Book Description

Contains answers to all odd-numbered exercises.

Customer Reviews (25)

Great Aid
This book works great in conjunction with the book Contemporary Abstract Algebra. I'm an undergrad taking Group Theory and completely lost! But with this book, I use the answers to better understand what the question is asking. I think that's how the questions should be made in general: Give the students the answer and ask them how to get to it. Students would better understand what the question asks and the material in general. Anyway, I would recommend this book for any student using the book as a text.

Depends on what you want...
If you are looking for a rigorous step in abstract algebra this is probably not the book you want.If you are taking a fairly elementary one semester undergrad course and will never see this subject again, it is great.The proofs are weak (compare to Hungerford - the intro NOT the grad text - or Dummit and Foote - which, admittedly is more advanced, but not that much).This subject (like topology and real analysis) tends to depend on where you are and what you want.

Great textbook
I am a math major in my junior year, and this is the first textbook I have actually enjoyed reading. It is full of useful examples and it is clearly written and structured so that it is very easy to follow.

I'd recommend this book to any student who is looking for a great resource to help them learn/understand abstract algebra.

It's a textbook.You're forced to buy it, but at least it does its job well.
Normally, mathematics textbooks are used as sleeping aids (Munkres' Topology, anyone?), but this one teaches you the concepts you need and doesn't do a terribly dry job of it.I'm assuming you're reading the review to learn the subject in independent study, because otherwise, who'd read a textbook review?

First of all, this book is thankfully small.Actually, quite a bit smaller than most mathematics textbooks I have been carrying around these years.But you didn't buy it for the size, so on to the contents and layout.

There are chapters and there are sections, like elements (latter) in sets (former); each section outlining some key concepts or theorems.The problems for each section do correlate closely to the course concepts.The author begins with a review of the foundations of mathematics and some property of sets and then begins with an introduction to groups before moving to a more detailed look.

With the curriculum in algebraic structures/abstract algebra fairly standardized, this book teaches you most, if not all, of what you would expect from a course in the upper undergraduate level.One thing you will not easily learn from the book, however, is that algebraic proofs rely more on a bag of clever, annoying tricks than some fundamental comprehension of the subject matter.And thus, if you ever find yourself stuck in a problem, ask your professor/mentor if you can borrow from her bag of tricks, or else you'd be kicking yourself in annoyance from unable to prove something so simple and elusive.

Overall, the book construction is fairly study, the material inside is comprehensive and fairly digestible, particularly with the subject matter broken down and explainedas Gallian does.And, there you have it.Buy it, learn it, and then sell it/treasure it/burn it; you won't be looking at it again unless you hit mathematics graduate school.

For Highschool Students, not serious undergraduates
Very general advice is very useless. I hope that the following comments are sufficiently specific so as to inspire a high school student to at least glance at the book and to help an undergraduate shy away from the book.

If you are studying pure mathematics for the first time, then I agree that a new take on exposition might be worthwhile.On the other hand, if you are serious about learning a subject, then a textbook which focuses almost exclusively on the subject is clearly the best choice.

To begin, the exposition in Gallian's book is tainted by the amount of unnecessary comments ranging from a short biography on a mathematician to superfluous quotes by Homer Simpson to insistent excerpts from Beatle's songs.If you want to study math history, then buy a book on math history; if you want Simpsons, look up some episodes, etc. etc.A valid question is: "But what if I want to know about a topic's history and applications?"...Answer: go to Wikipedia or ask a professor.

Gallian's confused exposition can be made slightly clearer by appropriately identifying its audience:

High school students: This text serves as a very good, but not excellent, introduction to abstract algebra.The first few pages of the book are quite decent for an introduction to elementary number theory with proofs.My advice would be to skip the "extra" sections on things like error correction codes in preference of focusing on learning the mathematics.The exercises in the first chapter, as they are throughout the entire book, are not exactly what a mature student would call "exercises", but instead "drills".Doing such drills will help you absorb the material, especially if you are studying this book on your own.You will learn the basics of cyclic groups and rings.

Undergraduate Math majors: Assuming you know a little bit about linear algebra, say at the level of Lang's "Introduction to Linear Algebra" or some introductory real analysis, then optimize your time by avoiding this book and instead study something serious, such as M. Artin's "Algebra" or Dummit and Foote's "Abstract Algebra".The exposition in this book is so clouded and the exercises so routine, that there is almost no way this book will prepare your for graduate studies in mathematics.On the other hand, Artin's "Algebra" D&F's "Abstract Algebra" will most certainly do the job.Compare, for example, Artin's section on equivalence relations and cosets to that of Gallian's.Artin introduces these concepts early on, which makes fundamentals like Lagrange's theorem and the first isomorphism theorem useful and natural.Gallian instead decides to delay these concepts until after he has defined isomorphisms (even more tasteless, homorphisms come after isomorhpisms).In addition, compare D&F's section on ring theory to that of Gallian's.D&F are succinct about the basic axioms (a0 = 0, etc.) and get right to structures like division rings to yield illuminating concepts.Gallian instead dedicates a whole chapter to almost useless things like "subring tests" (you don't need "tests" if you know the definition).These are only but a few of the drastic differences in exposition you will find.Finally, and perhaps not as important, is the notation.It is poor taste to use "Zp" to mean the ring of integers modulo p, versus what grown-ups label as "Z/pZ".In addition, the notation for cardinality could have been better: Gallian uses |G| instead of the unambiguous #G ( the |.| notation should be reserved for absolute value).

