Abstract Books

I saw this exhibit when it came to San Francisco's Palace of the Legion of Honor, and saw fit to buy the catalog two years later, it madde such an impact.

This is not a collection of Picasso's best or most famous work. Rather it collects unknown and semi-distinguished pieces all produced during the political upheaval of WWII. As such it tells the story of the occcupation of France through the perceptions of one artist who survived it, and transformed the experience for the world to see through his art.

While it gathers some curiosities, like developmental sketchs for the classic Guernica, the real star of this exhibit are lesser known classics like Night Fishing at Antibes.

Don't buy this for a general introduction to Picasso's art. Think of it as a kind of emotional history in pictures.

"Picasso and the War Years" surveys his art during his years of isolation in Occupied Paris, as well as the three years leading up to the cataclysm. Although several exhibitions have been held on this same subject in Europe, this is the first such survey of Picasso's wartime production to take place in the United States. A series of outstanding essays by several prominent critics explore the complex political, social, and personal circumstances which inspired these still-challenging paintings, and the initial reactions to them. A warning: this book is not for everyone. If you are disturbed by violent and harsh art, forget it. These images still retain their power to shock, disorient, disgust and sadden, even if sixty years have gone by since their creation. Yet all the pictures possess a deep geometric structure, formal balance, and intense affect which engraves them on the viewer's mind. The sorrowful, neurotic, and unforgettable face of Dora Maar, Picasso's mistress and model during these tragic years, is transformed in these paintings into a symbol of a world gone mad. This is definitely one of the most significant art books produced this year.

Beyond Brilliant. The Rothko Book: Tate Essential Artist Series is the most succinct exploration of the soul and embodiment of a true artist. Nothing I studied getting my MFA gave me the same profundity of an artist's journey into the creation of a new visual language. The struggles, investigations, successes and failures of the thought process as well as the physical prowess it takes to bring the vision of the artist to the appreciator of the art. Bravo to Bonnie Clearwater

Interesting historical material in the early part of the book. Lapses unduly into artspeak when discussing the later classical Rothko paintings.

There is a fantastic quality to the compliation of works in the Spiritual in Art, that indicates a profound understanding of the mystical forces of inspiration involved with the process of artistic endeavor. The book chronicles the exhibition of the same name organized by Maurice Truchman and Judi Freeman at the Los Angeles County Museum of Art. Many of the major artists of the 20th century are represented; Mondrian, Duchamps and Kandinsky to name a few. The ideosyncratic spin to the show lies in the examination of their work from a philospophical and spiritual standpoint that involves a more involved examination than is often given with the popular criticism styles of art history - ie; socio-political and aesthetic. With the aid of this book, the reader gleans a more profound understanding of the motivational forces at work in these artists whose creations transport viewers to new worlds and dimensions with only a glance.

I have owned this book for over twenty years and I never get tired of pouring over it again. It is an absolute treasure trove of information and is packed full of glorious illustrations- it's the one book I refuse to loan out. As an artist, this is the most important book in my collection.

Every wonder which state is the highest in residents who smoke? Or, criminal incidents in schools? Or, use of home computers? Statistical Abstracts has it all in there. It is THE source for backing up what you say with the "hard numbers"

Since 1878 the Statistical Abstract of the United States has been the single most popular source for statistics on the social, political and economic life of the nation.

The 1999 edition has over 1500 tables drawn from over 250 sources including 140 new tables covering many in-the-news topics such as cigarette use, firearms background (Brady Bill) checks and managed healthcare enrollment. Some other statistics in the news in the 1999 edition are: § School Violence § Community Recycling Programs § Use of Home Computers § Mutual Fund Ownership § Deforestation

The 1999 Statistical Abstract has twenty pages of tables with comparative statistics from the 20th century.

The Statistical Abstract includes Adobe® Acrobat Reader 4.0 to let you search the entire CD-ROM for a topic using keyword, phrase or full-text and print pages or sections that look just like they came from the printed edition.

You can download the data tables as Microsoft® Excel or Lotus® 1-2-3 spreadsheets and do your own data manipulation-- or launch your Internet browser to connect directly with the contributing agency or organization via the Web. Many of these spreadsheets include time series data not portrayed in either the print version or visible on your screen.

I've been reading Strangers in Paradise in pocket book form. (These are compilations of material that originally appeared in single issue comic book format.) This book is the last in the series, as the story comes to a close.

