock exchange. He is the author of several books.
Arthur Jones [1934-2006] and Kenneth R. Pearson [1943-2015] were Professors in Mathematics at La Trobe University, Australia. Each had a great passion for teaching and for mathematics.
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Abstract Algebra and Famous Impossibilities: Squaring the Circle, Doubling the Cube, Trisecting an Angle, and Solving Quintic Equations (Undergraduate Texts in Mathematics)
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Abstract Algebra and Famous Impossibilities (Hardcover)
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Springer International Publishing AG, Cham, 2022
ISBN 10 : 3031056973
ISBN 13 : 9783031056970
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Hardcover. Etat : new. Hardcover. This textbook develops the abstract algebra necessary to prove the impossibility of four famous mathematical feats: squaring the circle, trisecting the angle, doubling the cube, and solving quintic equations. All the relevant concepts about fields are introduced concretely, with the geometrical questions providing motivation for the algebraic concepts. By focusing on problems that are as easy to approach as they were fiendishly difficult to resolve, the authors provide a uniquely accessible introduction to the power of abstraction.Beginning with a brief account of the history of these fabled problems, the book goes on to present the theory of fields, polynomials, field extensions, and irreducible polynomials. Straightedge and compass constructions establish the standards for constructability, and offer a glimpse into why squaring, doubling, and trisecting appeared so tractable to professional and amateur mathematicians alike. However, the connection between geometry and algebra allows the reader to bypass two millennia of failed geometric attempts, arriving at the elegant algebraic conclusion that such constructions are impossible. From here, focus turns to a challenging problem within algebra itself: finding a general formula for solving a quintic polynomial. The proof of the impossibility of this task is presented using Abels original approach.Abstract Algebra and Famous Impossibilities illustrates the enormous power of algebraic abstraction by exploring several notable historical triumphs. This new edition adds the fourth impossibility: solving general quintic equations. Students and instructors alike will appreciate the illuminating examples, conversational commentary, and engaging exercises that accompany each section. A first course in linear algebra is assumed, along with a basic familiarity with integral calculus. This textbook develops the abstract algebra necessary to prove the impossibility of four famous mathematical feats: squaring the circle, trisecting the angle, doubling the cube, and solving quintic equations. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N° de réf. du vendeur 9783031056970
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Abstract Algebra and Famous Impossibilities: Squaring the Circle, Doubling the Cube, Trisecting an Angle, and Solving Quintic Equations (Undergraduate Texts in Mathematics)
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Abstract Algebra and Famous Impossibilities: Squaring the Circle, Doubling the Cube, Trisecting an Angle, and Solving Quintic Equations (Undergraduate Texts in Mathematics)
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Abstract Algebra and Famous Impossibilities: Squaring the Circle, Doubling the Cube, Trisecting an Angle, and Solving Quintic Equations
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Hardcover. Etat : Brand New. 2nd edition. 218 pages. 9.50x6.25x0.75 inches. In Stock. N° de réf. du vendeur __3031056973
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Abstract Algebra and Famous Impossibilities
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Springer International Publishing Nov 2022, 2022
ISBN 10 : 3031056973
ISBN 13 : 9783031056970
Neuf
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Vendeur : BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Allemagne
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Buch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This textbook develops the abstract algebra necessary to prove the impossibility of four famous mathematical feats: squaring the circle, trisecting the angle, doubling the cube, and solving quintic equations. All the relevant concepts about fields are introduced concretely, with the geometrical questions providing motivation for the algebraic concepts. By focusing on problems that are as easy to approach as they were fiendishly difficult to resolve, the authors provide a uniquely accessible introduction to the power of abstraction.Beginning with a brief account of the history of these fabled problems, the book goes on to present the theory of fields, polynomials, field extensions, and irreducible polynomials. Straightedge and compass constructions establish the standards for constructability, and offer a glimpse into why squaring, doubling, and trisecting appeared so tractable to professional and amateur mathematicians alike. However, the connection between geometry and algebra allows the reader to bypass two millennia of failed geometric attempts, arriving at the elegant algebraic conclusion that such constructions are impossible. From here, focus turns to a challenging problem within algebra itself: finding a general formula for solving a quintic polynomial. The proof of the impossibility of this task is presented using Abel's original approach.Abstract Algebra and Famous Impossibilities illustrates the enormous power of algebraic abstraction by exploring several notable historical triumphs. This new edition adds the fourth impossibility: solving general quintic equations. Students and instructors alike will appreciate the illuminating examples, conversational commentary, and engaging exercises that accompany each section. A first course in linear algebra is assumed, along with a basic familiarity with integral calculus. 240 pp. Englisch. N° de réf. du vendeur 9783031056970
