Book Description
This book explores the essential theories and techniques of modern algebra, including its problem-solving skills, basic proof techniques, many applications, and the interplay between algebra and geometry.It takes a concrete, example-oriented approach to the subject matter. ... Read more

Customer Reviews (4)

an excellent book for a student who will work hard
This is a very intelligent book, by a gifted expositor and teacher.The organization is based on thoughtful pedagogy rather than imitating other standard texts.E.g. it makes sense to begin with integers and polynomials and fields, instead of groups as most books do, because these are simpler and more familiar objects, and most people will find them more useful.

The abstract ideas that will occur in studying groups (and general rings) come up here in a more familiar setting.The author is always mindful of the interest of the material and gives significant applications as soon as they are feasible.

A particularly strong feature is the excellent sets of problems.Students should try all of them.The use of algebra to do some interesting projective geometry offers a fine glimpse of the more advanced use of the topic usually denied beginning students.

The book is written in a style suitable to a reader who has some mathematical sophistication, clear but not spoonfed.Shifrin never talks down to the student, and tends to present proofs in an articulate, but somewhat succint, rigorous, elegant style.A student with no experience at proofs will be challenged to understand some arguments, where parts are left for the student to fill in.

Thus reading this book is intended to be an active endeavor, pencil in hand, as it should always be.

The Worst Book of my Studies in Mathematics
This is the worst math book I have ever encountered.It is counterintuitative moving backwards compared to other text books teaching the same content.This book could have been so much more informative, however,there are little theorems that are missing.It could have had more pictures illustating the bigger ideas!There is no solutions to odd numbered exercises.I struggled to find other books to help me through this one, but no other book I found approaches the material in the same manner.

A clear and well organized book.
I took Ted Shifrin's Abstract Algebra course at UGA using the lecture notes that eventually became this book.Shifrin is one of the most decorated mathematics teachers around; his skill at presentation and hisconcern for student understanding come through in this book.

A coursetaught from this book will, of course, reflect its instructors abilitiesand compatibility with the text.As a book to read yourself this is anoutstanding text.The geometric flavor of the book works extremely wellfor the geometrically inclined.Because of its focus on clear instruction,its weakest role is as a reference book.

If they'd only release a secondedition fixing the books typos this would be more solid five star text. [...]

see below
I took a course which used this text, and I must say that that class was the least interesting class I have taken in my life.I think that looking at algebra from a geometric standpoint (and vice versa, an equivalent statement) ruins both algebra and geometry.Algebra is beautiful. Geometry is beautiful, but for a different reason.The intersection oftheir beauty (also, the beauty of their intersection) is the null set. ... Read more

Book Description
For use in your advanced abstract algebra course, Fundamentals of Abstract Algebra takes a blended theory and applications approach. Each chapter consists of definitions, theorems, proofs, and corollaries. Throughout the text you will find numerous examples that illustrate the concepts, historical background on the development of abstract algebra, and profiles of notable mathematicians. ... Read more

Customer Reviews (1)

Concrete Examples!
As one studies algebra, there is a common situation that the theorems get obscurity, immediately if you do not follow them on some concrete examples. And also a very common thing with the presentations is that the theorems follow without any motivation. This book provides lots of examples andmotivations which make one understand the concepts clearly. ... Read more

Book Description

Customer Reviews (5)

dense and rigorous
You can't skim through this book. You have to thought about each sentence before move to next one. There are tons of theorem and corollary. Each has rigorous proof and accessible examples.As people mentioned there is no answers for the exercise. But it doesn't matter. Once you feel you know all the material very well, you can tell whether you give an right answer to a question or not.

I like this excellent book. I am using it to review the abstract algebra course.

Not perfect but still very nice
I purchased this book to help me prepare for a graduate-level course as an undergrad. The book is written at a good level: not as rigorous as a typical grad textbook, but not as chatty as many modern undergrad textbooks. This allows the reader to focus on the material and have it well-explained without being distracted or treated like a junior high student. The book contains no answers for any of the exercises. If I was not using it for self-study, this wouldn't be a problem. There are a few places where he does a bit of handwaving or is a bit lazy in his definitions (see the definition of "subgroup" on p. 207 for an example), but this does not overly detract from the quality.

While it's not perfect, I'm very happy with the book for my somewhat limited purposes. I'd like to give it 3.5 stars, but I'll be generous and round to 4 since I can't.

A Readable Intro to Algebra
I have worked through the first 7 of the 13 chapters with the exception of chapter 4 (a tangent on Diophantine equations.) My own personal goal was to become acquainted with group and ring theory.If you proceed past chapter 7, then you will learn about polynomial rings, quadratic domains, abstract issues in linear algebra, and other topics.From what I read, I found Deskins' book highly readable.My math background consists of three college courses that I would consider rigorous and proof-oriented.If you have less of a background then it might be more challenging; however, the book builds its concepts very methodically and logically.Rarely did it leave me scratching my head and searching through previous chapters.

Deskins includes enough exercises to get a good mental grasp of the ideas.The level of difficult ranges from the very easy, definition checking problems to the sort of challenging.I say "sort of challenging" because none of the more difficult problems seem to be quite as difficult as the most difficult problems in other books.However, I have no experience with other algebra books, so this may be a characteristic of the subject.

All in all, I highly recommend the book as a text for teaching yourself abstract algebra.It is very readable and the well-chosen exercises help you understand the material.

It's a two-sided thing.
On the one hand, this book, like all Dover Mathematics books, is fairly dense, with few examples or pictures. It's a difficult read, but, again, like all Dover books, is totally comprehensive.

