A Book of Abstract Algebra: Second Edition

This is the best Abstract Algebra for someone that has no idea of what the subject is about. The learner only need "mathematical maturity" and proof and logic knowledge. Amazing book. I bought it at Amazon for $20 while I could have got a new book for $17. A was ignorant. Again, I cannot recommend this book enough. After finishing this book, it would be a good idea to Michael Artin or Dummit & Foote books. I think Artin's book is better.

Pinter writes a book the rest of us non-mathematical geniuses can understand. The book aims for the average higher level math student in group and field theory. I used it to supplement a college course in this area returning after 25 years out of college. The book is broken into nice, short chapters that progress well. A little light on isometries in R2 and a supplement with answers would be nice. The earlier editions are just as valid and much cheaper. This stuff hasn't changed much in a century or two.

Pinter's book compares very favorably to other elementary treatments, such as Gallian or Birkhoff+Maclane. The author has intentionally deviated from the established modern writing style in mathematics texts (theorem...proof...theorem...proof...), presenting instead an eminently readable work of mathematical prose which can be understood by any conscientious ninth-grader. Pinter's straightforward proofs of "Cayley's theorem" and the so-called "Fundamental Homomorphism Theorem" alone justify the purchase. This relaxed and readable style notwithstanding, a suitable level of rigor has been maintained throughout the text---which is fairly complete in its coverage of elementary topics. From basic group theory and ring theory to field extensions and Galois theory, many minor, auxiliary results are left as exercises to aid the student's facility in proof technique, while the important major results are explained in the most natural way possible. Most importantly, Pinter's book would serve as an excellent second reference for those students approaching the daunting subject with another text. Once you've read Pinter, you can read just about any other text on the subject and immediately grasp. For this reason, it IS the best "first course" text, as previously stated. I consider it a masterpiece in its genre.

The author does a good job of motivating the discussion, by describing how the next few pages relate to other areas of mathematics. The issue of motivation is extremely important; too many authors develop a very abstract view, and fail to properly motivate the student by providing an overview of the subject area.

All the material presented in this book is presented beautifully. All concepts are perfectly clear. It is definitely the best "first course in algebra" book I have ever seen. The problems are also great too.