At its heart, Strangers in Paradise is a love story. Katchoo and Francine meet in high school. They're perfect for each other. They should be together. But instead, they wind up apart for years, and when they find each other again, they're plunged into drama and intrigue: secret identities, organized crime and killers, marriages, divorces and, er, folksingers. You name it, it's all here, rolled into one entertaining, convoluted ride.

Let me get my criticisms of the series as a whole out of the way. It lagged at times. There were a whole lot of interludes with song lyrics and poems that I didn't feel contributed much, and that frankly I didn't think were very good. Also, some of this series was reorganized when it was reprinted in these Pocket Books, and the result is a long, odd tangent in one of the previous books that is too disconnected from the characters and story we've grown invested in. So... not all 6 Pocket Books would have gotten 5 stars from me. This one, though does.

Book 6 fulfills all the promise built up through the series. This final volume brings the multifaceted story to a close most effectively, and affectingly. I was left at the end with that bittersweet feeling you get at the end of a really good book or film: you know these people are fictional characters, but you will miss them, now that their story is over. I was so glad I took the time to read Strangers in Paradise.

The final volume of Terry Moore's landmark series is a perfect example of how graphic novels should be published. Tightly-written and beautifully illustrated by Moore and publshed by his own studio, this compact edition contains the last 14 issues of the comic, more text-heavy and less whimsical than when the book started a decade and a half ago, reprinted in a smaller format that brings out fine detail in the artwork.

This text will freak you out at first if you have never done proofs, or linear algebra at a rigorous level. My professor said that linear algebra and mathematical maturity are definitively things to possess before attempting to deal with this text, and not having those two things was a disadvantage.

However, if you're on your own (as I have been in my study of math), I can recommend some great preparatory books.

I am working on some analysis and algebra and the following have helped me:

Modern Algebra and Trigonometry - Moore (may be out of print - great book though)

Elementary Real and Complex Analysis - Shilov (calculus, basic measure)

Linear Algebra - Shilov

those three texts should get you to a point of mathematical independence where you may conquer dummit.

This book is the best to understand hard concepts of abstract algebra. The exposition is excellent and it is easy to find anything you need.

Compare this book to certain other ones (like Lang's Algebra, Hungerford's Algebra, etc.) and you'll agree, this one is way better. Most other books are too terse to study from, especially if you're studying on you own. But this one seems to cover the material pretty well, without falling into that trap.

D+F tries to straddle the line between being a book for advanced undergraduates and a book for graduate students and does a decent job. It is fairly readable, with many excellent exercises and lots of examples. The book also covers all the material in the standard graduate algebra sequence. The section on group theory is particularly good.

I think the biggest problem with D+F is that it is bland. The exposition isn't a joy to read and full of motivation like that of Halmos, Stillwell, or Eisenbud and it isn't full of deep insights like that of MacLane, Lang, or Artin. In addition Category Theory is pushed off to an appendix at the end of the book rather than integrated through the text. Finally the book is expensive and the binding is terrible.

If you want to learn algebra I would recommend purchasing some of these cheaper more focused texts since almost everything in D+F is treated better elsewhere:

Basic Algebra - Mac Lane + Birkhoff - Algebra 3rd Edition
Galois Theory: Stillwell - Elements of Algebra, Artin - Galois Theory
Commutative Algebra: Eisenbud - Commutative Algebra With a View Towards Algebraic Geometry
Homological Algebra: Weibel - An Introduction to Homological Algebra

If on the other hand you are already fairly comfortable with algebra and are looking for a one volume reference I would just buy Lang. It is less than half the price, more advanced, and has more material.

Hilariously, I found this book in a local library, in the section devoted to primary school and high school maths. I guess the "Algebra" in the title suggested this location to some librarian. Anyhow, not to worry. I informed the library and they will reshelve this book in a better place.

And what of the book itself? It makes an excellent text for an undergrad maths course. In no small part because the authors have stuffed a huge number of exercises into each chapter. An intense workout for the dedicated reader, and a wide variety of choices to the instructor.

Ring and module theories are developed at a fairly rigourous pace. While finite dimensional vector spaces are also covered, as a natural accompaniment. Some readers might be already familiar with its treatment of matrix manipulations and multilinearity. Indeed, the use of matrices may be more natural to you, when modules are discussed.

Terrible book, that was extremely overpriced. It had bad examples and few that pertained the the practice problems. it gave no insight into proofs.