Now, on the other hand,this book is, hands down, the cheapest abstract algebra book you will everfind (again, this is a trait of Dover). When I bought this book on Amazon,I searched for "Abstract Algebra", and despaired when I sawprices like $80.00, $90.00, etc. To find a good textbook for under $20.00is a godsend.

So, basically, if you're willing to put some effort intothis book and plow through it (and it's no more dense, really, than mostmath textbooks), it's very rewarding.

Abstract Algebra provides a clear course in Abstract Algebra
Abstract Algebra provides a helpful look into the great topic of Abstract Algebra.While, like most Dover books, it does not provide extensive amounts of problems or their solutions, Deskins attempts to explain eachtopic from elementary number theory to matrices building upon previousknowledge with the least confusion as possible.Deskins' book does notrequire extensive mathematical background or sheer mathematical genius. Instead, only the desire to learn is required to become enriched by thisbook.I recommend Abstract Algebra to any high-school or colledge studentwishing to expand their mathematical horizons. ... Read more

Book Description
The authors have used forty years of classroom experience to design a text that serves as a superb introduction to abstract algebra. All students, even those with no previous knowledge of abstract or linear algebra, will benefit from the Fifth Edition's organization and selection of topics.Outstanding features include: (1) builds abstraction on a solid foundation of concrete examples; (2) develops concepts gradually but allows for more rapid progress as students' mathematical maturity increases; (3) offers unparalleled problem sets; and (4) foreshadows important topics and then clearly presents and applies them to facilitate retention, not mere exposure. The historical and biographical notes on major contributors to the development of algebra show that mathematics continues to be created by real people. The preface shows how to use the text's flexibility to achieve any of several goals. ... Read more

Customer Reviews (6)

Really good book
I really loved this book. I used this book for my first
course in Algebra and we covered till chapter 4.5 and section 8.3 skipping some
of the sections after 3.5. The book is easy to read and with nice homework problems
. Also its not too wordy like some other book where you get lost in the myriad of
words to figure out what is the essence of all that blurb. Like other standard
books on this subject it is also interspread with biographies of notable mathematician
who contributed to the subject. When this book was assigned as the main text during the
start of the semester I was not sure if my instructor made the best choice because
the book has so few and average reviews, but now after the course is over I can
definitely say this it was the best choice. Use it you will love it.

Great Book
I don't know what Ita Cirovic's problem is, but this book, in my opinion, is the most well written, clear and straight forword book on abstract algebra I've read.

The explanations and proofs are clear and easy to understand, one can understand the proofs in a short amount of time, unlike many other abstract algebra books.

If you don't like this book then you must already know abstract algebra and want more detail or you've just got a problem and need to see a psychologist (kidding) :D

JOhn

Basic introduction
This book is subtitled, "A First Undergraduate Course", and that's exactly what it is. Don't expect in-depth technical treatment, but it's a decnt introduction to abstract algebra, covering basic properties of the integers, groups, sets & mappings, rings & fields, polynomials, Euclidean constructions, and some additional material on the integers and coding (from the table of contents). We used it in my undergrad course, and it was one of the simpler courses I've seen. All in all, not a bad way to go if you're just looking to dip your toes in abstract algebra. Look elsewhere for a deeper consideration.

Great Teaching Tool
My first course in abstract algebra was from a pre-publication version of this text.I remember Professor Alexanderson rushing into class at the last minute with the next few pages of the text still damp from the mimeograph machine.I have used the text in my abstract algebra courses ever since the first edition became available.The most distinctive feature of the text is the extensive and well organized sets of problems; the problems are the course.The problems at the end of each section not only give practice which reinforces the material in that section, but also leads into the next.There are many cases throughout the text where the main theorem in Section N has already been discovered at an intuitive level by the class from doing the problems in Section N-1.All that is left to be done in Section N is to give a precise statement and a proof of the theorem.I have found that students who are serious about mathematics thrive on this text.Two groups who find this approach to teaching/learning mathematics to be particularly beneficial are the students who intent to pursue graduate school and those who are preparing for secondary math education.I recommend the text highly to all my fellow mathematics professors who are looking for just the right text for their abstract algebra course.

Not so good for undergraduate text
Currently, I have this book for my undergraduate course in Abstract Algebra, and I really really wish that the professor picked another one. The main reason why I don't like this book is the fact that the explanations are very bad and there is like 2 pages max. for each topic and then around 30 problems at the end of each topic. I think that clearly this is not enough of theory and explanation for an undergradute text in Abstract Algebra. There are very very little examples, and if there are any then those would be proof of the theorems and that's it.I just don't feel comfortable with this book, and I had to search for other books in order to get through the class. I really like the contents, and I just wish the author would spend some more time explaining why and not just stating the theorem. That we can all found in Mathematical Handbook. ... Read more

Book Description

Customer Reviews (7)

exelent book
This book in an excellent choice. Well written not complicated lingo, and for visual learners the diagrams are intelligently selected. Very good introduction to group theory, with many examples. I am a computer programmer so I did not want a book with pure math and this book uses everyday examples to make a point.

Struggling a Little
I am struggling with this book.There are times when more explanation is needed and yet, at other times, there is too much.

Shortest journey from group theory to Galois theory
This book provides the shortest journey from group theory to Galois theory (which determines when a polynomial equation can always be solved by means of an algebraic formula).Any topic in abstract algebra that isn't absolutely essential to this "trip" has been omitted from this book.Hence there's no coverage of ideals of rings, Euclidean domains, etc. The coverage of Galois theory is very rushed and proves only half of the theorem that is the book's ultimate goal; namely, that a polynomial equation can be solved by means of an algebraic formula if and only if the equation's Galois group is solvable.Some of the important proofs later in the book are sketchy.

