Galois Theory (Universitext)

Rating:
Summary: Classical "Artin's" Galois theory
Review: From the definition of a conmutative ring to the fundamental theorem to solvability of equations by radicals in 65 pages, 80 theorems and 106 exercises. The exposition, wich follows the now classical tradition of "Artin's" Galois theory, is quite efficient, packing much material in a limited number of pages. The greatest asset of this book is its nice selection of topics, focusing on the fundamental theorem of Galois theory and its application to solbability of equations by radicals, but pausing to make excursions to finite fields or to work out explicitly some iluminating examples. The style is no-nonsense, crisp but nop hurried. The final 40 pages consist of appendices discussing group theory, ruler an compass constructions and old-fashioned Galois theory. This latter appendix deserves special mention, since it is not customary for a textbook of this size and scope to include such a detailed sketch of the historical motivations behind the theory it describes. One can only agree with the author when he wonders how such thoughts occurred to Galois in the late 1820's, and be grateful to him for providing his reader with material for an answer.

Rating:
Summary: Sweet and Concise
Review: I used this book as my course text book in my Galois Theory course in my undergraduate. It is pretty self-contained, so even if you forget some of Group and Fields Theory, you will still find it very readable. The little book guides to the Great Theorem by Galois (f is solvable by radical if and only if Gal(f/Q) is solvable) by breaking it into many nice sections. A drawback of this book is that some proofs at the end are omitted because they are put as execrises! Also, bear in mind that this book focus in Q and R (rational and real numbers) field only. In any case, I still recommend this book because it is sweet and concise, for which I can read it like a novel!

Rating:
Summary: Good Reference
Review: This text serves as a good reference, however, it is not necessarily well-suited for self-learning. The exercise sets need some revamping.