This is a cute little book that guides the reader into Galois theory starting all the way from the review of linear algebra and polynomial rings over fields and progressing all the way to the Fundamental theorem. There are moreover many nice sections on Finite fields, Noether equations, Kummer extensions and as a final chapter the application to solvability by radicals of a general polynomial and the ruler and compass constructions. So the book is pretty self-contained and contains lots of good stuff. Also, Artin has a knack of giving very down-to-earth proofs that could be characterized as computational (rather than conceptual). It depends on everyone's preference whether they like this approach but for me it was very refreshing change of pace (compared to abstract and ofter almost magical proofs e.g. from commutative algebra).
In any case, patient reader will walk away from this book with a feeling of having built the subject from the ground up.
Nevertheless, I can't give it 5 stars because the book is very lacking in exercises. There are some applications scattered here and there (e.g. on symmetric extensions of function fields and on symmetric functions) but this is hopelessly insufficient to solidify the knowledge gained from the theorems. To properly understand Galois theory one needs to get their hands dirty by investigating splitting fields and Galois groups of all kinds of polynomials and paying close attention to the interaction of roots and group actions. In this regard the book leaves the reader completely on their own and so should be complemented by some additional source of exercices.
- Paperback: 98 pages
- Publisher: Dover Publications; 2nd Revised ed. edition (10 July 1997)
- Language: English
- ISBN-10: 0486623424
- ISBN-13: 978-0486623429
- Product Dimensions: 14 x 0.5 x 21.6 cm
- Boxed-product Weight: 118 g
- Average Customer Review: Be the first to review this item
- Amazon Bestsellers Rank: 207,418 in Books (See Top 100 in Books)