Reviews (27)

The book after Herstein
I think I would only recommend this book to someone who has already had some exposure to algebra (or one especially gifted in mathematics). The beginning of the book is not too bad, but towards the end of Part I the pace quickens quite a bit. If you are willing to read over the text many times, and do all of the non-trivial exercises (there is an impressive olla podrida of algebra in them, most of which are the beginnings of some very deep ideas), then it should be a very rewarding experience. Namely because this is one of the most readable textbooks which covers everything from groups, rings, and fields to homological algebra and algebraic geometry. It is very rare to see this much material covered in one book, and for it to remain so structured (Rotman is an example of a book that covers a lot of material, but loses its structure somewhere).

Excellent book
I am surprised that this book has not got the 5 stars. It is very suitable for advanced undergraduates/first-year graduates. The book is full of examples; and the proofs are amazingly clear and succinct. The book introduces new concepts in the excercises long before the student encounters them in the sections.

This is a beautiful way to teach mathemtatics,--and indeed to learn it. The book is replete with examples that connect concepts from toplogy and real analysis with Algebra.

This book definitely deserves the 5 STARS.

Comprehensive book
I'm a graduate student in math. We used this book for the basic year-long abstract algebra sequence: group theory, chapters 1-4 and some of chapter 5; ring/field/galois theory chapters 7-9, 13-14. Some of my fellow students took a module theory course which was at least partially based off chapters 10 and (I think) 11. I'm sure more advanced courses could easily be based off chapters 15-end. Considering the cost of university books, I consider it very nice to buy one book for essentially 3+ courses.

The exercises in some sections are very diverse. My group theory professor made us do a huge number of them, and now I am amazed at how often I see questions similar to those from Dummit-Foote show up on past qualifier exams from many different universities. Regarding lack of answers in the back...well, you shouldn't need too many, and if you get really stuck, that's what the professor is for. And if you're learning it on your own then I'm thinking you should be brainy enough not to need answers!

The text itself is very readable and complete.

I don't think I'd recommend this as an undergrad textbook, although I've no doubt that there are some clever undergrads who could learn from it. I used Herstein's "Topics in Algebra" for my intro-to-abstract course as an undergrad. Herstein is designed to be introductory in nature, though still a wonderful book, while DF is more encyclopedic.

Reviews (9)

Deceptively Wonderful
OK here's the truth:This book is an awful text when accompanied by not so great prof is teaching from it (e.g. one who delivers nothing but the text). BUT... once you begin to understand enough to know that the "trivial" "exercise" and "left to the reader" proofs are quite straightforward, the book is probably the best reference in Algebra you can hope for.

Well worth the read for any budding mathematician
I've been acquainted with several introductory graduate algebra
books over the years, and prefer this one for its coverage of all the fundamental areas (groups, modules, rings, linear algebra, fields, and category theory), being concise, and providing great care when outlining each proof.

If one compare's the amount of material in this book to Jacobson's "Basic Algebra Vol 1", Grove's "Algebra", or Herstein's "Abstract Algebra", Hungerford's book gets the nod.
Moreover, I much more prefer the concise definition, example, theorem, proof format over the more colloquial approach, as can be found in Jacobson's text. For me at least, the payoff for reading an algebra text is the beauty found in the logic and reasoning from which very profound results arise from the complex interaction and use of more straightforward ones. And this is exactly where Hungerford's book shines through in tremendous glory. When outlining a proof he does an outstanding job in citating the results from previous Chapters that are used. For me this is the strength of algebra (In geometry I cringe when I get a picture for proof, and in analysis it is often quite complicated to verify that a given situation possesses the appropriate conditions needed to invoke some famous lemma or theorem).

One last good word about this book: I found the exercises both in abundance (after each section) and quite reasonable for a first year grad. student. Happy reading.

The bee's knees
This book is the Basic Language of Mathematics (by J. J. Schaffer) of the Algebra world.Without doubt it is an excellent dictionary of general facts about algebra.But learning by it will leave one with at best amusing memories and a nervous twitch.Just for a taste, "This proof has two parts.The first is easy.The second is left to the reader."About half the proofs in the book go like this.And so at the end of each section, the reader is left with just the dry theorems to attempt the exercises, without the slightest idea of how problems of a certain type are actually proven or even approached.And oh, the exercises.A few are easy.A few are open problems.The rest in between seem to at one point have been at the core of someone's respective masters thesis.

This book has three genuinely good uses.If you have a doctorate in pure Mathematics, a respectable doctorate that has nothing to do with PDEs and the thesis for which took longer to write on paper then it did to format the pictures to fit the margins, and you want to look up how much of the ring structure of R is inherited by R[x] in under 3 minutes, then this book belongs on your shelf.

