Reviews (16)

Truly a gem of mathematical literature
I knew I was going to at least smile when I read this book because of the fact that Gallian uses Beatles' song lyrics to open some of his chapters.But, I was concerned about the mathematical content.Those fears were put to rest basically the minute I turned the first page.
Wonderful Abstract Text
This is possibly the most addictive Abstract Algebra book ever. Filled with a wonderful selection of problems, Gallian discusses many aspects of groups and rings in a way that is enjoyable to study. The love of mathematics that is shown in this book is reflected by how Gallian eloquently weaves principles of group and ring theory with beautifully selected INTRUIGING problems. I enjoyed this book more than any other math text I have had.

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

Subjects:  1. Algebra - Abstract    2. Algebra - General    3. Algebra, Abstract    4. Mathematics    5. Science/Mathematics    6. Textbooks    7. Algebra   

Reviews (9)

classical
very well written text about the algebra of standard model,
A good *first* start
This book is good for what it is, namely, something to get your feet wet.When learning the basics of particle physics, e.g. as an undergrad or a beginning experimentalist, this is the quickest way to get a feel for the standard model gauge group. What do you need more?
I'd say that, at least, the Georgi's book is too underestimated here. Read more

Subjects:  1. Algebra - Abstract    2. Algebra - General    3. Group Theory    4. Lie Groups    5. Lie algebras    6. Nuclear Physics    7. Particle Physics    8. Particles (Nuclear physics)    9. Physics    10. S-matrix theory    11. Science    12. Science/Mathematics    13. Solid State Physics    14. Algebra    15. Mathematics for scientists & engineers    16. Particle & high-energy physics   

Reviews (22)

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
[...]
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.
Read more

Subjects:  1. Algebra    2. Algebra - Abstract    3. Algebra - General    4. Algebra, Abstract    5. Mathematics    6. Science/Mathematics   

Reviews (7)

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.
Great supplement
If you're taking a course in introductory modern algebra, you should have a copy of this book. As with many other Schaum's outline series books, you will find a concise, clear review of the theory, followed immediately by many problems with detailed solutions. My students tell me this Schaum's made a positive difference in their understanding. Beyond the introductory level, this book has limited use as it doesn't cover much of field and ring theory nor Galois theory very well.
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.Read more

Subjects:  1. Algebra - Abstract    2. Algebra - General    3. Mathematics    4. Science/Mathematics    5. Study Guides    6. Algebra    7. Mathematics / Algebra / General   

Reviews (2)

Another interesting, historical Galois Theory book
After some one hundred pages of semi-historical digressions on various scattered topics in classical algebra, we get to the main topic: the question of solvability by radicals of polynomial equations. The known solutions of equations up to degree 4 can be interpreted as relying on certain solvable auxiliary equations, the roots of which can be used to express the roots of the original equation. Lagrange then introduced the would-be analogous auxiliary equations for higher degree cases. Their roots, "Lagrange resolvents", can express the roots of the original equation, but their appearance suggests that they will not be solvable. However, proving this sort of thing seems to call for "a kind of calculus of combinations" (Lagrange; p. 146), i.e. permutation group theory, beyond his reach. The subsequent development followed the lines indicated by Lagrange to some extent; Gauss's proof that cyclotomic equations are solvable by radicals is based on solving iterated auxiliary equations, thus providing "remarkable examples of the step-by-step solution of equation as envisioned by Lagrange" (p. 185), and the Ruffini-Abel unsolvability proofs did indeed involve a little bit of permutation groups. But the paramount vindication and perfection came with Galois. Galois has his own "resolvents"--given an equation, a Galois resolvent is a calculable expression that can rationally express all the roots of the equation. Now, if one substitutes into these rational expressions another root of the minimal polynomial of the resolvent, then one still gets the roots, but they are permuted. All such permutations form a group--the Galois group--which is the key to solvability. Namely, solvability by radicals of the equation, i.e. solvability by +,-,*,/ and p:th roots, is precisely mirrored by the "solvability" of the corresponding Galois group, i.e. the decomposition of this group into a chain of normal subgroups of index p.

an idea of how mathematics is made
I have tried for several months to find a book wich could give me some inside of "GALOIS Theory", an idea of how people came to such abstract considerations.Read more

Subjects:  1. Algebra - Abstract    2. Algebra - General    3. Equations, Theory of    4. Galois theory    5. History & Philosophy    6. Mathematics    7. Science/Mathematics    8. Algebra    9. History of science   

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). ... Read more

Subjects:  1. Advanced    2. Algebra - Abstract    3. Algebra, Abstract    4. Mathematics    5. Science/Mathematics    6. Algebra    7. Mathematics / Advanced   

Reviews (1)

Perfect for Beginning Algebra Students
I used this as a textbook for an Abstract algebra course I took recently.It was surprisingly readable, and more importantly, there are plenty of examples that illustrate the definitions and theorems they've given.Read more