The reader should be very familiar with methods of proofs and should have had some previous exposure to abstract algebra, especially groups and vector fields.The treatment of Galois theory is so rushed that, for self-study, the reader should refer to a second book on abstract algebra that treats Galois theory -- such as Richard Dean's Elements of Abstract Algebra (1966), which is the basis of the Maxfields' book, or W.E. Deskins' Abstract Algebra (1996).

Excellent text for a first course
I taught out of the hardcover version of this book at SUNY College at Oneonta many moons ago.It was a course for first-semester sophomore mathematics majors.The goal of the book is to develop the subject matter that is needed to prove that the fifth degree polynomial is not solvable by radicals, i.e. there is no analogy to the Quadratic Formula for the quintic.(There is for the cubic and the quartic.)We had a good time because the course was focused on this one goal and the class knew exacly where we were headed.We got there, too.It was very easy to teach from this book and students rated it very highly.The students that I taught had Calculus I and II and a Foundations course as freshmen.The prior exposure to logic, sets and methods of proof (development of the integers) was very helpful, as was the maturity gained from the calculus (although the subject matter of Calculus was not necessary).I supplemented by rigorously developing the rational numbers, saving the reals for the Intro to Analysis course that followed this one.I am now a biostatistician outside of academia, but I hope that professors who are now teaching Abstract (Modern) Algebra will consider using this text in paperback form.

Roots (as in square roots)
This charming little introit to abstract algebra is keyed on a theme of the algebraic equation, and the discovery of the insolubility of the quintic. This includes the history and final plight of the circle-squarers, and some of the history of Galois and Abel, working heroically and heuristically in the early nineteenth century without the recent easier access to the subject now available.
All math is divided into three parts, analysis, algebra, and topology and abstract algebra is no doubt abstract, but less so than analysis, and shows the beautiful hidden sructure behind number systems, from monkey-see monkey-do to counting on your fingers, to the square root of minus one and beyond. The progression from simple groups, to rings, and fields and the rest is a revelation of the complexity behind simple things and it is a pity the educational system cannot bring more to these vistas, where the elegant Galois theory caps the summits. A good book to amateurize with, and with a good mouse-hole entry for a look-see to the ultra-clever Galois theory. Superb. ... Read more

Book Description

Customer Reviews (2)

An average resource
I used this book as a reference resource for an advanced algebra course.At times, wording of key concepts was a little long.This book is a good complementary reference to Joseph Gallian's Contemporary Algebra book.

Intuitive Algebra
This is the book version of a series of lecture notes on abstract algebra written by the author and still available on his web page. However, given the price (it's a Dover book...) it's worth buying just to avoid that thick pile of sheets lying around. The best thing about this book is that it avoids formalism whenever it can without sacrificing rigor. Many theorems are "proved" by means of an example of a general case. In this way, the reader gets the intuition behind the result without having to deal with the abstract and sometimes artificial constructs of a rigorous proof. In any case, supplying that rigorous proof can be seen as an extra exercise (or you can look it up elsewhere!). In other words, it's a great book to learn the ideas behind the theorems dealing with groups, rings, modules and fields.

The second part of the book deals with commutative algebra, algebraic number theory, algebraic geometry and homological algebra - areas where it's very hard to find intuitive explanations in the literature, since books on those subjects tend to assume (quite reasonably) the reader has a solid background in abstract algebra. Unfortunately, that means that examples and intuitive explanations are drastically reduced, sometimes to none at all. That makes this book even more attractive.

In any event, after you get the intuition, it will be much easier to to tackle the more rigorous approaches of Dummit & Foote or Hungerford (I don't know Lang's book but I'm told it's much dryer than these two).
Or you can start your study of algebra with any of these more traditional books and use Ash's as a supplement. If a theorem or its proof proof seems opaque, look it up on Ash. Chances are his explanation will clarify things. ... Read more

Book Description
A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains. ... Read more

Customer Reviews (2)

Abstract Algebra vol 2 by Spindler
Page 174 volume 2 the author did not follow completely the proof of Nagell theroem as in Algebraic Number Theory by Stewart & TallInstead Heintroduced the matrix [1 1, -2 0], We may name it here for short S, Theauthor claims that S**42k = [-1 -1, -1 -1] mod 3 which is wrong S**42k =+-[1 0, 1 0] 4|k or 2|k respectively and = +-S 4|k-1 or 2|k-1 respectivelyin both cases the first entery in the total matrix as S**(42k +13) * [0 1]would be -1 and destroy the logic of the author in his argument However itdeos not violate the theory for -1 in a field of chratersistic 3 need notbe -1 in the integral domain Z[sqrt(-7)] I do here thank Amazon.com for thechance to report that for neithe the author nor the editorial at thepublisher has an address to communicate with. Abdu Shokr35-17 Ditmarsblvd suite 202 NY NY 11105 August 3 2000

A thorough, accessible and indispensable resource on algebra
This two volume set is by far the most complete text on abstract algebra available.Rich in detail, a wealth of examples and clear yet concise explanations provide the reader an accesible source to deepen his understanding of abstract algebra.Spindler conveys his love of algebraand a desire to reveal its riches to the average student. If you'verelied on Hungerford's / Lang's Algebra or Warner's Modern Algebra, thistext is the last text you will need. ... Read more

Book Description
Based on lectures given at Claremont McKenna College, this text constitutes a substantial, abstract introduction to linear algebra. The presentation emphasizes the structural elements over the computational - for example by connecting matrices to linear transformations from the outset - and prepares the student for further study of abstract mathematics. Uniquely among algebra texts at this level, it introduces group theory early in the discussion, as an example of the rigorous development of informal axiomatic systems. ... Read more