***
Here is another telling part of the book: in proving Thm. 20.1 (pg. 352) that given a field F, an irreducible p(X) in F[X], then there exists an extension of F such that p(X) has a root: our author clutters the main point with useless commentary and four strings of equations.If you know what "projection" and "isomorphism" mean, then this "proof" is really just a one-liner, as follows: If x is the projection of X, where x is in F[X]/(p(X)), then p(x) = 0. done. ... Read more

Customer Reviews (23)

Fraleigh?awesome, sure
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.

No Student Solution Manual
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.

Fraleigh put into perspective
[...]
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 abit 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 froma 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 nobook 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.

Decent Book But Has Flaws
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.

Instructor's perspective:Excellent text for a university course
I am a mathematics professor at a small liberal arts university in Canada, and I use Fraleigh's book to teach a 300-level full-year introductory course in abstract algebra.I find it excellent.It is clear to me that Fraleigh has been teaching a course very similar to mine, to students very similar to mine, for probably three decades. He has figured out almost exactly the right way to introduce a difficult subject.He makes my job easy.

The book is broken into many small chapters, each of which can be easily translated into one or two hours of high-quality lecture. Thus, I can structure my lectures to closely follow the book, which has two advantages: (1) less preparation time for me (important when you have a heavy teaching load but still want to do a good job) and (2) The students have effectively a preprinted copy of the classroom lecture notes (so they can spend less time writing notes and more time paying attention and learning).

Fraleigh avoids the countless pitfalls which bedevil the naive algebra instructor (and many other textbook writers).He keeps things simple without making them stupid.Math students at my university have a wide range of background and skills.Some are highly talented and motivated, and I want to adequately prepare these students for graduate school.Others students are `future highschool teachers' (may God help our children) who apparently chose to study math because they thought it would resemble the polynomial arithmetic which they enjoyed in highschool, and who are often quite upset to discover otherwise.For these people, math is `supposed' to be computation, and any kind of logic or abstraction is anathema.

There are some abstract algebra texts (such as Bloch) which are designed to appeal to the `computational' crowd.Abstract algebra is one of the most beautiful and important parts of mathematics, and I describe these books as `algebra murdered and come back rotting from the grave'.There are also algebra books (such as Dummit & Foote, or Michael Artin) which are designed for `future graduate students'. Although I love these books, they are too sophisticated for most of my students.Also, their long chapters and sometimes poor organization means that preparing a decent lecture is often a lot of work.

Fraleigh finds an excellent compromise between these extremes.He develops some quite sophisticated material (including Galois theory and homology), but always finds a way to explain things simply and clearly.He provides exactly the right amount of information (e.g. the right number of examples and corollaries) to allow the instructor to move through the material efficiently (so you can actually finish the syllabus), while still explaining everything clearly.The exposition is lucid, and the books tightly organized. There are plenty of exercises which are challenging, but not too challenging, which is a boon when you are designing homework assignments.

I have a few small issues. For example, I don't think it's a good idea to develop group theory in terms of `abstract binary operations; one should develop it in terms of concrete symmetry groups.Also, I found that the section on the structure theory of finitely generated abelian groups and the chapter on homology theory were both a bit weak and needed to be supplemented.However, these are both very minor complaints compared to the overall quality of the book.

Teaching an advanced pure math course with a poorly designed textbook is a nightmare (and I should know).Teaching algebra using Fraleigh was a snap. ... Read more

Book Description

Customer Reviews (9)

DO NOT READ THIS PLEASE!IT COULD SAVE LIVES!
I think I bought this book only because it had that neat Moor Methodesque presentation.And because I like to buy math books.And because it was cheap.

So far so good, though I can't say that it differs particularly from any standard text on algebra.It's not big enough to be Lang.Not terse enough to by Hungerford.And not comprehensive enough to be Dummit and Foote.
It also costs about a fifth of the price of any of those and has a neat do-it-yourself kind of methodology.

Good Book on Algebra
I wanted to study Galois Theory to understand why the quintic is not solvable in radicals.I did some search on the net and ran into this book. My math background is in probability and analysis. With my background and interest this book I feel this book is perfect. It is not too difficult, plenty of exercises and I can follow the development; also I do not feel I am being talked down to by the author.I will have a good understanding of Galois and related theories after putting in the time and effort with this book.