As a student, how can I study without a solution manual? Is all Abstract Algebra classes this way? I have an awful time to study. I'm sorry.

This book was my introduction to algebra, and I can say that with me it hit its target - I not only learned and understood abstract algebra, but I grew to love it and be thrilled by it. If you are outside of mathematics and looking for the way in, I don't think you can do much better than Fraleigh. You'll outgrow it - almost as soon as you put it down. But that's just testament to how far it can take you in just a dozen or so chapters.

I would recommend, if you can afford it, also buying a copy of a zippier book like Hungerford or Dummit & Foote (ask around) and using it together with Fraleigh. Fraleigh won't let you down in terms of giving you the space you sometimes need to grasp things (for example, he gives Tons of examples, and there are plenty of easy exercises that allow you to soak in patterns in the structures for yourself) and an advanced book will give you increased perspective and power.

[...]
Although, I did not use Fraleigh's textbook directly in the class I attended, I did use it as a frequent source of
explanation and/or practice with it's problem sets. Lets be realistic here, I've seen too many reviews of differnt Algebra
texts from D&F, Artin, Lang, Galian etc., saying something along the lines of "Textbook is not rigorious enough," or
"textbook is weak on theory," "textbook is not approrpiate for undergraduate course," and so on and so forth.

Although I do not deny that certain texts may be written poorely, the vast majority of complaints seem to be generated by certain percieved "defencies" in texts that do not attempt to be laconic (i.e D&F). Obviouslly, there exist suffecient
differences amongst the students who will take Abst. Algebra such that differnt types of textbooks are created to meet the
varying needs of these students.

It is in this context that Fraleigh's textbook should be reviewed. After looking at all the major texts out there for basic undergraduate Algebra (Artin, D&F, Rotman, Herstein, Gallian), I'd say Fraleigh belong somewhere between Galian and Herstein. It is true that it does not cover as much material as D&F, but clearly it was not written with the same purpose in mind as D&F.

If we compare Fraliegh with Herstein we admit that they both cover most of the same subjects in more or less similiar depth.
Herstein beats out Fraliegh 10-1 in all things Linear Algebra. However, I'd say the first 250 pages of "Topics in Algebra" is
roughly equivelent to the 493 pages of Fraleigh. So the question that is asked is why is Fraliegh almost double the size of Herstein?

A quick browse of both books reveals that although the font size (for my copy) is the same, Fraliegh is much more liebral
with the placement of paragraphs and spacing. Whereas "Topics in Algebra" looks cramped and squeezed, Fraleigh's book is much more cosmetic, the pages are littered with
pictures/diagrams, "Historical Notes," numerous drawn out examples. I personally like the spacing in Fraleigh as opposed to Herstein since I feel the former text is much easier to read because of this layout.

If we delve into the actual text-material we do again admit that Herstein is slightly more "mature" then Fraleigh. I believe the exposition in Herstein is probably a little clearer, however, Fraliegh does more "work" for you and gives you more detail. Further Fraleigh gives more application such as to coding, chemistry, and quantum physics etc.. Those who do not believe that the exposition is roughly at the same level, I invite you to turn to p. 83 in Herstein and p. 253 in Fraliegh. Both start with the defintion of rings. Again Herstein spells out the actaul defintion in all 8 axioms. Fraleigh has 3 shortening them by merely giving the condition that a ring must be an abelian group under addition (note it is not always the case that Herstein introduces everything out the long way and Fraleigh the short, more on that later). After defintions, both text introduce examples, again I think most of the examples given by Herstein are rather trivial, whereas Fraleigh's examples are more intresting with some useful links back to Group Theory.

But Fraliegh clearly does more to motivate the reader to learn every new bit of material displayed in the book, althoguh the outline is not always the clearest. This is very evident when comparing the section introducing Fields. Fraleigh commutes the introduction of the topics of fields and homorphisms. Introducing homorphisms of rings first, although it makes little differnece in understanding the material, I muchl liked Herstein's direct introduction. I felt it was more natural to introduce fields then homorphisms, then ID, PID, ED
etc. It just made mroe sense to me, but this is my POV.

Fraliegh again says almost the exact same thing that Herstein does except he has far more exposition (although i found sometimes that the exposition could be a bit confusing). Another observation I'd like to make was I felt Fraleigh was far stronger in its Group Theory sections then it was with Fields and Polynomials. For some reason, the sections on polynomial rings were rather weak for the work we were doing in class and I cannot recommend Fraliegh for this if thats what you need. However, in general I found Fraleigh was easily digestable and could be read very leisurely.

