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Title: A Course in Galois Theory
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Manufacturer: Cambridge University Press
List Price: $31.99
Our Price: $17.98
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| A Course in Galois Theory by Cambridge University Press Galois Theory in the British Didactic Style: a gem. | Anyone who has at least perused the works of Hardy, Dirac, Swinnerton-Dyer, or any of their suit will know what I mean. There is something unmistakable about this style: pithy, perhaps to a fault, but without any loss of charisma, these authors sacrifice conversational ease for surveyability and structural integrity. With this book, Garling takes a place in the rich British tradition of mathematical artistry.
This is a pretty short book, and while it covers somewhat more than bare-minimum (the ch. on transcendental extensions is unusually deep, for example) it does not aspire to as complete a coverage as something like Dummit and Foote would give. But while theirs is an excellent "standard reference" type text, Garling conveys as much about craftsmanship and mathematical aesthetic as he does about fields and galois groups. This matching of topic and style of course works incredibly well, and here again we find a rich tradition of beautiful exposition (*cough* Artin).
Of course, I shouldn't neglect to mention my favorite part of any text (endeavor?): the problems. Here again Garling displays excellent taste ("Remember that mathematics is not a spectator sport!"). His rule of thumb is to can the (sometimes) dozens of trivial problems commonly presented, opting rather for a choice few interesting and challenging ones. I certainly learn better from this approach - perhaps more importantly, I have a lot more fun. Mathematics is for those with unrealistic daring, tempered
by a dedication so extreme as to make the former at worst asymptotically realistic. Joshua James Wiley | | A Course in Galois Theory by Cambridge University Press Product Description | | 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. |
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