Noanswerstoexercises,.


Itisinappropriateforself-study.

One of the most insightful introductory algebra books
I'm a math undergrad, and we're using this as our class text.While some of the criticizms in other reviews are true, Clark's treatment of algebra is thourough, rigourous, and full of many details that other books leave out.While it's true that this is a very concise text, I've found that Elements of Abstract Algebra offers deeper, richer insight into the topics it covers when compared to other intro books.

As an example - cosets.Many other texts completely leave out the fundamental concept of cosets:they are congruence classes modulo a subgroup.In at least three other intro texts I've looked at, the left coset of a subroup was simply defined as gH = {gh | h an elt of H}.While this is true and easier to cope with at first, Clark offers full discussion and suggests where the reader needs to fill in the gaps with proof.

For at least the first two chapters, the reader may want to consider supplementing this book with another, simpler book like Maxfield's "Abstract Algebra and Solutions by Radicals" (another great book).However, any beginner with enough time and discipline will find Clark's book to be a thorough and enlightening introduction.

Extremely compact, not enough discussion
Since the reviews have been generally positive, I'll start with the major negative. Clark does a poor job of motivating the material being developed. As a reader with no background in modern algebra, I found the group theory chapter tedious and uninteresting. Just because you can begin with a set of definitions and use them to prove very complicated theorems doesn't mean doing so is worthwhile. It wasn't until I read the fourth chapter on Galois Theory that everything clicked and I realized the importance of seemingly arbitrary definitions and correspondingly ponderous theorems. But even then I had to do considerable introspection. The proof that polynomials are solvable by radicals iff the Galois group of transformations is solvable is presented as just another theorem, whereas that proof is the principal purpose of most of the book to that point. I basically had to figure out Galois's original idea for myself and then go back and reread Clark's chapters 2-4 for the complete analysis. To be fair, this book has an introduction that sort of hints at Galois's idea, but I feel it is very poorly done. Perhaps a more thorough, more motivational introduction would make this a 5-star book.

Sometimes Clark appears needlessly complex. In one part, he defines the normalizer of a subgroup as the group of all elements in which the subgroup is normal. Then he proves, in a bizarre and tedious way, that the normalizer is the largest group in which the subgroup is normal. While I'm not a mathematician, it seems to me that this is obviously true by definition.

On the other hand, you can learn a lot from this book quickly precisely because of its compactness. I am fond of concise writing, but the whole purpose for a book is to guide the reader's thought. I almost recommend beginning this book with chapter 4 unless you have already expended considerable thought on equations. ... Read more

Book Description
If you want top grades and a thorough understanding of abstract algebra this powerful study tool is the best tutor you can have! It takes you step-by-step through the subject and gives you sample problems with fully worked solutions, including proofs of all important theorems. You also get additional practice problems to solve on your own, working at your own speed. In addition, this superb study guide gives you chapters on sets, integers, groups, polynomials, and vector spaces. Students' favorite, with more than 30 million copies sold, Schaum's study guides are the best value for your student dollar—clear, complete, and low-cost. ... Read more

Customer Reviews (8)

Average resource
This was an average resource for me in my advanced algebra course.I suggest if you are to use this book, to also get Joseph Gallian's Contemporary Algebra book as well.

lpescatori
Excellent for a quick and rigorous grasping of basic concepts. A huge number of problems helps fix the theory and gain problem solving capability.

Not much on the core subject of abstract algebra
This book has some good theoretical mathematics content, unfortunately not much of it is about the subject of abstract algebra. The first 80 pages of this book talk about sets, relations, operators, and number systems. The next 50 pages or so consist of elementary material ongroups, rings, fields, and polynomials, and act as a very basic introduction to abstract algebra. Then the author again diverges off into mathematics that does not relate to abstract algebra and talks about vector spaces, matrices, matrix polynomials, linear algebra, and boolean algebra. Again, this is all good mathematical material with some good problems, but I don't see what it has to do with learning abstract algebra. A better title for this book would have been "Schaum's Outline on the Foundations of Mathematics" since it is really supplying a good theoretical introduction to mathematics for the mathematics major at about the college sophomore level. If that is what you are looking for, I would give this book about four stars.
If you want a good introductory textbook on abstract algebra might I recommend "A First Course in Abstract Algebra, Seventh Edition" by Fraleigh. The author explains the concepts very clearly, has plenty of examples, and motivates the reader by showing example uses of the theory in applications such as error coding. There are more rigorous books out there, but Fraleigh's book is a great introduction, and used copies can usually be found for roughly $60, or about half of the price of a new book.

mm, not quite what I was hoping for...
This installment in the Schaum's outline series doesn't do it for me. I had reason to pick this one up simply out of curiousity (and out of habit, by usingother titles in this series for other lower-level undergraduate courses).It hardly stimulates any interest on the part ofthe reader; and the presentation is dry; not to mentionthat the selection of solved problems wasn't carefully thought out (most, I found, were proofs of some pretty standard results, which I would have rather not seen all over again). And the bare-hands computations weren't all that exciting,either.