Customer Reviews (5)

the ideal book for beginning undergraduate students
I fully disagree with the one star review...
This is a beautiful book though you have to belong to a certain reader segment to appreciate it.
The readers that will like this book probabely are beginning undergraduate students that want to build a mathematical career and want a first and quick introduction to abstract mathematics. The reader is not overwhelmed by exotic topics that are rarely used, but is introduced to abstract basic principles needed to understand other courses like for instance quantum mechanics,more advanced graduate courses in algebra or functional analysis.
The power of this book is that it covers just enough material to have a solid foundation of algebra for other abstract courses like functional analysis,
When I compare it for instance with the book of Shilov, I strongly prefer this book since it is better organised, covers less topics, but enough to know the basics. This book succeeds in providing shorter proofs compared to Shilov without sacrifying rigor and clarity. How is this possible ?? Ah my friend, this is a reward coming from abstract reasoning as illustrated by this book.

Is this really good?
I have just had a glimpse of all the three reviews here, and wonder whether the reviews are really true. I am now an undergraduate and taking a course which uses this textbook. Frankly speaking, I think this book sucks. If you carefully compare this book with Friedberg, Insel and Spencer's Linear Algebra, you will know the difference. This book misses out many things I consider important. Also, it does not contain many interesting and essential results, like all infinite-dimensional vector space has a basis. I don't think Zorn's lemma should not be mentioned in a book like this one.
Also, I can't really accept that it starts matrices like that. We all know that matrices come from linear transformations. Matrix multiplication comes from the composition of linear transformatiosn. This book does not mention this and start it right away. This approach is quite bad in my opinion.
Finally, I think that this book is messy. I think it is quite difficult to include introduction of linear algebra and abstract algebra at the same time, but if it's so difficult to do it, why don't you study it separately? I think the author tried hard to combine these two stuff, but failed to do that successfully. All my friends who have linear algebra and abstract algebra background agree with me. I definitely wont' recommend this book.

excellent
This book treats the basic principles of abstract algebra.
It is targeted to graduate students that need a more theoretical approach to mathematics (instead of the usual calculus courses)
This book is the best introduction to abstract algebra for the following reasons

-its style : good introduction in each chapter, making the reader curious to read further.
-its rigor : everything is well explained in full details with proof.
-its elegance : This book treats the abstract structural aspects of algebra and then suddenly shows how more concrecte applications follow from these abstract results. This is the kind of elegance and style that makes mathematics an art : build a very abstract theory and then see how more concrete stuff follows immediately as special case of this abstract framework. This way, new things can be discovered and most of the time (as in this book), you can explain practical calculation rules in a short and rigorous way.

Definitely the finest there is ....

math is art ...
Great book !
If you read this book, you will not only gain knowledge of abstract algebra, but also understand clearly why mathematics is art. It was a real fun reading this book. The topics are presented in such a way that the author leads you to a climax, making you curious to read further, and help you to explore the beauty in all the ideas of abstract mathematics. This book is the best book I ever read on abstract algebra.

The emphasis in on rigor and abstract structural concepts. It is nice to see that the more practical applications follow as a special result from the abstract structural concepts. This is a very elegant approach !!

A Great Structural Approach to Linear Algebra!
As a person who has a healthy interest in mathematics and has taken many classes, this is definatley one of the best!Professor Valenza taught it (he has been teaching this Linear Algebra class at CMC for ten years) and his book is essentially an excellent compilation of the lecture notes from his class.It takes a very different tack from most linear algebra texts: Usually, a linear algebra text begins by inroducing matrices and solving simultaneous equations, teaching computational methods.Prof. Valenza starts with the structure BEHIND all of that math however: Sets, Groups, and Vector Space properties.This structure is absolutely essential to knowing what's going on: My father took a (less superior) linear algebra class many years ago, and he never understood the concepts behind the mathematical manipulations; I actually sat down with him and taught him the things that I learned in Prof. Valenza's class.I really think that the knowledge in this book is invaluable to someone who wants to know what Linear Algebra is really about.

Just a few examples of the truly deep knowledge that this book communicates follows.For instance (this will ring a bell for those who have taken calculus) the "constant of integration" that must be added when doing an antiderivative is actually a property of group homomorphisms.The "absolute value" that must be introduced when taking square roots is structurally THE SAME property of group homomorphisms.Also, we all know that you can't divide by zero; it's just not allowed.But, the reason for that is ultimatley rooted in group theory; namely, the real numbers are NOT a group under multiplication.This type understanding has EVERYTHING to do with matrices and systems of equations!For instance, the fact that only square matrices can be inverted is a trivial consequence of a property of function mappings called "bijectivity." (a mapping from three- to two- dimensional space can't be bijective, for example)Many seemingly complex linear system problems can be simplified to a trivial questions by, for example, investigating the "span" of the column vectors of a matrix.There are countless problems that simply can't be understood withoutthe kind of structural knowledge that Prof. Valenza's book gives.

