Account Options Connexion. Version papier du livre. 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.

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Account Options Connexion. Version papier du livre. 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 exercises which provide a stimulating challenge to the reader. The axiom of choice and Zorns lemma. Automorphisms and fixed fields.

The theory of fields and Galois theory. Field extensions. Tests for irreducibility. Rulerandcompass constructions. Splitting fields. The algebraic closure of a field. Normal extensions. The theorem of the primitive element.

Cubics and quartics. Cyclic extensions. Solution by radicals. Transcendental elements and algebraic independence. Some further topics.

The calculation of Galois groups. Droits d'auteur. Informations bibliographiques. A Course in Galois Theory D. Garling Cambridge University Press , - pages 0 Avis Galois theory is one of the most beautiful branches of mathematics. Groups fields and vector spaces. Finite fields. Roots of unity. A Course in Galois Theory A course in.

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## B3.1 Galois Theory (2016-2017)

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.

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Would you like to tell us about a lower price? If you are a seller for this product, would you like to suggest updates through seller support? 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.

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