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Abstract Algebra and Famous Impossibilities
Edité par
Springer International Publishing, 2022
ISBN 10 : 3031056973
ISBN 13 : 9783031056970
Neuf
Couverture rigide
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Gebunden. Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Motivates the development of algebraic concepts through tantalizing geometric questions from historyIllustrates the power of algebraic abstraction for tackling concrete questionsEngages the reader with abundant examples, commentary, and exe. N° de réf. du vendeur 581554096
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Abstract Algebra and Famous Impossibilities
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Buch. Etat : Neu. This item is printed on demand - Print on Demand Titel. Neuware -This textbook develops the abstract algebra necessary to prove the impossibility of four famous mathematical feats: squaring the circle, trisecting the angle, doubling the cube, and solving quintic equations. All the relevant concepts about fields are introduced concretely, with the geometrical questions providing motivation for the algebraic concepts. By focusing on problems that are as easy to approach as they were fiendishly difficult to resolve, the authors provide a uniquely accessible introduction to the power of abstraction.Beginning with a brief account of the history of these fabled problems, the book goes on to present the theory of fields, polynomials, field extensions, and irreducible polynomials. Straightedge and compass constructions establish the standards for constructability, and offer a glimpse into why squaring, doubling, and trisecting appeared so tractable to professional and amateur mathematicians alike. However, the connection between geometry and algebra allows the reader to bypass two millennia of failed geometric attempts, arriving at the elegant algebraic conclusion that such constructions are impossible. From here, focus turns to a challenging problem within algebra itself: finding a general formula for solving a quintic polynomial. The proof of the impossibility of this task is presented using Abel¿s original approach.Abstract Algebra and Famous Impossibilities illustrates the enormous power of algebraic abstraction by exploring several notable historical triumphs. This new edition adds the fourth impossibility: solving general quintic equations. Students and instructors alike will appreciate the illuminating examples, conversational commentary, and engaging exercises that accompany each section. A first course in linear algebra is assumed, along with a basic familiarity with integral calculus.Springer-Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 240 pp. Englisch. N° de réf. du vendeur 9783031056970
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Abstract Algebra and Famous Impossibilities : Squaring the Circle, Doubling the Cube, Trisecting an Angle, and Solving Quintic Equations
Edité par
Springer International Publishing, 2022
ISBN 10 : 3031056973
ISBN 13 : 9783031056970
Neuf
Couverture rigide
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Buch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - This textbook develops the abstract algebra necessary to prove the impossibility of four famous mathematical feats: squaring the circle, trisecting the angle, doubling the cube, and solving quintic equations. All the relevant concepts about fields are introduced concretely, with the geometrical questions providing motivation for the algebraic concepts. By focusing on problems that are as easy to approach as they were fiendishly difficult to resolve, the authors provide a uniquely accessible introduction to the power of abstraction.Beginning with a brief account of the history of these fabled problems, the book goes on to present the theory of fields, polynomials, field extensions, and irreducible polynomials. Straightedge and compass constructions establish the standards for constructability, and offer a glimpse into why squaring, doubling, and trisecting appeared so tractable to professional and amateur mathematicians alike. However, the connection between geometry and algebra allows the reader to bypass two millennia of failed geometric attempts, arriving at the elegant algebraic conclusion that such constructions are impossible. From here, focus turns to a challenging problem within algebra itself: finding a general formula for solving a quintic polynomial. The proof of the impossibility of this task is presented using Abel's original approach.Abstract Algebra and Famous Impossibilities illustrates the enormous power of algebraic abstraction by exploring several notable historical triumphs. This new edition adds the fourth impossibility: solving general quintic equations. Students and instructors alike will appreciate the illuminating examples, conversational commentary, and engaging exercises that accompany each section. A first course in linear algebra is assumed, along with a basic familiarity with integral calculus. N° de réf. du vendeur 9783031056970
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Abstract Algebra and Famous Impossibilities | Squaring the Circle, Doubling the Cube, Trisecting an Angle, and Solving Quintic Equations
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Buch. Etat : Neu. Abstract Algebra and Famous Impossibilities | Squaring the Circle, Doubling the Cube, Trisecting an Angle, and Solving Quintic Equations | Sidney A. Morris (u. a.) | Buch | Undergraduate Texts in Mathematics | xxii | Englisch | 2022 | Springer | EAN 9783031056970 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand. N° de réf. du vendeur 121408795
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