Rings, Fields, and Vector Spaces: An Introduction to Abstract Algebra via Geometric Constructibility (Undergraduate Texts in Mathematics)

I used this book for two classes and found it to be tremendously helpful. In both cases, it was a supplement to the required text. First, in my Foundations of Higher Mathematics course, I found it to be an excellent resource for understanding some of the basic concepts of divisibility in integers, gcds, primes and the Fundamental Theorem of Arithmetic. When first learning to understand and write proofs, one must have good understanding of the basic material. B. A. Sethuraman leaves no stone unturned when it comes to this. The text helps you learn how to learn mathematics, and this can easily translate into better proof writing.Next, I found the book to be a valuable supplement to Algebra: Abstract and Concrete by Frederick M. Goodman, used in my Elementary Modern Algebra course. The explanations of rings and fields were excellent, but beyond this is a book replete with examples. When first discovering abstract algebra, one can never have too many examples!This book is a beautiful combination of close attention to details, without being pedantic, as well as a broad overview of abstract algebra. I highly recommend it for all beginning math majors and aspiring math teachers!

This book is aimed to prospected High School teachers. The author's main area of study is Algebra. I would not recommend this book to someone looking for rigorous mathematics."Rings, Fields, and Vector Spaces" is a detailed book so much that I found myself lost while following proofs. This book is also outdated and is sold as quick-xeroxed copies at the bookstore of California State University Northridge for the price of about $12. I would recommend the newest edition along with "Introduction to Abstract Algebra" by Neal H. McCoy.