Ploughing through a course text proper would better serve the serious student of mathematics. There areother well-written books devoted to solved problems in algebra (group/ring theory, for instance). It's just amatter of scoping them out carefully, and dishing out the money (for photocopies, even).

Not Great
Gallian's Contemporary Abstract Algebra is my required textbook for this course.I bought Schaum's Outline to supplement it and help me with some of the proofs.Instead, I found exactly the same worked-out examples from Gallian.My homework problems I was having trouble with were also under the "extra" problems section which does not have solutions.Basically this book was useless to me.If you aren't already using Gallian, that's the book you should get;this one would be okay if you want to save a few bucks. ... Read more

Customer Reviews (8)

A Tough Subject
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.

Not the best book for undergrads....
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!

A worthwhile pain in the....
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).

Very readable text, but problems often self-referential
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.

A good TEXTBOOK
This isa 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. ... Read more

Book Description
Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings.
* The emphasis throughout has been to motivate the introduction and development of important algebraic concepts using as many examples as possible. ... Read more

Customer Reviews (32)

Great graduate algebra text
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.

The Bible of Algebra
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.

useful text for an undergrad course
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.

Excellent for an introductory abstract algebra book; clear and comprehensive
This is a great book!It's introductory, appropriate for undergrads taking abstract algebra for the first time, but it is very comprehensive, useful for more advanced students as well.Although it explains the material in great depth and at a slow pace, it does so in a logically sound manner.The authors provide rich motivation and always introduce material with an eye towards more advanced material to come later.It is rich in cross-references, helping people to develop connections between the different parts of the material, and allowing the reader to jump around once she has mastered the basics.One of the best aspects of this book is that it contains a wealth of concrete examples in every section; this is critical for helping beginners master such an abstract subject.

I find this book to be ideal for self-study and outstanding as a reference: it is very comprehensive and its presentations are clear.The book is still valuable to advanced students, both as review and for the advanced material; the earlier chapter's exercises may seem easy, but they are a fun challenge if you try to do them in your head.Few graduate students will have already covered all the material in this book...it gets into some galois theory, representation theory, modules, homological algebra, even some algebraic geometry.It covers almost all the topics in algebra that a general mathematician would need (as well as many that she might not need); the only glaring omission is that lattices and boolean algebras are not mentioned, but this material is easy to find elsewhere.This book has a clearer presentation of some of the more advanced material than I have been able to find elsewhere--in particular, it has a gentle (and yet rich) introduction to modules.Even if you enjoy denser texts, you will find this book offers something they do not--it's great to fall back on if you absolutely need to understand something quickly and clearly, and the examples are immensely valuable.

I would recommend this book for use as a textbook at all levels from undergraduate through graduate work, although for graduate students it may be better suited for use as a reference or for self-study.This book would also be very useful as a supplement to an instructor teaching abstract alegbra courses at various levels.

This book is well-complemented by the books by Lang and Isaacs.Isaac's book offers a more streamlined, theorem-proof approach that is denser and devoid of examples, and his exercises are harder; this presentation will help the reader attain a greater degree of mathematical maturity.Lang's book is more sparse when it comes to proofs; reading it would be a good exercise to undertake after working through the background material in this book.Lang's book is also rich in examples, but it places more emphasis on applications to other branches of mathematics (i.e. outside of pure algebra), whereas this text focuses more on the connections within Algebra itself.

too wordy
This book is a standard one for graduate-level algebra courses.I practically wore mine out over a year-long course, and came to know it intimately.Dummit and Foote is a book that teaches via wordy explanations and lots of examples.Of course, examples are very important.However, the explanations are often muddled and not clear (e.g. see tensor products).They frequently relegate important theorems or definitions to the exercises, and the organization is poor.Consequently, it can be very hard to find things later when you might need them.Also, the bindings on this book frequently fail.My book fell apart very quickly, and I know other students who had the same problem.I recommend Rotman's Advanced Modern Algebra instead of Dummit and Foote. ... Read more

Book Description
This spectacularly clear introduction to abstract algebra is is designed to make the study of all required topics and the reading and writing of proofs both accessible and enjoyable for readers encountering the subject for the first time.Number Theory. Groups. Commutative Rings. Modules. Algebras. Principal Idea Domains. Group Theory II. Polynomials In Several Variables. For anyone interested in learning abstract algebra. ... Read more

Customer Reviews (5)

