Articles liés à Geometry: Euclid and Beyond
Synopsis
Preliminary Booksellers Text: Do Not Use This book takes Euclid's "Elements" ad the starting point for a study of geometry from a modern mathematical perspective. To begin, the reader will become familiar with the content of Euclid's work, at least those parts which deal with geometry. At a second level, the book studies the logical structure of Euclid's presentation. Euclid's "Elements" has been regarded for more than two thousand years as the prime example of the axiomatic method. At the third level of reading, involving rather broader investigaions than the first two levels mentioned above, the author considers various mathematical questions and subsequent developments which arise naturally from Euclid's
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Présentation de l'éditeur
This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, geometrical constructions and finite field extensions, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semiregular polyhedra. The text is intended for junior- to senior-level mathematics majors.
Biographie de l'auteur
Robin Hartshorne is a professor of mathematics at the University of California at Berkeley, and is the author of Foundations of Projective Geometry (Benjamin, 1967) and Algebraic Geometry (Springer, 1977).
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Geometry: Euclid and Beyond (Undergraduate Texts in Mathematics)
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Springer, 2010
ISBN 10 : 1441931457
ISBN 13 : 9781441931450
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Geometry: Euclid and Beyond (Undergraduate Texts in Mathematics)
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Geometry: Euclid and Beyond (Paperback)
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Springer-Verlag New York Inc., New York, NY, 2010
ISBN 10 : 1441931457
ISBN 13 : 9781441931450
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Paperback. Etat : new. Paperback. In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa rately. The remainder of the book is an exploration of questions that arise natu rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And in the last chapter we provide what is missing from Euclid's treatment of the five Platonic solids in Book XIII of the Elements. For a one-semester course such as I teach, Chapters 1 and 2 form the core material, which takes six to eight weeks. In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa rately. And in the last chapter we provide what is missing from Euclid's treatment of the five Platonic solids in Book XIII of the Elements. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N° de réf. du vendeur 9781441931450
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Geometry: Euclid and Beyond (Undergraduate Texts in Mathematics)
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Geometry: Euclid and Beyond
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Springer New York, Springer US Dez 2010, 2010
ISBN 10 : 1441931457
ISBN 13 : 9781441931450
Neuf
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa rately. The remainder of the book is an exploration of questions that arise natu rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And in the last chapter we provide what is missing from Euclid's treatment of the five Platonic solids in Book XIII of the Elements. For a one-semester course such as I teach, Chapters 1 and 2 form the core material, which takes six to eight weeks. 544 pp. Englisch. N° de réf. du vendeur 9781441931450
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Geometry: Euclid and Beyond (Undergraduate Texts in Mathematics)
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Geometry: Euclid and Beyond
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Geometrv
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Geometry: Euclid and Beyond
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Springer New York, 2010
ISBN 10 : 1441931457
ISBN 13 : 9781441931450
Neuf
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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid s Elements leads to a critical discussion and rigorous modern treatment of Euclid s geometry and its more rec. N° de réf. du vendeur 4173602
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