The major drawback of the book of course is its problem sets. Although they are good for extra practice, they are by no means challenging. In this respect, Herstein and the rest are lightyears away from Fraleigh. This setup again is proabbly mroe to do with the differnt philosophies of how a student should learn rather then some weakness in design. Fraleigh nurtures a student so he can take his first steps in the subject and walk. As opposed to D&F whose terse exposition is akin to throwing a child onto the floor and yelling at him to return to you on his own. Which is better? I don't know, but I must certainly say I felt much "happier" when I was reading "A First Course in Algebra."

Again, I feel that Fraleigh's text is a wonderful introduction and supplement to a student (like myself) who did not come from a long and prestigious mathematics background. For this audience, the book is perfect for the first half of Algebra (Group Theory) and somewhat lacking for the second half (Rings, Fields, and Galois) but no book is perfect and given its size and the wealth of knowledge (historywise and application wise) that is stored in this volume I am content with what it offers to the reader. Also, as mentioned, since it covers roughly the same as Herstein, a more difficult class could utilize this book by just offering differnt problem sets to the students with additional supplementary exposition from the instructor. Overall the book is, gentle, flexible, and broad.

I am laughing at the good professor's review below. I do believe he must be a professor: he writes a lot and conveys little in terms of detail or example.

Speaking of examples, an introductory book should have ample amount of them. The reviewer below says Dummit and Foote as well as Artin is too "sophisticated" for students. I disagree. They are wonderful books. Fraliegh, I have to agree with another reviewer on here, is really best kept as a supplement. Fraliegh lacked good examples that were of any real sophistication or had often masked some important developments in the exercises. Also, soem of the standard notion such as for automorphism (i.e. Aut) and others were blatantly missing. It is best to get students new to the subject emerged in the notation from the start and give clear examples that represent an easy one for clarity and introdcution, and then at least one other, preferably two, which take the reader to a more detailed and more challenging, sophistitcation of development. Fraliegh does not do that. Moreover, I think the transition to another higher level book will be more painful after Fraliegh alone. It should be read along side Dummit and Foote or Artin--two fantastic books.

Also I hated Galian's text myself, I have to agree with that reviewer on this: it is indeed to damn wordy. I like succint, straight to the point books that have well chosen exercises and especially numerous examples. Dummit and Foote (D&F)do that especially well, then Artin next. Fraliegh, while and excellent book, doesn't compare but after D&F and Artin, it is the best thing.

So, I give is three stars. Not bad at all.

I only wish I had seen this book before I started painting. It would have saved me time and money. Lots of great creative ideas and techniques. I recommend this book to beginners, like me.

This is a great book! It goes into the philosophy of abstract painting, methods, materials, composition, etc. The book also emphasizes each artist's creativity. The artist's interpretation and creativity is what art is all about, and even more so with abstract art, as abstract artists aren't painting something easily recognizable (i.e. a barn). The author did a great job in this book!

Good book. Really clues you in on the whys and what fors of abstract painting. After reading this book (more than once) I was not intimidated by trying my hand at abstract painting. The photos in the book are awesome. The author knows her art as does those artists who contributed to the book.

This book's images are impressive and provide motivation for the novice to explore abstract paintings. However, it really does not go into enough detailed instruction so that techiniques can be applied in the studio. I can't recommend this book except for those painters who 1) already have some experience with abstraction, and 2) novices who want a general introduction and can find other sources to help answer technical questions. It's a pretty book with little technical substance.

I have really enjoyed this book. It is informative on technique as well as rich in concepts, as the title suggests. It has many high quality photos, and is filled with wonderful examples. Thought provoking and well written. A welcome addition to my art library.

As most of the books written by Prof. Lang, this book is a great compilation, it has what it needs to have, nothing more, nothing less. If you are in Math or any related field, and need a book to refresh your knowledge on Abstract Algebra, this is your book. though, I took a course in Grad School from this book, and I don't recomend it. Fortunatelly I still had the books from my undegrad courses (Rotman's Group Theory book is great), and I did remember the old courses anyway, but I really discourage the usage of this book as a lecture book.