Excellent Introduction To Algebra
Rotman's book is a standard for first courses in Abstract Algebra.The book is easy to read and includes plenty of problems to work on.He even includes several standard syllabi in the preface, depending on the type of course that may be taught with it.It begins with some number theory, then goes into the traditional group and ring concepts.The only reason I would say to not buy this book is if you really don't like the theorem-proof, theorem-proof kind of writing, but if you don't, you're likely not interested in Abstract Algebra anyway.An excellent book for learning as well as reference.

no better than the first edition
It is always easy to add something to than to get rid of something from the book. I guess this is the case of the author when he prepares the second edition. However, I prefer the first edition because it is more readable, enjoyable, and most importantly, contains just enough information for the introduction to abstract algebra. There are huge number of textbooks on abstract algbra, and making another would not be the author's purpose of the revision, I hope, but it looks it is.
By adding more subjects in detail to the second edition, now it looks the same as any other, only to loose its expository and conversational style of writings, and became a reference-style textbook.

Boo
Before taking an abstract algebra course this semester I studied the material on my own using the introductory texts by Gallian and Hungerford.These books were very useful because they actually completed proofs instead of leaving them as exercises for the reader.Someone new to abstract algebra is also typically new to higher mathematics.This means a book should have clear and full explanations, not skip major points like Rotman does.Rotman commits another sin by failing to provide homework problems which correspond with the material he presents. One nice thing is that the book does provide a wide array of material (much more than most other introductory texts).This virtue soon turns astray however because by providing so much preliminary material on congruences, functions, divisibility, .... you'll be lucky if your teacher gets to groups by halfway through the semester.

I'd skip this one...
I was very disapointed with Rotman's attempt fix his first edition of this book.The wording is still overly dense, the topics skip around too much, and the examples are less than illuminating. At least he fixed the 10 by 10orthogonal latin square on the cover to be correct this time.I thinkHernstien's classic "Topics in Algebra" is a much betterintroduction

Excellent and aproacheable!
This is an excellent bookto use fo an introduction to modren algebra.It is clear and very accessible, with many useful examples.I highly recommend it. ... Read more

Book Description

This long-awaited revision provides a concise introduction to topics in abstract algebra, taking full account of the major advances and developments that have occurred over the last half-century in the theoretical and conceptual aspects of the discipline, particularly in the areas of groups and fields.

Key features include:

Customer Reviews (6)

DON'T BUY THIS BOOK
This book is full of wrong concepts, wrong definitions, misleading explanation, wrong proofs, ... A math book like this is a real shame! I have thrown this book to the garbage!
As it is possible that nobody has corrected this book before putting it in the sale?

this book is out of date
I think that most of schaum's series are out of date. In particular, Schaum's "abstract algebra" is not an exception. I bougut this book to prepare my course, Abstract Algebra 1. But this book was full of stuff which is not relevant to the subject.For example, it deals in matix and boolen algebra, which are excluded in most of Alstract Algebra courses in universities. And it doesn't contains stuff about Galois' Theory. Galois' theory can be called the aim to learn Abstract Algebra. I cannot help confessing that to read this book is to waste time. It would confuse you rather than help. You cannoutbuild the outline of Abstract Algebra with this book. I think that it is becase this book was too old-fashioned.

Full of errors
~I usually gave books I bought not bad reviews. But this one, I hate to put it in this way, is full of wrong concept, unclear definition, misleading explanation, incomplete proof, ... A mathmactics book like this is a real shame!

The reason I did not give it one star was I like Schaum book's style: definition, then example, then exercise, then answer at the end (this one doesn't have).

In sum, you can't use this book for any purpose, except as one reviewer pointed out, the errors really~~ make you think about the concept. But before you can do that, you should already know some basic abstract algebra and have a logic mind.~

Not impressed
I was not impressed with this book.The author appears to make quite a few errors, both in the definitions and in the examples, enough so that I could not be sure what was intended.I cannot recommend this as a tutorial in abstract algebra.However, the confusion did force me to think about the subject.

invaluable asset to the Mathematician/Philosopher
The subject of "modern abstract algebra" is daunting!I was intimidated to launch into a study of the subject, and was referred to this Schaum's Outline by a professor, who advised me that it was the best introduction for me to consult.He was right!It is so clearly writtenand so "poetic" in its treatment of modern algebra, that itpresents mathematics as a beautiful language of the pure forms andsymmetries and logic in elegant simplicity! But it appears to me to besomewhat radical in its approach to the many different topics; suggestingin a brazen way, a synthetical cohesion say between groups and modules,andrings. At any rate, it is probably too adventurous for the general market -even for the few readers who would understand, let alone appreciate, thedaring philosophical assertions the author makes - it will probably enjoyonly a brief run....maybe to be celebrated later (as often great thingsare) as "visionary"! I'm glad I at least had the great fortune ofseeing Mathematics from such a lofty height, because of this book! ... Read more

