Customer Reviews

A First Course in Abstract Algebra, 7th Edition

5 star:		(5)
4 star:		(6)
3 star:		(2)
2 star:		(1)
1 star:		(4)

 

 

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.

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

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

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

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

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

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

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

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

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

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

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.

My undergrad Abstract Algebra I & II classes used this book (or rather the 6th edition which Amazon is no longer carrying). I think it's a very good book with a sufficient number of examples and detailed explanations. The reviewer who stated that this is not a book for mathematicians is correct; this is a book for undergrad students taking their first course in theoretical mathematics. The title of the book, "A FIRST Cource in Abstract Algebra", assumes this which is why proofs and explanations are often incorporated together. I think that most students would appreciate the lengthly explanations and lack of overly technical proofs. Having a good professor to go along with this book, however, is what sold it to me.

I used this book for my 1st Abstract Algebra course. At first, the discussion seemed to be somewhat lengthy but if you can get yourself into the author's style, you will enjoy it. True, it's not a book for those who want a well-structured proof but that won't matter much considering this book is intended to a beginner who take his/her 1st algebra course.

Lots of examples to test your understanding and lots of problems with increasing difficulty. Most of the problems are very stimulating.

Even after I took my second class in Algebra (i used diff book), i often go back to this book to see some additional information. What I like best about this book though is that the author likes to explain things in terms of mappings and, of course, lots of diagram to help you better understand the concept!

If you're a beginning student and considering to buy this book, then go for it - it worths the money! I think i'll bring this book with me to grad school. :) good luck.

I enjoyed reading this book very much. It is very appropriate for first time study of abstract algebra.
Pros: Very well written, easy to read. Examples and answers to odd problems. Each chapter is written for a 50 min class, good for pacing yourself when self studying. Enough material for more than 1.5 semesters. All chapter exercises are broken down in 3 categories: computations, concepts and theory.
Cons: none

This book provides a pretty nice track on group, ring, vector space and toward Galois theory. It is not a easy book, i.e. people who want to self study may feel frustrated. When I read the proof, sometimes I felt like doing exercise. Abstract algebra is indeed abstract, so example are extraordinary important. The examples in the text is not enough, thus doing problems are absolutely required.

However, I still trying to emphasis my positive opinion on this book: most due to clarity and completeness. Theorems are very organized, not cumbersome. Proof are succinct and suitable for review. This book almost covers all important topics in fundamental algebra, thus become a very good reference.

I used this text for an introductory abstract algebra course and was very pleased with it. I still refer back to it to review particular topics because the discussion is more in depth than other texts. With that said, Fraleigh does not go off on tangents. The writing is very precise and to the point. I just went over the entire preliminary chapter and was very impressed with the amount of material that he covered and the way that he covered in a short amount of time. I also looked up the answers to the odd exercises to make sure that I was getting the ideas.

This is where one of the problems comes in. The odd answers are provided, except for the proofs. So if this book is being used for a class, that's not necessarily a bad thing. If, however, you are using it for self-study, then it's a problematic omission. For many, abstract algebra is a starting point for the world of mathematical proofs. It would have been nice to include the answers to proofs in the back of the text as well.

After surveying some of the other comments, I agree that it seems much stronger on group theory than on polynomials and their related fields. Also, I did not find the exercises weak. Proving the cardinality of R as Aleph 1 in the preliminary chapter is not obvious in an introductory abstract algebra course in my opinion. In many ways, it's a strength of the book to include exercises that are not difficult to figure out. It makes the student feel like they are understanding the concepts. There are challenging ones as well, for an introductory course.

On a final note, I used the International Student Edition and did not notice any discrepancies while taking the class. If anyone wants more information on such editions, let me know.

To be honest, I don't think very highly of this book. It is well-written, with many examples that help guide the reader. I feel that this is a good book for people who want to learn some algebra but haven't learned proof techniques. It is certainly easier than, say, Artin's Algebra or Herstein's Topics in Algebra. It is fairly slow-paced, and there is a lot of a kind of hand-holding. The exercises include true-false questions (e.g. Every field is an integral domain; if F is a field then F[x] is a field) and simple computations (e.g. How many elements are in S_4 X S_3?). Many of their exercises asking for proofs are rather trivial, but there are some challenging ones too. I think that a student who has taken a proof-based course before and has some mathematical maturity will find this book too easy. I also feel that this book is not good for delving into the heart of the ideas of the theorems. What I like about Herstein and Artin is that they really grapple with the major ideas and tie everything together, in a sense: for example, Artin does this (most of the time) by looking closely at important examples. Fraleigh's style resembles a high school calculus textbook: the theorems seem like the analog of formulas that you have to remember, but that you don't develop a very good intuition of. My impression is that if you use Fraleigh, you may know the theorems but you won't have as intimate an understanding of the material as you would after reading Artin. For all these reasons, I think the book is good if you're a beginner, but if you consider yourself relatively advanced when it comes to thinking abstractly, a book like Herstein would be better.

I can not improve on the comments made by most reviewers. I took my first abstract algebra course using the 1st edition and found it to be an excellent introduction. I've looked at subsequent editions and see the same high quality and clarity, along with minor improvements in each edition.

If you want a solid intro to the topic, check this book out.

Finally, as usual, there was one reviewer who simply "didn't get it".