Field and Galois Theory (Graduate Texts in Mathematics Book 167) 1st Edition by Patrick Morandi (PDF)

Description

In the fall of 1990, I taught Math 581 at New Mexico State University for the first time. This course on field theory is the first semester of the year-long graduate algebra course here at NMSU. In the back of my mind, I thought it would be nice someday to write a book on field theory, one of my favorite mathematical subjects, and I wrote a crude form of lecture notes that semester. Those notes sat undisturbed for three years until late in 1993 when I finally made the decision to turn the notes into a book. The notes were greatly expanded and rewritten, and they were in a form sufficient to be used as the text for Math 581 when I taught it again in the fall of 1994. Part of my desire to write a textbook was due to the nonstandard format of our graduate algebra sequence. The first semester of our sequence is field theory. Our graduate students generally pick up group and ring theory in a senior-level course prior to taking field theory. Since we start with field theory, we would have to jump into the middle of most graduate algebra textbooks. This can make reading the text difficult by not knowing what the author did before the field theory chapters. Therefore, a book devoted to field theory is desirable for us as a text. While there are a number of field theory books around, most of these were less complete than I wanted.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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 has to be my favorite Galois theory book. The proofs are very smooth and clear, and so the book is perfect for a first graduate (or even undergraduate) course on the subject. On the other hand, there are several advanced topics that can’t be found in other beginning Galois theory books (such as infinite and transcendental extensions), which make the book an excellent reference.

⭐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.

⭐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.

⭐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.

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