ISBN0030105595

I agree with what the other previous reviewers have mentioned: that this is a clear, readable text with lots of helpful examples and problems. Note, again, that rings are developed before groups. Having taught a course using this text as an additional resource, I do have one small issue with it. It seems that an inordinate number of problems require the results of a previous problem (or two) to construct the proof. So, if you are an instructor, pick your assignments carefully. If you are a student, look to previously-proven results from problems you may (or may not!) have been assigned to help you if you are stuck on a problem. All in all, this text provides a bit gentler approach to the material than Herstein's classic work Topics in Algebra, yet is nonetheless faithful to mathematical rigor. It also includes a nice array of interesting topics which augment the standard aspects of the subject matter.

This text was my first exposure to the beauty of Algebra and as my first text I must pay respect to Hungerford for his excellent, original and well written book. Hungerford has an uncany nack for presenting material in a straight-forward and consistent manner as well as providing a rich graded (i.e. they ascend in difficulty) section of exercises that, yes, do depend upon prior results. This dependence does not in any way limit the quality of the book since, such inter-connected-ness shows how certain seemingly un-related aspects are indeed related and, moreover, if you are using this text and have not noticed that this theme is prevalent throughout the book, then you may want to stop and take a closer look. Hungerford begins with the familiar integers, their basic number-theoretic properties and then uses these ideas, suitably abstracted, to introduce operations on and within rings all the while reminding the reader of the similarities. Only after an introduction to rings, their ideals and ring homomorphisms does Hungerford give the reader a glimpse of groups and their basic properties, again reminding the reader along the way how these operations are generalizations of the previous and more familiar operations. Now, the approach of Hungerford in this introductory text is definitely non-traditional since he introduces rings before groups and for some this may be a problem, why I am not sure, but it is pedagogically sound. Remember that in this day and age of American academia that most students have had very little exposure to rigorous mathematics and hence for the sake of most undergraduate students it is important to continually progress from the more familiar and less abstract (integers) to the less familiar and much more abstract (groups). Another positive aspect of this text is the inclusion of an appendix in which solutions and or hints to selected problems is contained, this feature is, again, beneficial to the student. As for those that require a student solutions manual, well my only comment to you is find another major that requires less work and or brain-power. Mathematics is about discovery, patience, persistence and truck-loads of hard work, which is partially realized as a direct result of struggling through difficult, challenging and often self-referential problems. Again, in defense of this book and the author, consider the following fact, Hungerford received his Ph. D under the direction of the legendary Saunders MacLane, so if you are at all familiar with the name then you should be familiar with his standards and hence should expect nothing less from the work of Hungerford. Thus, this book, aside from the ridiculous price, is a great introduction to abstract modern algebra. As for the negative side of this text, aside from what I have already mentioned, this book can be much too wordy and contains entirely too many examples for my tastes but these are petty and trivial. So what are you waiting for buy it (used).

This was the text used in both semesters of my undergrad algebra and I was really disappointed in it. The sequence we used was to start with rings and then into fields. During the first semester the instructor did an excellent job in making up for shortcomings in the text. The second semester (group theory) was a complete loss as I had both a bad text and a bad instructor. Joseph Rotman writes a FAR better algebra text, especially on the topic of group theory. I study algebraic topology and thank GOD everyday for Rotman!

I bought this book because I was having such a difficult time with a similar book by Serge Lang, Undergraduate Algebra, and I needed to pass the course I was taking. This book did help. It was more understandable. Lang's book has no answers to exercises and this book has "selected odd-numbered" answers which, while better than nothing, was still not enough. This book sometimes omitted proofs by leaving them to the reader, but not nearly as much as Lang's book. It would also be better if this book followed the normal convention of presenting Groups then Rings instead of the other way around.

While most books start by introducing group theory, Hungerford's text begins with Rings. The general hypothesis is that if you can learn rings, you already know a lot about groups which should make that section go more quickly. I'm not really sure how true that is, so I'll leave that issue alone.

My instructor and I had talked about this book before class started. She hadn't taught algebra in this order before, and had some concerns about changing her usual plan. I can't really say how well this plan did or did not work. The book uses mod spaces (clock arithmetic) as a gentle example introduction to the topic, which I personally found confusing. Generally speaking, once we got past the first 2 chapters the rest of the text was very clear. The initial two (theory of mod spaces, applicable theorems, and division algorithm)were somewhat difficult because I had no general basis against which to understand what I was doing. Once rings, fields, and integral domains were introduced the material we had started with (mod spaces) became much more clear...although after the fact.

Generally speaking, though, the text isn't bad. I have qualms with the order in which it introduces material (namely, introducing examples then trying to generalize from them felt very awkward for this material. I would have preferred to see the theory THEN the examples), but not to the extent that I would recommend against using the text. In terms of difficulty and clarity of the material presented, I didn't find it any more or less difficult or clear than other texts I've seen.