Understanding the basic properties that underlie so many mathematical objects has been a true delight for me, and anyone who wants to know what is really going on "behind the scenes" with linear equations would be wise to investigate Prof. Valenza's book.It's no accident that he also wrote a book on Fourier Analysis; understanding structure is simply the key to higher math. ... Read more

Book Description

About the first edition:

Customer Reviews (5)

has great potential, but could use a second edition.
The title of the review pretty much says it all. For a first edition, this isn't bad. I've taken copious notes from this book, and I've learned quite a bit. It's much more comprehensive than most other algebra books on the market, to be sure. I'd be hard pressed to find another introductory algebra book that actually makes it to the Adjoint Functor theorem, tripleability, and Birkhoff's characterization of varieties. However, the book also has its flaws. The most annoying one is probably Lemma 10.6.8 on page 331, which says that afinite dimensional division algebra over an algebraically closed field has dimension 1. This is clearly false. (Consider the quaternions and the complex numbers). The error in the proof is that he assumes commutativity (probably the easiest blunder to make in algebra, so it's a minor offense).Thankfully, no subsequent use of this "lemma" is made in the book (making me wonder why he's choosing to call it a lemma).In some places, Grillet doesn't really have the slickest proof on the market, which would be nice if he's trying to be comprehensive (the book wouldn't be quite as much of a wrist cracker). For instance Jacobson's proof of the simplicity of PSL is much slicker and isolates the hypotheses (dim V >2 or |K|>3) The chapter dependency chart is useful, although he breaks the logic somewhat by using fields in the chapter on group theory.Chapter notes at the end of each chapter would be very useful.
All of these problems can be easily fixed in a second edition. Another idea would be for the author to maintain some sort of errata page (John Lee does this for his books on manifolds). For the most part, the book has great potential because it's got a nice, ambitious logical structure that you won't find elsewhere. I'd rather see someone go out on a limb and try to write a comprehensive, up to date, state of the art algebra book than simply rewrite an existing book focusing only on classical algebra.
For professors who are thinking of using this book for their algebra classes, I'd suggest going through it yourself before the term starts (give yourself a few months) so that you can tweak it a little. That way if you use the book for you class you can catch any mistakes.

Full of Insight
This book does not complicate every concept, on the contrary, and for example, this is the only algebra text I am currently aware of that actually provides insight into the 'mechanics' ofmorphisms between various types of sets.To be precise, in section 1.6 (The Isomorphism Theorems), Grillet, introduces and describes both factoring through a domain and codomain.For the student, this provides insight into what is happening 'behind-the-scenes' in the homomorphism theorem and,in turn, acts as a vehicle that enables the student to fully understand and appreciate the isomorphism theorems.Of course one must take in to account the ability of the student using this text and, given this, I would say Grilet's text requires nothing more than an elementary introduction to the basic algebraic structures.This text is not overwhelmingly wordy like that of Dummit and Foote or baby Hungerford, nor is it stale and lifeless like Lang's.Instead, it is well written, definitely insightful, covers all the material needed at the begining graduate level and this text can be used, like Rotman and Lang's text, as a reference.If this book seems daunting based on the size, then I would recommend either just dealing with it or using Martin Isaacs or Papa Hungerford's since both are complete, challenging and manageable.Enjoy!

Not recommended
A bad textbook I have read for algebra.The author seems to be complicating every concept thats simple to understand.
Also most of the proofs given are not straight forward and forces you to refer to some other books for a clear understanding and definitions of the same concepts given in the book.
Not at all recommended.
Better buy a Fraleigh or Herstein or Thomas Hungerford even if your teacher recommends this one.

Excellent intermediate text
Having used this book in a graduate algebra course, I feel that it is an excellent text for those who have already had a rigorous introductory exposure to modern algebra (say, via Dummit and Foote or Fraleigh).Grillet writes clearly and concisely and leaves several challenging (but doable) proofs to the reader.His wry sense of humor is also reflected in his writing.

On some subjects, it is more of a survey of topics (such as category theory, universal algebras, exterior products), the point of which only becomes clear after one needs to use these tools in other areas.

If you are new to the subject, however, the texts by Dummit and Foote or Fraleigh, e.g., are more appropriate.

another good algebra text
This text is designed for beginning graduate students. The book includes all the basic parts of algebra any mathematician should know. The presentation and proofs are clear and easy to follow. People with no priorexposure to abstract algebra might have problems learning algebra from thisbook as quite a few important theorems and results are left with no proof.Instructor can easily supplement those missing proofs if he/she thinksthat's appropriate. Overall, it's an excellent reference book forresearchers, but only a good textbook for students. ... Read more

Book Description
This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and in the information and physical sciences. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility and relevance of algebra today. In particular applications to Polya coloring theory, latin squares, Steiner systems and error correcting codes are described. Another feature of the book is that group theory and ring theory are carried further than is often done at this level. There is ample material here for a two semester course in abstract algebra.

The importance of proof is stressed and rigorous proofs of almost all results are given. But care has been taken to lead the reader through the proofs by gentle stages. There are nearly 400 problems, of varying degrees of difficulty, to test the reader's skill and progress. The book should be suitable for students in the third or fourth year of study at a North American university or in the second or third year at a university in Europe. ... Read more

Customer Reviews (1)

Compact introduction to algebra
The first thing to not about this book is that it is dense.In my abstract algebra course we covered chapters 3-5 in an entire semester.However, it contained every proof we needed in class, and although it reads slowly, it was usually crystal-clear.Especially good is its treatment of group actions, which is sometimes lacking in introductory-level algebra books.There is a lot of additional material -- the author recommends covering chapters 1-7 in one semester, which may be feasible at institutions like MIT, but for the majority of students, the information contained in this book would be more than a year's worth.Chapter 8 contains almost a semester's worth of advanced linear algebra.Sometimes I wish there were a few more exercises in each chapter; especially in the beginning, because the proofs were relatively easy, it seemed like there wasn't a good enough selection of topics.The book is mercifully cheap, but even though it's paperback, it's very sturdy, and for such a low-cost choice, it has tons of content.Recommended. ... Read more

