Customer Reviews

A Book of Abstract Algebra

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

 

 

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.

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.

This is perhaps the best textbook I've ever seen on any subject. It is extraordinarily easy to follow, yet very rigorous; it is an excellent self-contained course on group theory starting from an introduction to the topic all the way to Galois theory. The book is broken down into 33 bite-sized chapters with plenty of very good exercises at the end of each one (the only way to really learn a topic like this). In each chapter these exercises range from simple play-with-the-definition types to those that illustrate much deeper concepts. It is one of the few math books that even an imperfect student could probably successfully learn from very well, entirely on his/her own.

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.

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.

I am only giving it two stars because it is way over-priced. As a means of getting introduced to Abstract Algebra is really good. I also know that there are other sources that are also good. For one look at Groups and their Graphs by Israel Grossman. It is not as extensive as Pinter's, but will give you a great running start at this subject at a small fraction of the cost. Also try web resources, or your local university library.