As others have said, this is not a book to begin learning algebra, but is a necessary book for most students to have on their shelves. Why is that? Basic topics are discussed from scratch in this book from the most advanced possible viewpoint. Hence few can learn them here for the first time, but no one can graduate to professional status without eventually arriving at this perspective.

In particular the categorical point of view is simply essential to a research mathematician to acquire at some point, and Lang uses it here from the beginning, while Dummitt and Foote place it in appendix II, after page 800. So Lang's goal seems not to introduce basic algebra, but to provide essential algebraic facts not found elsewhere, and to give them all from a professional's perspective.

This is probably a third book on algebra in today's world, and that is assuming the student is pretty good. The only current book I know of out there that is really aimed at students and also written by a top professional is Artin. If you can, begin with Artin, then read Dummitt and Foote for topics Artin omits, then read Lang to see how you should view the same material and find things Dummitt and Foote left out.

Then you are ready to do research with these tools. For instance one of our research professors tells his students the prerecquisite for working in algebraic number theory is to become comfortable with algebra at the level of Lang. But our course in PhD prelim preparation for algebra will probably use Dummitt and Foote, just because it is a more feasible book for the students to read at that stage. Attempts to use Lang in trhe past have been disastrous.

Nonetheless, even students who found Lang a frustrating text, still use it as a necessary reference, and even find it has too little.

Just compare the treatment of groups in Lang and Dummitt and Foote. Lang covers the whole subject in more depth in 60 pages (2nd edition) while D/F use up over 220 pages on groups, and still do not introduce the categorical point of view, and in particular do not prove the existence of "direct sums" i.e. coproducts (which they do not even define), of groups.

So if you only have Lang, you will almost surely not see enough detail to understand the material, and if you only have D/F you will not see it from quite the right perspective, and will still not know some basic results.

Lang's book has numerous frustrating traits, misprints, errors, many uses of the word "obvious" for arguments that need a great deal of filling in, careless slipups ad nauseam, dyslexic things like saying clearly when to use product as opposed to coproduct, then getting it precisely backwards himself. or a whole discussion of Galois groups as permutations of roots of polynomials while forgetting to assume the polynomial is separable.

Your margins in Lang will be full of corrections, comments and added details, but now and then he will make something so clear in a word or two, that it will forever seem easy to you. In sum it is a locally flawed and carelessly written book, but globally impressive, and one for which there is no adequate substitute to my knowledge. Not least, Addison Wesley has always done a good job of making the type look beautiful on the page. The integrity of some recent bindings of course is another story.

I have owned this book for many years now and I find that even after I have learned a topic in Lang or elsewhere, I still find that yet another careful reading of Lang will rearrange my thinking. I hear and read a lot of people complaining about this book, and I think most criticisms come from not having enough patience or energy to climb the book. (Yes, reading this is more like climbing!) There are few better things that you can do for yourself than hanging out with Lang.
The book does deserve some criticisms. His chapter on groups is just too small and insubstantial. Go elsewhere for that, like Rotman. The real purpose of that chapter is to introduce Category Theory, and it takes the wrong tack a few times there, I feel. So learn category theory somewhere else too. And all algebra books fail to explain what the algebra is good for. This one is no different. It is a shame because too many people think that Algebra is mostly for algebraists. But the truth is you can't do anything great without algebra.
The chapters on Homology theory are good in places, and the places where they are not so good, try the book by Weibel.
So, yeah, he is often a bit terse and leaves steps out. That's just an invitation to think things over. And it keeps the text clean. He is respecting you, honoring you, inviting you to the real party. He's not cheating you. He's giving you the real goo! You want the real goo, don't you?

Most critisism of the book are based in the fact that topic are not treated in deep, and the reason is that there is no need to do that. Lang's porpouse is to introduce the reader to HIGHER ALGEBRA, while for example Dummit & Foote just end in Category Theory or Homological Algebra. He just introduce what he consider necessary to know about groups. Of course, if your porpouse is to learn, let's say Group Cohomology, then its good for you to know as much as possible about groups, modules and stuff, but Lang's try to focus on what HE consider is important to be known.
One has to have in mind that its easy to present the basic form of Cohomology or modules as Dummit does, but its has no continuity in the sense that will follow you to nothing, just to know some basic concepts. That's why i disagree with the people that say that is like an encyclopedia. Lang's development in Algebra is AMAZING. Ok, one can argue that it can be stated more ''friendly'' such as Galois Theory by Artin book does. But for Galois theory that's easy while in General Algebra is doesn't. Just take a look at Galois Theory section [which is, as every book, based on Artin works], there is nothing that is understandable in it, and its not an extensive work, because Lang will not USE in his HIGHER ALGEBRA.
The whole thing can be explained if you notice the Algebraic Number Theory book of Lang... you can consider Algebra as a preparation for his real book.
My education in math [academically] is minimal, but i always recommend this book, because when i get a subject i go directly to Lang and everything seems clear. Also, notation is really CLEAR and, comparing with authors like Jacobson, he doesn't mess with [unless necessary] formalizations.
So, my advice:
If you want to LEARN algebra, and work in algebra, READ LANG, READ LANG, READ LANG.
If you want to get some knowledge about algebra, and take a course, this is not your book.

