Abstract Algebra with GAP. Contemporary Abstract Algebra 7th EDITION. Ment the textbook Contemporary Abstract Algebra' by Joseph A. CONTEMPORARY ABSTRACT ALGEBRA, EIGHTH EDITION provides a solid introduction to the traditional topics in abstract algebra.

I knew I was going to at least smile when I read this book because of the fact that Gallian uses Beatles' song lyrics to open some of his chapters. But, I was concerned about the mathematical content. Those fears were put to rest basically the minute I turned the first page. His clarity in stating and proving theorems as well as providing NUMEROUS concrete examples (over 20 in the introductory group chapter alone!) at every point in your algebraic journey make this book a terrific read. He's also willing to go back and review a previous theorem or example if it illustrates a point; another excellent feature.

Not only that, but his problems are well-chosen; not only are there so many of them, but there are 'warm-up' problems to get your hands dirty right away and test your understanding of the basics, followed by some harder problems and some very interesting (i.e., difficult!) problems in each section. He also includes supplementary problems to get you to extend your understanding with new groups, definitions, etc. Whenever I get confused about anything in algebra, I can usually turn to Gallian to help me out.

Some have complained about the emphasis on group theory as opposed to ring/field theory. I don't see this as a hindrance, but rather as an advantage because, in a first algebra course, I feel learning the ins and outs of group theory as detailed as possible makes one really ready to study rings, fields, modules, etc. And then go back and say, 'Hey! This isn't so hard; it's just like (blah) with groups!' You also get the advantage of having selected answers and hints in the back to check your work along the way as well as more advanced topics like the beginnings of Galois Theory, crystal and frieze groups, symmetry groups, etc.

The book, regrettably, is missing a detailed treatment on group actions (though you do use them throughout, just not calling them that! Chopin Polonaise In A Flat Major. ) and some advanced linear algebra, but this is not enough for me to downgrade the book! For a book its size, it packs a lot of information and, in fact, I can't think of a single grad student in my department who either doesn't have a copy of the book or has at least looked at it when doing homework; it is really THAT good! Thanks, Gallian! This book is more than a find --- it's a treasure chest.

Gallian does more for the reader than just throwing a bunch of theory at them and laughing as the reader struggles to understand proofs and apply them himself; he provides a multitude of examples. And by a multitude, I don't mean three or four comprehensive examples per chapter: I mean three or four *per proof*. And often Gallian steps back a moment to discuss the proof or theorem he just outlaid in more conceptual terms, sometimes just as good as an example. The book is a delight, and absolutely perfect for the independent learner. Gallian gives a good background on integers, modular arithmetic, induction and the like in his chapter 0, and then eases his way into group theory in the next two chapters. He goes on to then concentrate on the most important forms of group the student will use, taking him through subgroups, cyclic groups, and permutation groups. Then he outlines some of the most important tools the reader will use when he's trying to deduce the properties and structure of a groups, like isomorphisms, cosets and Lagrange's Theorem, external and internal direct products, normal subgroups and factors groups, and homomorphisms.