A course in galois theory

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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 po...
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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.
Uitgever Cambridge University Press
Druk 1
ISBN/EAN 9780521312493
Auteur Garling, D.J.H.
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