Rating: 
Summary: Very readable text, but problems often self-referential
Review: 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.
Rating: 
Summary: Overall a good mathematics book
Review: If you've already taken some undergrad courses in number theory, discrete mathematics, or linear algebra, then you'd be more than enough prepared to go through this book on your own. It's highly readable, and the problems aren't that hard to solve. He also breaks up the problems in 3 sets with the last being the hardest. There is also an appendix that helps refresh basic concepts of proof, logic, and set theory. Reading through the appendix is enough to prepare anyone that has taken calculus for the material in the book. My only complain is that there is no student solutions manual.
Rating:
Summary: Overall a good mathematics book
Review: If you've already taken some undergrad courses in number theory, discrete mathematics, or linear algebra, then you'd be more than enough prepared to go through this book on your own. It's highly readable, and the problems aren't that hard to solve. He also breaks up the problems in 3 sets with the last being the hardest. There is also an appendix that helps refresh basic concepts of proof, logic, and set theory. Reading through the appendix is enough to prepare anyone that has taken calculus for the material in the book. My only complain is that there is no student solutions manual.
Rating:
Summary: A great text for an introductory course.
Review: NOTE: 2nd edition, 1996? has been publishedThe author presents a very readable text for someone entering the world of modern algebra. At times, it almost appears to read like a high school text; that may be a bit of an exaggeration, but the comment is meant to convey the clarity and simplicity that Hungerford strives for. Likewise, his examples are often illuminating and thought provoking. But make no mistake, this text provides a very thorough coverage of abstract algebra. There are numerous exercises which are graded A,B, & C according to difficulty. Some solutions are provided. The content is typical of most intro algebra texts. Though, his approach is not quite along traditional lines; he presents ring theory before group theory, and makes a good case for doing so. Toward the end of the text, there is material on applications as well as advanced topics leading up to Galois theory.
Rating: 
Summary: Student Solution Manual
Review: This book should be accompanied by a student solution manual, with full solutions to every odd question. Is frustating not being able to do some of the proofs.
Rating:
Summary: Very readable text, but problems often self-referential
Review: This is a good book for an introductory course in Abstract Algebra.The subject is slowly introduced with clear examples and a good set of problems.The problems are sorted based on the difficulty level starting with the easiest and going to a bit harder problems.The 5 minus 1 rating is for the fact that you will enjoy doing these problems *with a good guide*.Its better you have a good guide to check if you are on the right track.Otherwise its an excellent text book that lays a strong foundation of Abstract Algebra.
Rating:
Summary: A good TEXTBOOK
Review: This is a good book for an introductory course in Abstract Algebra.The subject is slowly introduced with clear examples and a good set of problems.The problems are sorted based on the difficulty level starting with the easiest and going to a bit harder problems.The 5 minus 1 rating is for the fact that you will enjoy doing these problems *with a good guide*.Its better you have a good guide to check if you are on the right track.Otherwise its an excellent text book that lays a strong foundation of Abstract Algebra.
Rating:
Summary: A worthwhile pain in the....
Review: 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).
Rating:
Summary: A worthwhile pain in the....
Review: 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).
Rating: 
Summary: Not the best book for undergrads....
Review: 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!
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