Subjects:  1. Algebra    2. Algebra - Abstract    3. Algebra - General    4. Algebra, Abstract    5. Applied    6. Mathematics    7. Science/Mathematics    8. Mathematics / Algebra / General   

Subjects:  1. Algebra    2. Algebra - Abstract    3. Mathematics    4. Science/Mathematics    5. Mathematics / Advanced   

Subjects:  1. Algebra - Abstract    2. Categories (Mathematics)    3. Logic    4. Mathematics    5. Science/Mathematics    6. Algebra    7. Mathematics / Logic    8. Mathematics | Logic   

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!
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!Read more

Subjects:  1. Algebra    2. Algebra - Abstract    3. Algebra - General    4. Education    5. Mathematics    6. Study Guides    7. Mathematics / Algebra / Abstract   

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.Read more

Subjects:  1. Algebra    2. Algebra - Abstract    3. Algebra - General    4. Mathematics    5. Representation Of Groups    6. Rings    7. Science/Mathematics    8. Mathematics / Algebra / General   

Reviews (4)

A Classic Text
I had been studying group theory on my own independently using this book for the last seven months when I misplaced it while at work - along with the notebook which I had painstakingly and carefully created from my hundreds of hours of study in this book. To say the least, I've been absolutely devastated at losing my notes; but the Schaum Outline I can easily replace.
Comprehensive but Dated
This is a reprint of a book that's been around since the sixties. It needs an update, especially the exercises, which are somewhat disorganized. The authors, like many mathematicians, have difficulty with the spoken language and do not adequately motivate the material, on an historical or intellectual basis. That said, this is still one of the best introductions to the subject available, at less than 20% the going cost of a textbook.

Outdated notation and very dull
I know maths books aren't meant to be fun to read, but this book is *extremely* boring. It's got, in my opinion, too much content, and its content could've been explained more efficiently.Read more

Subjects:  1. Algebra - Abstract    2. Algebra - General    3. Group Theory    4. Mathematics    5. Science/Mathematics    6. Study Guides    7. Groups & group theory    8. Mathematics / Algebra / General   

Reviews (1)

Coherent and Useful
This book does a good job at introducing some of the most interesting combinatorial problems in monomial resolutions.Although their chapter on toric varieties is somewhat weak, most of the other chapters (square-free monomial ideals, Borel-fixed ideals, staircases associated to monomial ideals in three variables, etc.) are very well written with challenging and revealing exercises at the end. ... Read more

Subjects:  1. Algebra - Abstract    2. Algebra - General    3. Discrete Mathematics    4. Geometry - Algebraic    5. Mathematics    6. Science/Mathematics    7. Fields & rings    8. Groups & group theory    9. Mathematics / Algebra / General   

Subjects:  1. Algebra - Abstract    2. Mathematics    3. Science/Mathematics    4. Teaching Methods & Materials - General   

Reviews (12)

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. ... Read more

Subjects:  1. Algebra - Abstract    2. Mathematics    3. Science/Mathematics    4. Algebra    5. Mathematics / Algebra / Abstract   

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.
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. ... Read more

Subjects:  1. Algebra - Abstract    2. Mathematics    3. Science/Mathematics    4. Mathematics / Algebra / Abstract   

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. ... Read more

Subjects:  1. Algebra - General    2. Algebra, Abstract    3. Mathematics    4. Mathematics / Algebra / Abstract    5. Outlines, syllabi, etc    6. Science/Mathematics   

Reviews (3)

A beautiful text
Fashions come and go, even in mathematics textbooks.Books from the 60s and 70s often have a set-theoretic flavor to them, because that was the fashion.Few books of any period are well written enough to resist such aging.spivak/calculus is one, and birkhoff&maclane is another. This is how algebra texts ought to be written
I have just started reading this book, and already I am A smorgousborg of symmetries of the square
Modern algebra is an extraordinary topic and Birkhoff and MacLane do a superb job of exploring it. However, as is often the case with mathematical texts, the material can be somewhat dry. ... Read more

Subjects:  1. Algebra    2. Algebra - Abstract    3. Algebra - General    4. Algebra, Abstract    5. Mathematics    6. Science/Mathematics   

Subjects:  1. Algebra - Abstract    2. Combinatorial Analysis    3. Combinatorics    4. General    5. Mathematics    6. Science/Mathematics    7. Word problems (Mathematics)    8. Algebra    9. Combinatorics & graph theory    10. Mathematics / General    11. Mathematics / Probability    12. Medical-General   

Reviews (1)

Pretty good
This book is an advanced treatment of field theory and Galois theory and is meant for those readers who have a substantial background in graduate algebra. The subject matter used to be thought of as purely mathematical, but due to the influence of the field of cryptography, it now has many applications. I only read part 1 of the book, so my review will be confined to this part. Read more

Subjects:  1. Algebra - Abstract    2. Algebraic fields    3. Galois theory    4. Mathematics    5. Reference    6. Rings (Algebra)    7. Science/Mathematics    8. Fields & rings    9. Mathematics / Algebra / Abstract