Verwandte Artikel zu Abstract Algebra and Famous Impossibilities (Universitext)
Inhaltsangabe
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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Reseña del editor
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.
Reseña del editor
The famous problems of squaring the circle, doubling the cube, and trisecting the angle have captured the imagination of both professional and amateur mathematician for over two thousand years. These problems, however, have not yielded 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. This text aims to develop the abstract algebra.
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Abstract Algebra and Famous Impossibilities
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Paperback. Zustand: Good. No Jacket. Pages can have notes/highlighting. Spine may show signs of wear. ~ ThriftBooks: Read More, Spend Less. Bestandsnummer des Verkäufers G0387976612I3N00
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Abstract Algebra and Famous Impossibilities (Universitext)
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Abstract Algebra and Famous Impossibilities
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Abstract Algebra and Famous Impossibilities
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Abstract Algebra and Famous Impossibilities
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Zustand: Fair. This is an ex-library book and may have the usual library/used-book markings inside.This book has soft covers. In fair condition, suitable as a study copy. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,400grams, ISBN:0387976612. Bestandsnummer des Verkäufers 5569769
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Abstract Algebra and Famous Impossibilities
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Abstract Algebra and Famous Impossibilities
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Abstract Algebra and Famous Impossibilities
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Zustand: New. pp. 204. Bestandsnummer des Verkäufers 18315939
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Abstract Algebra and Famous Impossibilities (Universitext)
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Paperback. Zustand: new. Excellent Condition.Excels in customer satisfaction, prompt replies, and quality checks. Bestandsnummer des Verkäufers Scanned0387976612
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Abstract Algebra and Famous Impossibilities
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Paperback. Zustand: Brand New. 187 pages. 9.25x6.00x0.75 inches. In Stock. Bestandsnummer des Verkäufers zk0387976612
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