# A Course in Galois Theory

## D. J. H. Garling

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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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Recensione:

"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

Contenuti:

Preface; Part I. Algebraic Preliminaries: 1. Groups, fields and vector spaces; 2. The axiom of choice, and Zorn's lemma; 3. Rings; Part II. The Theory of Fields, and Galois Theory: 4. Field extensions; 5. Tests for irreducibility; 6. Ruler-and-compass constructions; 7. Splitting fields; 8. The algebraic closure of a field; 9. Normal extensions; 10. Separability; 11. Automorphisms and fixed fields; 12. Finite fields; 13. The theorem of the primative element; 14. Cubics and quartics; 15. Roots of unity; 16. Cyclic extensions; 17. Solution by radicals; 18. Transcendental elements and algebraic independence; 19. Some further topics; 20. The calculation of Galois groups; Index.

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## 1.A Course in Galois Theory

Editore: Cambridge University Press 1986-12 (1986)
ISBN 10: 0521312493 ISBN 13: 9780521312493
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Descrizione libro Cambridge University Press 1986-12, 1986. Condizione libro: 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. Codice libro della libreria NU-LSI-06850654

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## 2.A Course in Galois Theory (Paperback)

Editore: CAMBRIDGE UNIVERSITY PRESS, United Kingdom (1987)
ISBN 10: 0521312493 ISBN 13: 9780521312493
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Descrizione libro CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 1987. Paperback. Condizione libro: New. 224 x 152 mm. 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. Codice libro della libreria AAV9780521312493

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## 3.A Course in Galois Theory (Paperback)

Editore: CAMBRIDGE UNIVERSITY PRESS, United Kingdom (1987)
ISBN 10: 0521312493 ISBN 13: 9780521312493
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Descrizione libro CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 1987. Paperback. Condizione libro: New. 224 x 152 mm. 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. Codice libro della libreria AAV9780521312493

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## 4.A Course in Galois Theory

Editore: Cambridge University Press (2016)
ISBN 10: 0521312493 ISBN 13: 9780521312493
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Descrizione libro Cambridge University Press, 2016. Paperback. Condizione libro: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Codice libro della libreria ria9780521312493_lsuk

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## 5.A Course in Galois Theory

Editore: Cambridge University Press (1987)
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Descrizione libro Cambridge University Press, 1987. PAP. Condizione libro: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria LQ-9780521312493

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## 6.A Course in Galois Theory

ISBN 10: 0521312493 ISBN 13: 9780521312493
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Descrizione libro 1987. Paperback. Condizione libro: NEW. 9780521312493 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0453627

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## 7.A Course in Galois Theory

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Descrizione libro Cambridge University Press, 1987. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria IQ-9780521312493

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## 8.A Course in Galois Theory

Editore: Cambridge University Press (1987)
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Descrizione libro Cambridge University Press, 1987. Paperback. Condizione libro: New. book. Codice libro della libreria 0521312493

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## 9.A Course in Galois Theory

Editore: Cambridge University Press (1987)
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Descrizione libro Cambridge University Press, 1987. Paperback. Condizione libro: New. Codice libro della libreria DADAX0521312493

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## 10.A Course in Galois Theory

Editore: Cambridge University Press (2017)
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Descrizione libro Cambridge University Press, 2017. Paperback. Condizione libro: New. This item is printed on demand. Codice libro della libreria 0521312493

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