Contemporary 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!) 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!

Gallian's algebra book is an excellent first course. It provides an inviting and clear introduction to abstract mathematics. Though not a rigorous, encyclopedic work like my own, it offers a fresh, friendly, and approachable style that will appeal to students from a wide variety of backgrounds. And if you aren't captured by the mathematics, the many Beatles references and other well placed quotes will still make this book a delight to read.

I used this book for my Abstract Algebra course at Whitman College. It is genuinely fun and interesting to read. It has many interesting quotes and biographical sketches. The problems are just the right difficultly to be challenging but not frustratingly hard. One interesting thing is that the problem sets include computer application questions. Our class did not use these sections, but some of the problems looked interesting.I found the text to be well organized and understandable. Numerous examples are included which help for understanding abstract concepts. Neither my friends nor I have noticed any typographical errors. Theorems and corollaries are shaded in a blue background for ease of reference. Every time new notation is introduced, possible ambiguities are discussed. Also, possible confusions about new concepts and common mixups are addressed.I have only taken one semester of algebra at the current time, so have only used the first half of this book. I feel that it is one of the best textbooks I have used for a mathematics class.