When I examined this book as an undergraduate I did not like it; often this is a sign that a book is poorly written, but in this case I just needed more background. Now I see this text as a gold-mine: clearly written, provocative, and rich in examples.

I find it refreshing that Lang does not get caught up in tedious proofs (one of my criticisms of Isaacs, another of my favourite algebra texts); anything that is tedious but not difficult, Lang leaves to the reader. Yet the book is not overly concise--a lot of ideas are explained in depth.

This book serves as an excellent reference for several reasons. First of all, it's unlike any other algebra book. The choice of topics is unusual; it will certainly expose you to some things you haven't seen before, but at the same time, it is not a comprehensive slice of modern algebra (it doesn't even mention lattices). However, the best aspect of it are the presence of examples, something sorely lacking from most other abstract algebra texts. Whenever a new concept is introduced, Lang presents a variety of examples from material elsewhere in the book as well as other fields of mathematics. These examples alone make this book precious. Although the biggest exercise is just reading and understanding the book, the exercises at the end of each chapter open up a whole other world; they are quirky and creative like the rest of the text.

I recommend this book for any serious mathematician to add to their collection. However, it would be waste of time to read it until you already know a great deal of mathematics. This is one of those books that becomes a must-read once have already read 25 or so other serious math books.

This book clinches for me a caveat to live by in my future mathematical career: Never undertake to learn any new subject in mathematics from a text that is described as "chatty" or "informal". Herstein's prose is mildly amusing up until page 3, whereafter it becomes a nuisance and later a downright irritant. And that's the least of this book's problems.

We start with the first sentence: "For many readers this book will be their first contact with abstract mathematics." That straightaway blows away any excuse Herstein might muster to save face in light of the content on subsequent pages.

First, each section usually has exercises divided into three categories: "Easier", "Middle-level", and "Harder". The easier problems range from mundane pencil-pushing to rather stiff analyses; the mid-level problems are typically quite difficult or nearly impossible; and the harder problems are almost universally intractable - mainly because they have little bearing on what the author discusses. To wit: any problem will be "hard" if you give your student absolutely nothing to go on. To entice a reader to try out a harder problem, the competent instructor knows to leave a few bread crumbs that lure the reader into the forest. Herstein does not do this. Harder problems are routinely bolts from the blue presented in vacuo, mere non sequiturs in the eyes of the struggling newbie. We need not discuss the so-called "Very Hard Problems" some sections feature, as the mathematical community is still researching them in a feverish competition that surely will bag someone a Fields Medal.

The beginner (the book's alleged target audience) will find section 2.2 utterly demoralizing. The exercises are not categorized as described above, and guess what? They're ALL "harder problems", most of which I still can't solve to this day - and I've moved on successfully to graduate-level abstract algebra. And guess what the title of the section is? "Some Simple Remarks". Herstein is either arrogant beyond the ken of mortal men, or the most sadistic professor to come down the pike since the days of Attila the Hun. By page 50 the book is sending you a clear message: "You are an abject idiot. A gibbering nincompoop. Why are you still even trying?"

Some crucial definitions are couched in the thick of exercise sets where they do not belong. You know, little things like the definition of a cyclic group.

Crucial results used to prove pivotal theorems are sometimes poached from exercises from earlier sections, so the book, damningly, is NOT self-contained. It is inexcusable to have the proof of Cauchy's theorem, for example, hinge on asinine parenthetical statements like "see Problem 31 of Section 4" or "See Problem 16 of Section 3, which you should be able to handle more easily now." What the hell is that about? I've NEVER seen a math text do this at the introductory level. It's gross academic negligence of the highest order. The rule is this: exercises build on definitions and theorems, NOT the other way around!