Book Description
The authors gradually introduce and develop concepts to help make the material more accessible.This text is intended for the introductory course in algebraic structures and covers groups before rings.This course often is used to bridge the gap from manipulative to theoretical mathematics and to help prepare secondary mathematics teachers for their careers.This text includes some optional sections to give instructors flexibility. ... Read more

Customer Reviews (4)

My Best Math Book
This is definitely one of my best math books. The main feature of this book is that the readers feel very easy to follow the provided concepts and understand what is important. I really don't know any other book as good as this one. Probably only David C. Lay's "Linear Algebra and Its Applications" can compete with this one. I truly recommend anyone who studies modern algebra to take a look at this. Good luck!

thats how math books should be written!!! (but plz, change that price there)
It is surely one of the books I most enjoyed!!
But its pricey, thats why a lot of colleges (or professors) try to avoid it.

The book has eight chapters:
1) Fundamentals
2) The integers
3) Groups
4) More on Groups
5) Rings, Integral domains, and fields
6) More on rings
7) Real and Complex Numbers
8) Ploynomials.

Definitions and Theorems stand out in Boxes, then later comes the examples!! (Plz Mathematicians who write books, just take a look here, see how nicely a book can be written, then go for the challenge).

one of the good things in this book, is that it does not assume you took a class in number theory before, so it introduces in the first two chapters everything (from a typical number theory class) that you would need in modern algebra class. (that might be a drawback for a student who took number theory class, and his professor is determined to start from the first chapter in this book).

other than the definitions and theorems stand out clearly, The author give examples on how that theorem can be used!! and The examples sometimes are really good!!

What's best in this book, are the problems after each chapter, they rank from direct applications to theorems, to CHallenging problems! (at least challenging for me). But note that some of the problems depend on each other! so if ur stuck on one problem, that means you might need to use a result from an earlier problem in the same chapter. its a drawback that the author does not say "use problem ... to solve this one", I think they assume that anyone solving the problems, is solving all of them in sequence, which what students SHOULD do. There is no way you can get a good grasp on the material in this book, unless you are a genius, or you solve ALL the problems after each chapter (at least a very good amount of them). I found best thing to do is try solving them in sequence, if you dont have time to solve all of them, then skip the ones that you REALLY think you can solve, and this way you can use the result later on.

I would recommend this book to anyone interested in modern (abstract) algebra! But I think a pre-requisite to self-study in this book is exposition to how to write proofs rigorously. (well sure thats the pre-requisite for any math course, but usually this subject is one of the first subjects studied in upper level math courses, and you better take another course that exposes you to how to write proofs, if your buying this book for self-study).

An excellent introduction to higher mathematics
I thoroughly enjoyed my modern algebra class, with an excellent professor and this excellent book. The book is very clearly written, and the concepts of sets, groups, rings, fields, and number systems are explained with detail. This is especially important since my summer research in number theory requires an understanding of these algebraic structures.

Great Book
I found the ideas in this book to be very accesible to the student with little mathematics experience (as I have).It is very straight foward, contains illuminating example problems, and even has an application sectionat the end of each chapter.Many abstract algebra books assume that youcan prove anything. However, Gilbert's book focuses on the techniques oflearning how to prove. ... Read more

Customer Reviews (1)

Just lists of dictionary definitions and blank ruled pages
The format of this book is not suited to math. Instead of presenting theorems, math definitions, worked problems or useful commentary, the book consists of pages of dictionary definitions on the left facing blankruled pages on the right. That's it. Worthless. The book is for the 5th edition of Gallian, not the 6th, but it hardly matters, since there is nothing of value in it. Pass on this one. ... Read more

Book Description

With the advent of computers that can handle symbolic manipulations, abstract algebra can now be applied. In this book David Joyner, Richard Kreminski, and Joann Turisco introduce a wide range of abstract algebra with relevant and interesting applications, from error-correcting codes to cryptography to the group theory of Rubik's cube. They cover basic topics such as the Euclidean algorithm, encryption, and permutations. Hamming codes and Reed-Solomon codes used on today's CDs are also discussed. The authors present examples as diverse as "Rotation," available on the Nokia 7160 cell phone, bell ringing, and the game of NIM. In place of the standard treatment of group theory, which emphasizes the classification of groups, the authors highlight examples and computations. Cyclic groups, the general linear group GL(n), and the symmetric groups are emphasized.

With its clear writing style and wealth of examples, Applied Abstract Algebra will be welcomed by mathematicians, computer scientists, and students alike. Each chapter includes exercises in GAP (a free computer algebra system) and MAGMA (a noncommercial computer algebra system), which are especially helpful in giving students a grasp of practical examples.

Book Description
A revision of McCoy's classic text, Introductory Abstract Algebra, Sixth Edition, retains the goals of earlier editions by providing the key information for a first course in abstract algebra in an easily understood, digestible manner. The material in the sixth edition is kept at approximately the same level as that in the previous editions with a number of comments, remarks, and exercises that point students toward more advanced topics. Rings are presented before groups because the ring of integers is already known to students and easily serves as a source of examples.

