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. The book has been read, but is in excellent condition. Pages are intact and not marred by notes or highlighting. The spine remains undamaged.

Codice articolo GOR006357867

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Dati bibliografici

Titolo: A Course in Galois Theory
Editore: Cambridge University Press, United Kingdom, Cambridge
Data di pubblicazione: 1987
Lingua: Inglese
ISBN 10: 0521312493
ISBN 13: 9780521312493
Rilegatura: Paperback
Condizione: Very Good
Peso: 322 grammi

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Riassunto

This textbook, based on lectures given over a period of years at Cambridge, is a detailed and thorough introduction to Galois theory.

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

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