A Course in Galois Theory

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9780521312493: A Course in Galois Theory

Galois theory is one of the most beautiful branches of mathematics. By synthesising the techniques of group theory and field theory it provides a complete answer to the problem of the solubility of polynomials by radicals: that is, the problem of determining when and how a polynomial equation can be solved by repeatedly extracting roots and using elementary algebraic operations. This textbook, based on lectures given over a period of years at Cambridge, is a detailed and thorough introduction to the subject. The work begins with an elementary discussion of groups, fields and vector spaces, and then leads the reader through such topics as rings, extension fields, ruler-and-compass constructions, to automorphisms and the Galois correspondence. By these means, the problem of the solubility of polynomials by radicals is answered; in particular it is shown that not every quintic equation can be solved by radicals. Throughout, Dr Garling presents the subject not as something closed, but as one with many applications. In the final chapters, he discusses further topics, such as transcendence and the calculation of Galois groups, which indicate that there are many questions still to be answered. The reader is assumed to have no previous knowledge of Galois theory. Some experience of modern algebra is helpful, so that the book is suitable for undergraduates in their second or final years. There are over 200 exercises which provide a stimulating challenge to the reader.

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"This is a marvellous little book. It is characterized by good mathematical taste, plain and elegant language, and an earthy but precise style." Carl Riehm, Mathematical Reviews

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D. J. H. Garling
Editorial: Cambridge University Press (1987)
ISBN 10: 0521312493 ISBN 13: 9780521312493
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Descripción Cambridge University Press, 1987. Paperback. Estado de conservación: New. A Course in Galois Theory Brand new item sourced directly from publisher. Packed securely in tight packaging to ensure no damage. Shipped from warehouse on same/next day basis. Nº de ref. de la librería 1111-9780521312493

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Garling, D. J. H.
Editorial: Cambridge University Press 1986-12 (1986)
ISBN 10: 0521312493 ISBN 13: 9780521312493
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Descripción Cambridge University Press 1986-12, 1986. Estado de conservación: New. This item is printed on demand. Brand new book, sourced directly from publisher. Dispatch time is 24-48 hours from our warehouse. Book will be sent in robust, secure packaging to ensure it reaches you securely. Nº de ref. de la librería NU-LSI-06850654

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Garling, D. J. H.
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Descripción Cambridge University Press, 2016. Paperback. Estado de conservación: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Nº de ref. de la librería ria9780521312493_lsuk

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D. J. H. Garling
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Descripción CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 1987. Paperback. Estado de conservación: New. Language: English . Brand New Book ***** Print on Demand *****. Galois theory is one of the most beautiful branches of mathematics. By synthesising the techniques of group theory and field theory it provides a complete answer to the problem of the solubility of polynomials by radicals: that is, the problem of determining when and how a polynomial equation can be solved by repeatedly extracting roots and using elementary algebraic operations. This textbook, based on lectures given over a period of years at Cambridge, is a detailed and thorough introduction to the subject. The work begins with an elementary discussion of groups, fields and vector spaces, and then leads the reader through such topics as rings, extension fields, ruler-and-compass constructions, to automorphisms and the Galois correspondence. By these means, the problem of the solubility of polynomials by radicals is answered; in particular it is shown that not every quintic equation can be solved by radicals. Throughout, Dr Garling presents the subject not as something closed, but as one with many applications. In the final chapters, he discusses further topics, such as transcendence and the calculation of Galois groups, which indicate that there are many questions still to be answered. The reader is assumed to have no previous knowledge of Galois theory. Some experience of modern algebra is helpful, so that the book is suitable for undergraduates in their second or final years. There are over 200 exercises which provide a stimulating challenge to the reader. Nº de ref. de la librería AAV9780521312493

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D. J. H. Garling
Editorial: CAMBRIDGE UNIVERSITY PRESS, United Kingdom (1987)
ISBN 10: 0521312493 ISBN 13: 9780521312493
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Descripción CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 1987. Paperback. Estado de conservación: New. Language: English . Brand New Book ***** Print on Demand *****.Galois theory is one of the most beautiful branches of mathematics. By synthesising the techniques of group theory and field theory it provides a complete answer to the problem of the solubility of polynomials by radicals: that is, the problem of determining when and how a polynomial equation can be solved by repeatedly extracting roots and using elementary algebraic operations. This textbook, based on lectures given over a period of years at Cambridge, is a detailed and thorough introduction to the subject. The work begins with an elementary discussion of groups, fields and vector spaces, and then leads the reader through such topics as rings, extension fields, ruler-and-compass constructions, to automorphisms and the Galois correspondence. By these means, the problem of the solubility of polynomials by radicals is answered; in particular it is shown that not every quintic equation can be solved by radicals. Throughout, Dr Garling presents the subject not as something closed, but as one with many applications. In the final chapters, he discusses further topics, such as transcendence and the calculation of Galois groups, which indicate that there are many questions still to be answered. The reader is assumed to have no previous knowledge of Galois theory. Some experience of modern algebra is helpful, so that the book is suitable for undergraduates in their second or final years. There are over 200 exercises which provide a stimulating challenge to the reader. Nº de ref. de la librería AAV9780521312493

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Garling, D. J. H.
Editorial: Cambridge University Press (1987)
ISBN 10: 0521312493 ISBN 13: 9780521312493
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Descripción Cambridge University Press, 1987. PAP. Estado de conservación: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. de la librería LQ-9780521312493

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Garling, D. J. H.
Editorial: Cambridge Univ Pr (1987)
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Descripción Cambridge Univ Pr, 1987. Paperback. Estado de conservación: Brand New. 176 pages. 9.00x6.00x0.25 inches. In Stock. Nº de ref. de la librería __0521312493

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Garling, D. J. H.
Editorial: Cambridge University Press (1987)
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Descripción Cambridge University Press, 1987. PAP. Estado de conservación: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. de la librería IQ-9780521312493

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D. J. H. GARLING
ISBN 10: 0521312493 ISBN 13: 9780521312493
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Descripción 1987. Paperback. Estado de conservación: NEW. 9780521312493 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Nº de ref. de la librería HTANDREE0453627

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Garling, D. J. H.
Editorial: Cambridge University Press
ISBN 10: 0521312493 ISBN 13: 9780521312493
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Descripción Cambridge University Press. PAPERBACK. Estado de conservación: New. 0521312493 New Condition. Nº de ref. de la librería NEW7.0205580

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