* Simple, clear, motivating style
* Many examples to illustrate concepts and theories ... Read more

Customer Reviews (1)

Abstract Algebra 6th edition
Very clear and concise book for beginners interested in a little of rigor. This book proves understandably essential proofs such as that of the Fundamental Theorem of Arithmitic,and the Division/Euclidean Algorithm, among others. But it lacks few basic spell out proofs that could be used to prove major results. This books is independent of Linear Algebra. I think that the first three chapters of the following book is a great complement because of its basic proven and spelled out results : "Beginning Number Theory, 2nd edition" by Neville Robbins. ... Read more

Book Description
This is a survey, accessible to junior/senior undergraduate students and containing many examples, solved exercises, and sets of problems, of some parts of abstract algebra that are of use in many other areas of discrete mathematics. Three major themes are particularly relevant to computer science, Boolean algebras and switching circuits, finite fields and algebraic coding, and semigroups and automata. The topics of the book can be studied independently of each other, although the book is a mathematics book, the authors have made great efforts to address the needs of the users of the techniques that are being discussed. There is a special emphasis on fully worked out computational examples. More than 500 exercises accompany the 40 sections. This new edition includes major changes to the first edition: corrections and improvements to the first four chapters, a new chapter on Cryptology, and an enlarged chapter on Applications of Groups. An extensive chapter has been added to survey other (mostly recent) applications, many of which were not included in the first edition, nor are commonly found in undergraduate texts. The book assumes knowledge of the material covered in a course on linear algebra and, preferably, a first course in (abstract) algebra covering the basics of groups, rings, and fields. ... Read more

Book Description
This book's organizing principle is the interplay between groups and rings, where “rings” includes the ideas of modules. It contains basic definitions, complete and clear theorems (the first with brief sketches of proofs), and gives attention to the topics of algebraic geometry, computers, homology, and representations. More than merely a succession of definition-theorem-proofs, this text put results and ideas in context so that students can appreciate why a certain topic is being studied, and where definitions originate.Chapter topics include groups; commutative rings; modules; principal ideal domains; algebras; cohomology and representations; and homological algebra.For individuals interested in a self-study guide to learning advanced algebra and its related topics. ... Read more

Customer Reviews (5)

excellent
This is a very clear introduction to graduate-level algebra.It is much better organized than Dummit and Foote.I particularly like the treatment of modules.

The worst mathematics book I have ever read!!!
I gave this book one star only because I couldn't give it a score of zero!!! Although many professors say that this book is excellent, remember they are professors who already understand the material. This book shows no examples, and the examples that it does show end abruptly with comments such as "all items are routine." Routine!!! Please show me what to do so that I don't have to spend more money on a separate study guide. Aren't mathematics texts expensive enough? This book may be an excellent addition to a professors library but this book should never, ever be used as a primary text for students.

Good for Self-Study
This is a tough book to review, because it is not clear who the real audience is supposed to be.The author says that it is aimed at first-year graduate students, with a bunch of extra material that can be referred back to during the second year and beyond.The earlier chapters also include efficient reviews (with sketched proofs) of material that should be familiar to those who have taken undergraduate algebra.

This characterization is debatable.Based on my experience reading most of the first six chapters (the first 400 out of about 1000 pages), I would say that the level of sophistication is roughly that of Dummit and Foote's "Abstract Algebra", which is usually considered an undergraduate book.D&F can sometimes be harder to read, and that is in part because Rotman's exposition is better (in my opinion), but also because D&F introduce more difficult material earlier.Whether D&F's approach is better is questionable; I find Rotman to be a much smoother read, but the organization is quite different -- for example, one does not encounter noncommutative rings until deep into the book, whereas Dummit and Foote introduce them immediately upon defining rings.On the other hand, early in the coverage of D&F's chapter on rings, one has to digest Zorn's Lemma and its applications almost from the beginning, whereas Rotman (I think wisely) pushes this back into a later section.In general, D&F introduce a lot of hairy examples that by themselves require a lot of effort to digest (thereby impeding the reader's progress through the core material), whereas Rotman's examples tend to be straightforward, at least as new concepts are being presented.

So, overall, the exposition flows more smoothly in Rotman's book, and the reader can cover the basics more quickly with less time spent on tangential examples and early generalizations.Also, Rotman's proofs are usually much cleaner and the overall style is very nice.It's more pleasant to read than Dummit and Foote.But this comes at a cost: Dummit and Foote do cover more material, and generalize at an earlier stage, than Rotman does.

But my biggest gripe concerns the exercises.Put simply, Rotman's are far too easy for what is being pitched as a graduate course.In fact, they are in general far easier than the homework problems I sweated through when I took honors undergraduate algebra. They're barely adequate to convince the reader that he has a basic grasp on the material, and there are almost no hard ones, let alone really tough, thought-provoking open-ended problems like one encounters in Herstein's "Topics in Algebra" (an undergraduate book).There are certainly no exercises in Rotman's book that would be of any use for a graduate student preparing for qualifying exams.They're not even much of a workout for a decent (honors student) undergraduate.

So, what is this book good for?I think it's great for reading material that is usually harder to understand elsewhere.Rotman has a real knack for clear mathematical exposition, and some of the chapters are a real joy to read.(Side note: there are also a lot of typos, at least in the first printing.The author maintains an errata list at his web site, and a second printing is coming soon.There are still many errata that he didn't catch, but they're fairly minor and do not detract significantly from the reading.) But this is simply not suitable for a primary graduate text or reference.Most good schools are going to demand more of their graduate students, and one is inevitably going to have to read Lang or Hungerford (and work through their exercises) to achieve competence at the graduate level.Rotman's book is a kinder, gentler book upon which to fall back when those books are inscrutable, as is all too common.I do recommend it highly for that purpose -- I think it's a very good secondary book.

An excellent Text
To begin with, don't let the title scare you.After having read through Rotman's book I am suprised that this text had not crossed my path earlier.It is a wonderful book and must have for any inspiring Algebraist.Moreover, I am quite shocked that the larger universities have not adopted this book.