If you have taken at least two algebra courses at the graduate level (Real graduate, not graduate equivalent.Most of my Algebra I class had two pretty good undergrad algebra classes coming in, and got slaughtered by Hungerford), then this book can make for a good review of basic algebra you should already know.

Reviews (21)

Wedderburn, Waring and Hamilton
Not necessarily in that order.President McCosh of Princeton
waxes eloquent in his Scottish Philosophy book somewhere on
the internet, re: Dugald Stewart, Kant and Hamilton.

Hamilton is a strong vice, but clearly represented in Herstein.

Good Introduction, useful for self study
I am an engineer by training and a sales man by profession, with a a strong liking for mathematics.
I found this book to be an very readable introduction to a subject (abstract algebra), I had never been exposed to during my engineering math - other than matirx theory, which was obviously taught extensively.
The proofs are generally easy to understand, but certainly not trivial.
A pleasure to read

Reviews (19)

Medium-level Book: Use only as a supplemental
The last edition of this book was my first exposure to this amazing topic.My experiences with that edition, however, were not very favorable.The pedagogical style was Byzantine and not well laid out.Many key ideas of the text were introduced in the exercises and never fully developed in the main text itself.Despite being highly verbose at times, ironically little detail and clear exposition was given to illuminate either the motivation behind a topic or proof or such presentation in a succinct, clear fashion.Moreover, many of the key, standard notations used in modern abstract algebra were also blaring absent or hidden, again in the exercises instead of explicitly emphasizing them in the main body of the text.This in itself made for a less than ideal first exposure, which was made all the more complicated by our instructor Linda Chen (Ohio State University).She seemed barely familiar with the poor nature of the book, suggesting that we use Gallian or Artin as "supplemental" readings.I wish she had chosen Artin, a book of great clarity and maturity in both the treatment of the subject and the reader as well.Gallian, in contrast, was even more obtuse in being ever more verbose in the proofs compared to Fraleigh.Adding more to the confusion was the fact that Ms. Chen largely made up her own problems, which often proved flawed with errors that made some of the assignments outright intractable.She would assure us "this is a difficult subject and you'll need to spend more time with it."Apparently it is a difficult subject, so much so that she herself had problems with both mastering some of its subjects and teaching it to others.This was underscored dramatically when one of the students came a couple of minutes late to class and in the middle of her proceeding to explain how to solve one of her bogus problems.He sat there quietly and listen and then cleared his throat, gently interrupting her, stating that the problem was in fact unsolvable and the only thing you cold prove about it was that it was unsolvable.She then handed him the chalk incredulously to do just that.And he did, much to her red-faced embarrassment and our great amusement.I mention this not condemn Ms. Chen, but to offer sympathy to those that have had such similar experiences.All it not lost.Many, including some truly brilliant professors, have had similar problems in their undergraduate programs and didn't do so well the first run with this subject either.I truly didn't like this topic at first, but have now come to love it and am never disappointed in the freshness of its richness, finding it in a broad range of topics.This new edition of Fraleigh, seems a much greater improvement, but I would suggest it be used as a "supplemental" text.Instead Herstein, Artin, or Robinson should be used.Herstein and Robinson are much slimmer books, succinct, and the the exposition direct and clear.I learned in a couple of months more than I did in nearly nine months with Fraleigh and Ms. Chen. Yes, the subject is challenging, but far from insurmountable.If you have a less than enthusiastic and absent-minded professor that seems indifferent, do not let this be an obstacle to your learning either.Go buy these other books and use Fraleigh as a supplemental.Be consistent in setting time aside to read and do the problems of the text.Work as independently as possible and then go to group meetings-not the other way around, as is often told by instructors.I'm now a third year graduate student and focusing my work in algebraic topology-of all things!And I love it.This subject is a real gem and will doubtless never cease to impress you as you grow with it.Best wishes in your learning and educational endeavors.

Classic textbook
THE definitive text for introductory algebra classes, this book is a classic. And for good reason. It introduces each concept with solid examples and a lengthy discussion. There are always a few nice problems for each chapter, some of which provide meaningful results for later sections. One criticism of this book is that Fraleigh often assumes that the reader has completed all of the problems and forgoes explanation on many areas. Overall, he presents the material in a nice, clean package: perfect for a first course in abstract algebra.

Reviews (12)

A Bible for Linear Algebra
This is a holy bible for linear algebra beside P R Halmos(Finite dimensional vector spaces). I can assure you that if you understand this book, no one can teach you linear algebra no matter you go. Personally, I will rate this book 7 stars and 7 diamond. It is a superb. Buy and don't miss it. Add to your collection.