Book Description
Highly regarded by instructors in past editions for its sequencing of topics as well as its concrete approach, slightly slower beginning pace, and extensive set of exercises, the latest edition of Abstract Algebra extends the thrust of the widely used earlier editions as it introduces modern abstract concepts only after a careful study of important examples. Beachy and Blair's clear narrative presentation responds to the needs of inexperienced students who stumble over proof writing, who understand definitions and theorems but cannot do the problems, and who want more examples that tie into their previous experience. The authors introduce chapters by indicating why the material is important and, at the same time, relating the new material to things from the student's background and linking the subject matter of the chapter to the broader picture. Instructors will find the latest edition pitched at a suitable level of difficulty and will appreciate its gradual increase in the level of sophistication as the student progresses through the book. Rather than inserting superficial applications at the expense of important mathematical concepts, the Beachy and Blair solid, well-organized treatment motivates the subject with concrete problems from areas that students have previously encountered, namely, the integers and polynomials over the real numbers. ... Read more

Customer Reviews (5)

A very nice, detailed exposition to Abstract Algebra
This is the best introductory text I've read.I like it much better than Durbin, and it's easier to read than Herstein (though Herstein is still a great book!).The author takes a lot of time explaining proofs in the beginning.Over time, they leave more to the reader.The exercises are bountiful, and I often find a few interesting ones in each section.I highly recommend this text to anyone interested in higher mathematics.It's very thorough, yet very readable.

only for brainiacs
This book has some nice proofs in it (though, disappointingly, many key results are "left as an exercise"), and some nice diagrams as well, but it is way too light on methodology. Unless you're blessed with brilliance, inpiration, and limitless free time, avoid this book. I've read many chapters two or three times over and still cannot apply what I've learned to the problems at the end of the chapter. In that respect, this book fails as a student textbook. It is concise enough to serve as a reference, but doesn't offer much for someone who is genuninely interested in the subject but doesn't already know everything.

Buy this book!!
Not only is the best book I have seen on Abstract Algebra, this is the best mathematics book I own. I have used it as a suppliment while studying, in research, and in teaching. It is clear and readable. The authors also have a wonderful web site with scores of resources on the subject.

Carefully develops proof writing skills
This excellent book was my textbook for 2 semesters of senior level abstract algebra. The unique feature of this book is that elementary number theory, equivalence relations, and permutations are carefully introduced at the beginning. Other books launch right into groups and then have to make long digressions to cover these topics. Comparing this book to the best-selling Contemporary Abstract Algebra by Joseph Gallian, I like that Gallian's book adds many applications which students will find interesting. However, Beachy and Blair's book puts a greater emphasis on developing student's ability to do proofs. The book also incorporates more number theory than many other texts. Answers to selected problems are included, so I recommend this book for self study as well as a textbook for any undergraduate abstract algebra course.

to slow
In trying to teach students algebra, I tried to use this book to teach them from, but I found that all the concepts were introduced at what is seemingly high school level.I think that a moderate high school student (with some curiosity) could teach himself the basics of algebra with thisbook.As an undergraduate text, though, it is way too slow and way tooelementary. ... Read more

Customer Reviews (13)

An Embarrasing Monument to Pedagogical Incompetence
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 (were he still alive) might muster to save face in light of the content on subsequent pages.

First, each section usually has exercises divided into three categories: "Easier problems", "Middle-level problems", and "Harder problems". The easier problems range from mundane pencil-pushing to rather stiff analyses; the mid-level problems are typically quite difficult or even 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 knowsto 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.

More information please!
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.

Excellent Introduction 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.

baby Herstein!
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.

Best at what it is
(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"... ... Read more

Book Description
The Third Edition of Introduction to Abstract Algebra continues to provide an accessible introduction to the basic structures of abstract algebra: groups, rings, and fields. The text’s unique approach helps you advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. ... Read more

Customer Reviews (1)

Very good introductory text
The first time I took Abstract Algebra. I used Herstein's text the most cryptic text I have yet to use. I read the book cover to cover several times and still lacked a firm grasp on the material. Nicholson's book takes the time to present many examples and to thoroughly cover each topic. The examples of groups most frequently discussed are all placed at the beginning allowing the reader to have many examples to go on. While the book is not a terse reference it is a great introduction to the world of abstract algebra. It gives the undergraduate a chance to make that large step to this higher level of abstraction.However, the exercises are a little easy and the counterside to the above is that it is quite long. ... Read more