It's fair to sometimes ask the reader to provide the proof of a lemma, corollary, or minor theorem in an exercise. What is decidedly NOT helpful in the least is scattering the proof of a major theorem all over the map, with some scraps coming before the theorem and remaining scraps coming after. One of Herstein's favorite stunts: a sort of heuristic "hand-waving" argument that weaves around like the Mississippi river, culminating with a statement along the lines of "We have now proved the following theorem...". It's okay to do that once in awhile to break the monotony, but NOT two-thirds of the time in a pathetic attempt to seem less formal and be the student's "buddy". Students of algebra do not need a buddy, they need a teacher who knows how to present material nonrandomly.

The reader almost has to hire a private investigator just to sort out the precise definition of congruence modulo n. What does "a = b mod n" mean? Why, "a ~ b", of course. But what's "a ~ b" mean? Merely that "n | (a - b)", silly goose. Ah, and what's "n | (a - b)" mean? GOTO Chapter 1, where you'll finally reach the end of your quest. For something so important as the concept of congruence modulo n, one would think its definition would be enshrined right under the bold heading "Definition". But no: it's buried in an inane example.

Other times Herstein has it in for private investigators, and right smack in the middle of a theorem readers are reminded that "Ker phi" means "the kernel of phi". Wow, thanks! My only explanation for this behavior is that Herstein is violently allergic to theorems that are expressed in only one line; so, he'll pack them with irrelevant crap to ensure they're at least two lines long.

Then there are the tragic expressions of the various correspondence theorems that each utterly fail to mention the relevant correspondence. One concludes with the statement "This sets up a 1-1 correspondence between all the ideals of R' and those ideals of R that contain K." The understandably befuddled novitiate is led to ask: "Well isn't that special. So...what is it?" Herstein seems incapable of placing himself in the shoes of beginners and seeing that what's obvious to him can be a mystery to someone else. An appropriate function must be defined, then demonstrated to be bijective. By no means trivial! Then two pages later 2-by-2 matrices are kicked around like the reader is a drooling retard who's never seen them before.

A lot of "examples" are actually fake fronts for exercises, so don't let their apparent abundance bedazzle you overmuch. Others are laughably trivial or ludicrously irrelevant.

Finally, it's breathtaking that Herstein can have an entire section titled "Cycle Decomposition" without ever defining what it means. Just another example of lousy organization and a ham-fisted presentation that never survives the rough-draft version of worthier texts.

(I am writing about the 2nd edition, which I used as an undergraduate.)

This book is intended for a one semester senior-level honors course at a reasonably good undergraduate institution, for which it is perfect. Students who are less interested in pure mathematics or are somewhat weaker should go to Gallian's book, which is also excellent. Students who are weaker still maybe should seek out Fraleigh.

Other reviewers are correct about the group theory being the strength of this book; ring and field theory are OK but short, but remember that this book is intended for a one semester undergraduate course. (Herstein was a ring theorist. It is natural to speculate that he chose the topics he did because of the course, not because of personal interest...) The optional topics (simplicity of A_n, Liouville's Criterion, etc.) are excellent.

"Topics in algebra" is supposed to be a year-long version of this book. That one is sometimes called "Herstein" and this one is "Baby Herstein". Happily though, Baby Herstein still has content, unlike "Baby Hungerford"...

Most abstract algebra courses are used to give an introduction to the methods of reading/writing of proofs. Herstein seems to have misunderstood the concept of introduction. This is a sink or swim book when it comes to learning how to write proofs! You will surely want to buy an additional book on how to write proofs if your school is using this book for a intro course to abstract algebra.

My first introduction to abstract algebra has been by this book and I've found it to be an excellent choice. It is a concise book with lots of content. Topics are discussed very fluidly. One really gets the essence of the topics with a lot of insight. The book is simply too elegant. Another great asset of the book is its high quality exercises. Most of the exercises are difficult, nontrivial and provide further insight. This is the only abstract algebra book I've seen, but I don't think any other book could surpass this one in the quality of treatment.

I had this text for an intermediate course (after the 1st one) on abstract algebra including groups, rings, fields and homomorphisms, quotient structures, etc right up to where Galois Theory would start, and it was good for that. I wouldn't say that this book is good for someone who has never seen algebra before because the easy problems are still kind of hard compared with other books. If you've seen a bit of algebra before though this book would be really good. It's got tons of problems at the end of almost every section also.