A Course in Galois Theory (1986) Front Cover Book Details Author D. J. H. Garling Genre Galois Theory Subject Galois theory Publication Date 1/30/87 Format Paperback (224 x 152 mm) Publisher Cambridge University Press Language English Editor Plot 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. Personal Details Collection Status In Collection Location TV ROOM Condition Near Mint Index 561 Owner Paulo Mendes Read It No Links Amazon US Amazon UK Barnes & Noble Powell's Collection # 00449H Product Details LoC Classification QA171.G277 1986 Dewey 512/.32 ISBN 0521312493 Edition 01 Printing 1 Country USA Cover Price $31.99 Nr of Pages 176 First Edition Yes Rare No Original Details Original Publication Year 1986 Notes Includes index.