Book Description
This is a self-contained text on abstract algebra for senior undergraduate and senior graduate students, whichgives complete and comprehensive coverage of the topics usually taught at this level. The book is divided into five parts.The first part contains fundamental information such as an informal introduction to sets, number systems, matrices, and determinants.The second part deals with groups. The third part treats rings and modules. The fourth part is concerned with field theory. Much of the material in parts II, III, and IV forms the core syllabus of a course in abstract algebra.The fifth part goes on to treat some additional topics not usually taught at the undergraduate level, such as the Wedderburn-Artin theorem for semisimple artinian rings, Noether-Lasker theorem, the Smith-Normal form over a PID, finitely generated modules over a PID and their applications to rational and Jordan canonical forms and the tensor products of modules.Throughout, complete proofs have been given for all theorems without glossing over significant details or leaving important theorems as exercises.In addition, the book contains many examples fully worked out and a variety of problems for practice and challenge.Solution to the odd-numbered problems are provided at the end of the book to encourage the student in problem solving.This new edition contains an introduction to categories and functors, a new chapter on tensor products and a discussion of the new (1993) approach to the celebrated Noether-Lasker theorem.In addition, there are over 150 new problems and examples. ... Read more

Customer Reviews (7)

one of the best books on abstract algebra
I like this book very much. Pure math, all the proofs are complete and relatively easy to follow. Solutions for the odd numbered problems are provided. If you like math and want to learn the fundamentals of abstract algebra then this book is exactly what you need. It's written in theorem-proof/corollary style. I think every undergraduate student of mathematics, physics or information sciences should be able to use this book.

too concise in some parts, good elsewhere
I picked this book up at my students' society used bookstore for $10, it turned out to be a pretty good bargain. However, there are some theorems where the authors say something is obvious & I didn't think so. It isn't very often though, the rest of the book is pretty good, and I was a bit surprised because I had only heard of the well-known authors like Gallian, Herstein, Lang, etc. It covers maybe 3 courses worth of material too, including groups, rings, fields, vector spaces & modules, Galois Theory (complete with every possible application!), and more advanced stuff like a separate chapter on modules (in addition to the section with vector spaces), tensor products and principal ideal domains. There are also complete solutions to the odd-numbered problems. This book is surprisingly good except in certain parts, I like it.

A must for every math library
Bhattacharya is very concise and readable for a very difficult subject, if you are new to abstract algebra.His proofs are complete and expert and his outline is great.Also his problems are useful

Good but...
I agree this is a very clear and easily readable text but a graduate textit is not. One would need to know most of this material before startinggraduate level. Lots of stuff is left out and I think a rather better bookthat is equally clear and readable etc. but much more comprehensive withmore worked examples and historical motivation is Malik et.al. inMcGraw-Hill "Fundamentals of A.A.".

An extremely good text book
This is an excellent book containing more than enough examples.And the concepts are explained very very clear.The most improtant is that, although this book is easy to follow, but its content is not simple. ... Read more

Book Description
The simplicity of the language, the organization of the ideas, and the conciseness with completeness are this book's main strengths as it introduces abstract algebra. It plunges directly into algebraic structures and incorporates an unusually large number of examples to clarify abstract concepts as they arise. Theorem proofs do more than just prove the stated results, they are examined so readers can gain a better impression of where the proofs come from and why they proceed as they do. Most of the exercises range from easy to moderately difficult and ask for understanding of ideas rather than flashes of insight. ... Read more

Customer Reviews (4)

A good book for a great class
I used this text for a one semester course on Group Theory in the spring of 2007. It's a great text for reference, but time is required to really grasp the concepts. I wouldn't recommend it as a book to teach yourself with, but with a good professor on your side it's a valuable asset. Another interesting (I'm not sure if I would consider it positive or negative) thing about this book is that problems are not merely examples of material covered in the text, but important theorems are also assigned for the students to prove on their own.

Excellent
This book had some great examples. The examples help me to understand abstract concepts. The proofs were very well constructed.

A wonderful text.
Concise and wonderfully coherent, this book isn't filled with "fluff" such as dumb examples and spoonfed advice.Clearly targeted for a mathematically inclined class of undergraduate modernalgebra students, you will find the immense amount of knowledge and theprice of this book to be absolutely pleasing.

okay
All the material here is very thorough, which leaves very little unclear about the material.I do have one hang-up with this text: the problems are uninteresting.Nearly all of the problems are trivial.The text to consult: "A Book of Abstract Algebra", Charles Pinter ... Read more

Book Description
This text is aimed at the abstract or modern algebra course taken by junior and senior math majors and many secondary math education majors. A mid-level approach, this text features clear prose, an intuitive approach, and exercises organized around specific concepts. New to this edition are additional applications exercises to improve student learning. ... Read more

Customer Reviews (4)

Not at these prices ($100+)
I am only giving it two stars because it is way over-priced. As a means of getting introduced to Abstract Algebra is really good. I also know that there are other sources that are also good. For one look at Groups and their Graphs by Israel Grossman. It is not as extensive as Pinter's, but will give you a great running start at this subject at a small fraction of the cost. Also try web resources, or your local university library.

Best introduction to abstract algebra
Pinter's book compares very favorably to other elementary treatments, such as Gallian or Birkhoff+Maclane. The author has intentionally deviated from the established modern writing style in mathematics texts (theorem...proof...theorem...proof...), presenting instead an eminently readable work of mathematical prose which can be understood by any conscientious ninth-grader. Pinter's straightforward proofs of "Cayley's theorem" and the so-called "Fundamental Homomorphism Theorem" alone justify the purchase.