(a)This book could quite easily be used as the standard third/fourth year undergraduate introduction to Abstract Algebra.In particular, the first four chapters provide a solid foundation for a moderate paced one semester course at which point the instructor has many different options for additional topics based on the performance of his/her class.

(b)Those students that move on to the graduate level, and obviously to a university using this book, would both be familiar with the temperment and flow of the author as well as devoid of the requirement of having to purchase another expensive Mathematics text.For example, my undergraduate Algebra text was Hungerford's and post completion the logical step, being familiar with his style, was to purchase Hungerford's graduate text.For those not familiar, let me tell you there is a night and day difference with repsect to how the material is presented.

(c) The remaining 7 chapters take the willing student on a pleasant tour of ring/module theory, some advanced group theory (for the inspiring group theorist I highly recommend the authors graduate text "Group Theory"), algebras(linear included), Homology(some cohomology) and finally some algebraic number theoretic concept under the heading of Commutative Rings III.

(d) Lastly, Rotamn does not get needlessly bogged down in any one section of the book.The flow is smooth, to the point with precise definitions, examples, and ample exercises.

I have only two negative remarks: one, the failure to include more aspects of field/Galois theory.This may be due to the author already having published a book entitled "Galois Theory". Two, the failure to devote an entire section to Finite Fileds and possibly some its applications.But this failure is minimal since, at present, the majority of Algebra texts, fail to adequately introduce and motivate Finite Fields.

Great Book!...
I previously purchased Rotman's First Course in Abstract Algebra, and fell in love with it.So when I saw he a Second Abstract Algebra book, I had to have it.I am currently taking a Graduate Level Modern Algebra course, and I find this book to be a great help in my Studies.I wouldn't be as interested in Modern Algebra as I am now if it weren't for this book.I love this book and I would reccomend it to anyone who is interested in Modern Algebra, or taking a course in Modern or Abstract Algebra. ... Read more

Book Description
Eliminating the need for heavy number-crunching, sophisticated mathematical software packages open the door to areas like cryptography, coding theory, and combinatorics that are dependent on abstract algebra. Applications of Abstract Algebra with Maple and MATLAB®, Second Edition explores these topics and shows how to apply the software programs to abstract algebra and its related fields.Carefully integrating Maple and MATLAB®, this book provides an in-depth introduction to real-world abstract algebraic problems. The first chapter offers a concise and comprehensive review of prerequisite advanced mathematics. The next several chapters examine block designs, coding theory, and cryptography while the final chapters cover counting techniques, including Pólya's and Burnside's theorems. Other topics discussed include the Rivest, Shamir, and Adleman (RSA) cryptosystem, digital signatures, primes for security, and elliptic curve cryptosystems.New to the Second Edition · Three new chapters on Vigenère ciphers, the Advanced Encryption Standard (AES), and graph theory as well as new MATLAB and Maple sections · Expanded exercises and additional research exercises · Maple and MATLAB files and functions available for download online and from a CD-ROMWith the incorporation of MATLAB, this second edition further illuminates the topics discussed by eliminating extensive computations of abstract algebraic techniques. The clear organization of the book as well as the inclusion of two of the most respected mathematical software packages available make the book a useful tool for students, mathematicians, and computer scientists. ... Read more

Book Description

Customer Reviews (2)

One of the best intro to algebra texts
My first taste of algebra came from Lang's book (big mistake).I then read Gallian's undergrad. book and tried Lang again, it was still very difficult.I finally found Grove.This is a great book.Very easy to read and understand.Although it doesn't cover everything in Lang, it covers everything that commonly comes up in a first year graduate class.The book's only drawback is it's difficulty to find.If you're looking for a good intro. to algebra text (and if you can find it) buy it!

Well written and concise. Makes an excellent reference
This is one of my favorite beginning graduate texts. Although it follows a very terse definition-example-theorem-proof style, the proofs and examples seem very enlightening. Each Chapter comes
with numerous exercises interleaved with the material, as well as
exercises at the end of the chapter. Groups, rings, fields, and modules are covered in depth. ... Read more

Book Description
Most abstract algebra texts begin with groups, then proceed to rings and fields. While groups are the logically simplest of the structures, the motivation for studying groups can be somewhat lost on students approaching abstract algebra for the first time. To engage and motivate them, starting with something students know and abstracting from there is more natural-and ultimately more effective.Authors Anderson and Feil developed A First Course in Abstract Algebra: Rings, Groups and Fields based upon that conviction. The text begins with ring theory, building upon students' familiarity with integers and polynomials. Later, when students have become more experienced, it introduces groups. The last section of the book develops Galois Theory with the goal of showing the impossibility of solving the quintic with radicals.Each section of the book ends with a "Section in a Nutshell" synopsis of important definitions and theorems. Each chapter includes "Quick Exercises" that reinforce the topic addressed and are designed to be worked as the text is read. Problem sets at the end of each chapter begin with "Warm-Up Exercises" that test fundamental comprehension, followed by regular exercises, both computational and "supply the proof" problems. A Hints and Answers section is provided at the end of the book.As stated in the title, this book is designed for a first course--either one or two semesters in abstract algebra. It requires only a typical calculus sequence as a prerequisite and does not assume any familiarity with linear algebra or complex numbers. ... Read more

Book Description
Learn abstract algebra the easy way with CONCEPTS IN ABSTRACT ALGEBRA! This mathematics text shows you how mathematics proceeds, how to use techniques that mathematicians actually employ, and the art of constructing mathematical arguments. Extensive discussions, examples, repetition, development in nontrivial contexts, and exercises help you learn definitions and results. Examples show you how elementary material is developed and give you a template for writing your own arguments. ... Read more