Customer Reviews

Abstract Algebra: An Introduction

5 star:		(8)
4 star:		(4)
3 star:		(3)
2 star:		(1)
1 star:		(1)

 

 

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.

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.

NOTE: 2nd edition, 1996? has been published

The 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.

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).

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.

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.

If you're looking to gain experience in with algebra before you take a honors class or are just interested in self-study have some limited knowledge of the field, then Hungerford is the book for you! It is clear, concise, and there is a plethora of problems that range from computational to challenging. Even if you have a very limited background, the appendix provides a great reference for anyone.

If you're using a book such as Herstein's Topics In Algebra, this provides a great supplement, since you can practice in the easier problems and then be prepared to tackle Herstein's more difficult problems.

I have already had abstract algebra with Gallian and I got an A. Nonetheless, I wanted a different point of view and I heard good things about Hungerford's book from the reviews on amazon. I bought the book and I was not disappointed. I like Gallian but I love Hungerford. Hungerford's proofs are better than Gallian's in my opinion. He develops modular arithmetic completely in terms of sets. The book is elementary but the author does not shy away from defining concepts and proving theorems. Another advantage of Hungerford over Gallian is that Hungerford lets you know when he is going to change his notation. For example, [5] is not really 5, but Hungerford makes this change because so many authors use it. He tells you when he makes this transition. Gallian leaves you hanging in this regard. My review mainly concerns the first part of the book.

Hungerford introduces you first to the integers and modular arithmetic. This makes sense because many the ideas presented later in the book draw from these initial topics. He then introduces the concept of a field and gives plenty of examples. The exposition is clear and detailed. Hungerford does not take notorious leaps of faith, which is a welcome change. The problem sets are very workable and informative. I found that even the hardest problems can be solved with time and thought. You should do them because they reinforce the ideas and help you remember the theorems. I like the fact that Hungerford introduces fields first. In doing so, Hungerford allows the reader to quickly get to some of the interesting details about fields without getting bogged down with groups. Note that some of the problems that seem hard become crystal clear when you find out that they follow immediately from previous theorems. Hungerford teaches you to use prior results to make a potentially hard problem an easy one. I like this approach. Extension fields are fascinating and are covered beautifully. The same is true for polynomials, ideals, quotient rings, congruence classes, etc.

A word of honesty is in order. I have read 1-6 and done all the problems. I have skimmed the rest of the book. I will keep you posted. I have done half of Chapter 7 and it is awesome. I ran out of time but I plan to resume reading when I am able.

The only warning I would issue is that the reader should be familiar with induction/strong induction and some the very basic ideas of set theory, such as union and intersection. Also, the reader should have seen some of the ideas of basic logic, such as proof by contradiction, contra-positive statements, etc. This will help with some the "proceeding in this fashion" proofs. Again, these obstacles are minor.

Loved this subject and the book, it has clear proofs and plenty of descriptions of concepts, and it works from the very beginning and builds on itself. I would reccomend it. It is an expensive book, but I got it for a much better price here on amazon, I think it was less than half of what they were asking at the UCLA bookstore. I will certainly be buying my textbooks here from now on.

This is a great introduction to abstract algebra. I really like this book and it goes through examples and proofs enough for you to understand even if you have to go back over them again. I have used this book in my undergraduate studies. I highly recommend it and Hungerford's approach is different from most modern algebra texts because he introduces ring theory before group theory. Even if this book is not your text and I am sure it would be good help as a supplementary one. It even has solutions, answers or hints to some of the odd numbered exercises. This book will really get you to understand modern algebra if you take the time.