A Course in Galois Theory

A Course in Galois Theory
- Used Book in Good Condition
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.
Country USA
Brand Cambridge University Press
Manufacturer Cambridge University Press
Binding Paperback
ItemPartNumber illustrations, index
ReleaseDate 1987-01-30
UnitCount 1
EANs 9780521312493

Country	USA
Brand	Cambridge University Press
Manufacturer	Cambridge University Press
Binding	Paperback
ItemPartNumber	illustrations, index
ReleaseDate	1987-01-30
UnitCount	1
EANs	9780521312493

A Course in Galois Theory

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