This relaxed and readable style notwithstanding, a suitable level of rigor has been maintained throughout the text---which is fairly complete in its coverage of elementary topics. From basic group theory and ring theory to field extensions and Galois theory, many minor, auxiliary results are left as exercises to aid the student's facility in proof technique, while the important major results are explained in the most natural way possible.

Most importantly, Pinter's book would serve as an excellent second reference for those students approaching the daunting subject with another text. Once you've read Pinter, you can read just about any other text on the subject and immediately grasp. For this reason, it IS the best "first course" text, as previously stated. I consider it a masterpiece in its genre.

An excellent introduction to algebra.
The author does a good job of motivating the discussion, by describing how the next few pages relate to other areas of mathematics.The issue of motivation is extremely important; too many authors develop a very abstractview, and fail to properly motivate the student by providing an overview ofthe subject area.

awesome
All the material presented in this book is presented beautifully.All concepts are perfectly clear.It is definitely the best "first course in algebra" book I have ever seen.The problems are also great too. ... Read more

Customer Reviews (1)

Good Text Book
I like it. It works. Lots of examples of problems which is nice for such a difficult subject. DON'T BUY THE SOLUTIONS MANUAL. If you can get the book cheaper by itself do it. The solutions manual is the odd answers which are in the back of the book! Total waste of money and paper. Major disappointment with that. ... Read more

Book Description

This traditional treatment of abstract algebra is designed for the particular needs of the mathematics teacher. Readers must have access to a Computer Algebra System (C. A. S.) such as Maple, or at minimum a calculator such as the TI 89 with C. A. S. capabilities. Includes “To the Teacher” sections that Draw connections from the number theory or abstract algebra under consideration to secondary mathematics. Provides historical context with “From the Past” sections in each chapter. Features “Worksheets” that outline the framework of a topic in most chapters. A useful reference for mathematics teachers who need to brush up on their abstract algebra skills.

Customer Reviews (1)

Innovative approach but many errors
I liked the layout and how information was presented. However there were many typos and errors in the book that some times made it difficult to determine if the book or I was in error. Not a good situation. I do think the concept of associating the material to what teachers are teaching in High School is an excellent idea and wish I would see that in all my graduate level math books. If it weren't for many errors due to insufficient proof reading I would have given this book a higher rating. ... Read more

Book Description

Prior to the nineteenth century, algebra meant the study of the solution of polynomial equations. By the twentieth century algebra came to encompass the study of abstract, axiomatic systems such as groups, rings, and fields. This presentation provides an account of the history of the basic concepts, results, and theories of abstract algebra.

Book Description
In the same way the subject evolved historically, Ronald Solomon lets the abstract concepts emerge gradually from less abstract problems about geometry, polynomials, numbers, and more. Solomon also strongly emphasizes the connections between algebra and other areas of mathematics -- analysis (the infinitesimal calculus) and geometry. Readers will see that the various areas of mathematics are not hermetically sealed off from each other and that most of the truly important achievements in mathematics have been the product of a fruitful interaction of different areas. Using this book, readers will gain a true understanding of the subject while being creative mathematically as opposed to simply imitating template problems. ... Read more

Book Description
Concrete Abstract Algebra develops the theory of abstract algebra from numbers to Gr"obner bases, while takin in all the usual material of a traditional introductory course.In addition, there is a rich supply of topics such as cryptography, factoring algorithms for integers, quadratic residues, finite fields, factoring algorithms for polynomials, and systems of non-linear equations.A special feature is that Gr"obner bases do not appear as an isolated example.They are fully integrated as a subject that can be successfully taught in an undergraduate context. Lauritzen's approach to teaching abstract algebra is based on an extensive use of examples, applications, and exercises. The basic philosophy is that inspiring, non-trivial applications and examples give motivation and ease the learning of abstract concepts.This book is built on several years of experienced teaching introductory abstract algebra at Aarhus, where the emphasis on concrete and inspiring examples has improved student performance significantly. ... Read more

Customer Reviews (1)

Very suitable textbook for courses in abstract algebra
The subject matter of a first course in abstract algebra is almost universally the same to all people. It begins with some fundamental background in number theory, relations, functions and a survey of notation. After this, it is groups, rings, fields in their various incarnations. Within these categories, the coverage is also generally the same, the pedagogical examples are well known and they are used in all books. Therefore, when making a choice concerning what book to adopt for a class, the decision is based largely on the clarity of the explanations and how one reacts to it on an emotional level.
The quality of the exposition in this book is excellent; it is easy to follow the explanations and proofs from start to finish. A large number, generally over 50, of exercises are included at the end of each chapter. If and when I teach abstract algebra again, this book will be given the most serious consideration for adoption.
... Read more