Best intro to linear algebra I've seen.
I simply loved this book.Hoffman and Kunze have written a very sturdy book that begins with the most basic concepts of linear algebra(such as echelon form) and goes through cannonical forms, inner product spaces, and Bilinear forms.The proofs are complete and at an appropriate level for a first look at the subject.Perhaps one of my favorite aspects of this book was the treatment of dual spaces and tensors.It seems many linear texts deal with one subject or the other but rarely do I see both subjects dealt with in the same book.

The only non-positive comment I would like to make about this book is that its beauty is not in its appearence.When you open the book and flip through the pages you feel a little uneasy.The typeset looks uninviting.Take heart!The beauty of the book lies in its content.Give it a thorough chance, and I don't think you will be disapointed

I highly recomend this book for both learning and reference.

Reviews (15)

Wonderful Abstract Text
This is possibly the most addictive Abstract Algebra book ever. Filled with a wonderful selection of problems, Gallian discusses many aspects of groups and rings in a way that is enjoyable to study. The love of mathematics that is shown in this book is reflected by how Gallian eloquently weaves principles of group and ring theory with beautifully selected INTRUIGING problems. I enjoyed this book more than any other math text I have had.

Great Book!
I'm in a 4th year group theory class and have found this book to be highly useful in learning my course material. It gives lots of proofs, lots of excercises with lots of theory and good explanations. I have no complaints!

Gallian's poor algebra book.
I agree with the other reviewers in the sense that it is ture Gallian's book is soft on theory and rigor, but oppositely I find this lack of real substance to be Gallian's deepest flaw. I give Gallian one star, basically for effort.

I divide my critique into the following subcategories:

Organization:

Gallian's book is organized well enough in the sense that he opens each chapter with some commentary about the problems to be studied, or motivation, and then proceeds to go example, theorem, proof, example, example, example, example,..., example. This doesn't work, I think, because he spends too little time actually showing theorems and proofs, and sometimes he'll build an entire chapter on just two or three theorems, and fill the rest with useless commentary (which I'll mention again below).

Readability:

As for readability, for people who read math books at all (i.e., those who study outside of class), this book should be a nightmare. If you were to strip away all of the useless commentary/endless biographical insets/weblinks you would be left with probably about 30 pages of theorems and cumbersome proofs (by cumbersome, I don't mean involved, I mean unrefined). Gallian has failed to make a readable text because he presumes to have the omnipotence and foresight required for putting a full understanding of algebra and algebra history into one book. As a result, the excess commentary he makes and useless statements (for example, "In high school, students study polynomials with integrer, rational, real, and sometimes complex coefficients") distract a reader from the main points, and I rarely found myself rubbing my chin thinking how insightful something he said was. All in all, I feel as though the reading felt "hoakie" at best--like he was elbowing me in the side, winking, trying to get me to lie and say I thought what he was saying was insightful.

Exercises:

The exercises are often clumsily put together and the quotes before each problem set can get extremely patronizing. I remember thinking how cocky this Gallian fellow must be to presume that people can't do "his" problems. A joke, to say the least. In any case, they seem fine for all purposes -- if you're going into chemistry or an applied science that uses group theory. It's very obvious that our author believes that group theory is the pinnacle of the algebra experience and struggles to present topics from rings and fields. IF you are someone who likes group theory, fine. BUT Artin's book does everything Gallian does and more with group theory and builds the same ideas on more solid footing, using linear algebra excessively throuhout the book. For example, if you think I'm joking about Gallian's weakness, just look at the chapters on isometries and compare them to the chapters in Artin, and you'll see what I'm talking about.

Peter Rabbit:

Well, I do have at least one nice thing to say. As anyone can see, Gallian has a lot of examples, but this seems to be the only redeeming quality of the book. But that alone doesn't make an algebra book.

Broad Commentary:

Reviews (6)

Symbolic computation
This book explains and illustrates the algorithms used by symbolic math packages such as Mathematica, Maple, CoCoA, MatLab, MuPAD,... to solve problems involving polynomials in many variables, and along theway teaches the elements of real algebraic geometry-- most mathematics texts concentrate on the complex-variable version. It is not just for undergraduates; electrical engineers, for instance, should see it.Lots of pictures!

Easiest introduction to Algebraic Geometry
This is the easiest introduction to algebraic geometry and commutative algebra, the authors had done a great job in writing a book that assume very little from the readers. To learn some algebraic geometry, you can either start with this book, or you can spend a year to read a lot of background materials in algebra and then go to a Graduate Text like Harris' book. Of course, if you want to be an expert in algebra, you eventually need a lot of background, what this book can help you is to offer you a quick start, much quicker than you would ever imagine.