Customer Reviews

Field and Galois Theory (Graduate Texts in Mathematics) (v. 167)

5 star:		(2)
4 star:		(1)
3 star:		(1)
2 star:		(0)
1 star:		(0)

 

 

This book provides a lot of examples to demonstrate the theorems in the book. So you can understand the theorems without much difficulty. Besides, the author gave many details of the proofs in this book. Although it may hurt the concisity of the book, for the begginers, it is very useful.

This is a nice book that introduce the reader in a nicely way to Galois and Field theory. This book not only concentrate in the classic topics but also covers so much about areas not covered in other books. For example the topics of normality and separibility and pure separability are very well covered and the concepts of infinite extensions; among many others. This books also contains a nice feature and is tons of examples and exercises. Definitely a very good book. I took the course of Galois Theory with this text and I learned a lot.

Since other reviewers have not mentioned about the index of the book, I would like to add this: do not use this book if you are among the people who make an extensive use of index. The indes of this book is in the state of frustrating chaos, being disastrously flawed hence completely unusable. I suspect the proofreader was sleeping when reading the draft. As the content covers many topics in a leisurely, detailed and easy-to-read fashion, I really regret that the quality of the index terribly mars the real value of this book.

This book is really about field extensions, Galois or otherwise. The book is understandable for someone with a modest background in abstract algebra (like me), particularly, if the appendices are read first. Only the very few chapters where topology is used are difficult if one only knows about topology what is written in the relevant appendix.
The proofs are generally "just right": Not too easy, but also not too hard.

Many examples show, what is "meant" by the notations introduced.
I found chapter 15: "Ruler and Compass Constructions" particularly interesting and well written.

The book has a fair number of misprints, most -but not all- of them quite harmless. These misprints are even found in the index as one reviewer also noted.

All in all this is a very good introduction to the subject I think.